Natural sciences and chess: A romantic relationship missing from higher education curricula

Abstract

Chess is a game that delicately weaves analytical thinking around artistic experience, yet recent conversions of STEM (Science-Technology-Engineering-Mathematics) to STEAM (Science-Technology-Engineering-Art-Mathematics) have omitted adding chess as an elementary coursework to K-12 and higher education curricula. Chess, as per arguments presented in this essay, can be considered as a language and a tool for furthering the development of artistic skills among scientists and analytical, pattern-recognition skills among artists. It can also serve as a missing link between science and art in STEAM curricula thanks to its finding itself halfway between the two. A handful of analogies are drawn here from chess, illustrated sporadically with positions from real-life chess games and converted to lessons in creativity for students in natural sciences. The discussion centered around these analogies is reinforced by a literature review of studies conducted over the past 80 years to assess the effect of exposing students to lessons in chess on their learning in distant domains. Overall, great benefits can emerge from complementing science education with chess and it is hoped that chess will become an integral part of basic education in primary schools and universities worldwide in the near future.

1. Introduction

Board games have been the source of entertainment, social cohesion and sharpening of intellects among humans since the ancient times. Games such as Senet and Mehen, which were played in Predynastic Egypt in the early Bronze Age, before 3000 BC [1,2], Backgammon and the Royal Game of Ur, which originated in Mesopotamia at around the same time [3,4], Go, which was invented during the Zhou dynasty period in China, around 500 BC, Xiangqi and Shogi, aka Chinese and Japanese chesses, respectively, all have histories dating back well over a thousand years in the past. Out of all the board games with a long tradition, however, chess, whose origins date back to the early 7th century, can be reasonably considered the closest that humans have come to actualizing the concept of Das Glasperlenspiel, aka “the glass bead game”, an elusive marriage of science and art envisaged by the German expressionist novelist, Hermann Hesse [5]. The artistic richness of chess may be best illustrated by the life story of one of the pioneers of the 20th century conceptual art, Marcel Duchamp, who thoroughly gave up art in his early 30s and dedicated himself from then on solely to chess, having begun to consider it as more artistic than any visual art, classical or modern [6]. In turn, how scientific chess really is can be illustrated by the famous Serbian-American scientist, Nikola Tesla's claiming that “chess restores the state of equilibrium in the mind”. Chess, also, is the only board game that is being recognized by the International Olympic Committee as a sport and there is an active ongoing campaign to have it included at the 2024 Summer Olympics in Paris [7]. For myself, a researcher and an instructor in various fields of physics, chemistry, biology, pharmacology and medicine, chess represents a favorite pastime, presumably because of its capacity to satisfy our inner cravings for both the aesthetic and the intellectual stimuli in a manner that is, importantly, inherently playful.

In the classroom and in the lab, however, as a teacher and a mentor, respectively, I wish to draw parallels between creativity in scientific research and creativity in chess more often than I do. To be able to draw such parallels in an intelligible fashion, the students' having a decent level of chess literacy is an obvious prerequisite. This collective fluency in chess, however, is wholly missing from today's western education. Citing conflicting evidence with respect to the scholastic benefits of chess, the majority of western educational systems have hesitated to integrate it into their curricula [8]. Therefore, lest my analogies meet a wall of incomprehension, I shy away from invoking such analogies in my lectures. Still, I wish secretly that a day would come when chess would be a component of elementary education – not only the elementary rules of the game, but its overarching aesthetics. To be a mere chess aficionado and not an active professional, and yet to evidence the immense gap in knowledge of chess between the science instructor that I am and students in natural science classes has convinced me that general education should include chess alongside art in basic science curricula more commonly than it does. This conviction has been the key motivation for the writing of this work.

2. Literature review

The evidence of benefits that may result from a greater degree of mingling education in chess with education in natural sciences is sparse, but certainly not lacking across literature. In an earliest tackling of this subject, one of the world's most notable experimenters and authorities in the cognitive science of chess between the 1940s and the 1960s, A. D. de Groot claimed that the educational benefits of chess instruction are likely to culminate only in the improvement of the attention span and the overall interest in learning, but would not be able to enhance intelligence, spur creativity or lead to more superior scholastic accomplishments [9]. In the last 50 years, this view has been both reiterated and contended by numerous studies [10]. Among the sceptics about the educational benefits of chess instruction, it is generally held that these benefits range between miniscule and nil [11]. This view has been rooted in de Groot's classical assessment of the subject, but also in more recent studies, including the one from 2002 that went so far as to assert that there is no direct connection between chess skill and intelligence [12] and the one from 2007 showing that practice is a significantly greater determinant of the chess skill acquisition than intelligence [13]. A meta-analysis taking into account 24 separate studies involving a little over 5000 subjects, correspondingly, came to conclusion that educational interventions fare generally better than chess instruction when scholastic improvement is intended [14].

On the other hand, there has been a number of studies whose results were in favor of the positive effect chess has on learning. Prior to the turn of the century, a handful of studies were conducted, starting from the seminal work by Albert Frank in Zaire in the 1970s, that showed a direct correlation between exposure to chess instruction and the development of analytical and, interestingly, verbal aptitudes [15]. As for studies conducted in the new century alone, one from year 2000, involving African-American students in Louisiana, showed a general improvement in math skills among the group exposed to chess instruction relative to a control group [16]. In 2008, a study was performed in Germany, showing a steady improvement in basic math skills, such as counting and addition, among students with disabilities who received chess lessons [17]. In 2011, another study was performed in Texas, involving also students with disabilities and showing the improvement in both math test scores and end-of the-year grades among students who did receive chess instruction over the course of the school year [18]. A study conducted in Spain in 2012 demonstrated significantly better scores on tests measuring problem-solving performance along with various analytical intelligence indicators by students who attended chess classes than by students who participated in sports events instead [19]. A study conducted in Iran on the same year showed a significantly higher metacognitive ability and mathematics scores among students who received chess instruction than among the control group [20]. A year later, a study was conducted in Italy, showing that chess lessons do not only induce a moderate improvement of problem-solving skills, but that the degree of this improvement is also directly proportional to the amount of chess instruction received [21]. A study conducted in Romania in 2014 showed that the school performance increased significantly more in a group of students given chess lessons than in a group given fun math instruction [22]. Next, a metastudy commissioned by the Chess Club and Scholastic Center of Saint Louis in 2014 took into account all 24 eligible quantitative studies on academic chess instruction at the time and came to conclusion that attending chess classes had a statistically significant positive impact on the general cognitive outcomes, with a most pronounced effect on the outcome of the students’ tests in mathematics [23]. In 2015, a study was conducted in Italy that reiterated the direct positive correlation between chess training and math testing scores [24]. A year later, two studies conducted independently in Turkey again showed higher end-of-the-year grades among students who practiced chess at school versus students who did not [25,26]. When it comes to the more subjective and less quantifiable measures of perceived benefits of scholastic chess among students that were a part of the Chess in Schools program implemented in 2017 across the southeastern United States, a study released in 2021 demonstrated that these students experienced positive outcomes on every level of assessment due to the exposure to chess instruction [27].

Therefore, the so-called far transfer of learning [28], where instruction in one discipline promotes comprehension and scholastic success in a relatively remote discipline, can evidently occur between chess and any of the numerous natural sciences. Albeit feasible, however, this transfer has been understudied in educational settings. Despite that, prior studies did confirm different routes by which this positive transfer of learning involving chess can occur, including: (i) the lateral, in which case the working memory or the concentration ability improve with chess [29]; (ii) the vertical, in which case improvements in creativity, intelligence or overall school performance may result from the formation of abstract generalizations as connections between distant domains [30]; (iii) the sequential as the blend of the lateral and the vertical; (iv) the specific, which proceeds via direct examples and case comparisons driven by obvious similarities between the learning domains [31]; and (v) the unspecific, implying an advantage for learning in a domain that shares no similarities with the one where a learning task is being performed, as when studying chess motivates students to get preoccupied with books or computers in independent learning activities [32], or improves their reading [33] or poetry analysis skills [34].

3. Methodology

The central premise of this essay is that exposure to chess instruction could strengthen creative problem-solving skills in natural sciences. To illustrate the many points of connection between chess and scientific creativity, I will mention and discuss some of such analogies in the sections that follow. The ultimate goal of this discourse is to contribute to the collection of a sufficient body of evidence that might eventually convince the crafters of today's higher education curricula in the merit of including chess as a mandatory university coursework in lieu of its being an occasional elective at selected schools. The emphasis in the discussion that follows, however, will not be on constructing a systematic advice on how to integrate chess into primary schools and universities. Instead, I will throw at the reader a number of correlations found to exist between chess and natural sciences in a variety of scholarly and institutional contexts, each of which could present a seed from which a portion of the content of courses on the connections between chess and natural sciences could sprout. Concordantly, the direction in which this discourse is to take these aforementioned crafters of higher education curricula is much more than to introduce an elective on chess strategy fundamentals or chess history alongside the core science courses already comprising the curriculum. Rather, it is to create coursework through which students would actively explore the ties between various elements of chess and sciences to which they have devoted their academic training or careers. Such explorations should result in the discovery that chess can be an inspiration and a guide in the way they approach problem-solving in their scientific fields of interest. Naturally, students benefitting most from these types of courses would be those at the highest points in their education, where creativity in research, development, writing and management matters most. Whereas courses on the basics of chess strategy and tactics would fit better primary and secondary education, courses toward which the discussion that follows leads would be most suitable for tertiary education because of their revolving around the concepts of critical assessment and analysis, review, discussion, innovation and creative thinking.

4. Results and discussion

4.1. Chess instructs about the importance of the sense for beauty in science

To be a scientist, as we are being colloquially told, is to master the exhibitions of logic and logic alone and remain untainted by “dark” intuitions, lyrical inspirations and any hints of “mumbo jumbo” aesthetics. And yet, artistic senses represent a perfect complement to the purely logical skills; they two, like the two brain hemispheres, form an indivisible whole required to fully grasp the physical reality. Not only is an eye for the artistic beauty able to spin the wheels of motivation and home the vehicles of science in humanistic directions, but it is also an orientation device that guides its holders to destinations of greater grace and virtue than of those tuned only to the rather ruthless rules of the game, the sole parameter of which is the success of and for the self.

Chess offers an excellent aid and model in teaching this necessity of viewing the world through the eye of an artist in order to grow into a creatively fertile scientist. For, what has attracted artists all the world over and across all ages to chess was primarily the aesthetic element of the game. For example, to sacrifice a piece or many and with one such disregard of the material possessions set grounds for winning the game is an approach that has an almost divine element of beauty to it. In the most simplistic terms, it teaches that the material wealth is secondary to subtler and incommensurable aspects of our experience. Needless to add, this is a powerful lesson, particularly relevant in the developed regions of today's world, where love of science has become pushed to the side as a major reason for a career in sciences compared to the pursuance of monetary benefits and cushy vocation. To gain tenure at a major western university by proving oneself capable of attracting large sums of money to fund one's research and then dedicate oneself to commercialization of research is, sadly, the path to success in today's natural sciences. One, simply, is not impelled to even vaguely consider developing pedagogic methods that would inspire students in the classroom or in the lab about the wonders of Nature. Rather, there is a pervasive focus on the material resources over the inspirational aspects of science as art. And yet, anything that instructs about the latter, chess included, can be considered a healing agent, a cure to this illness striking the modern academic world.

In fact, the philosophy of poverty that I have advocated over the years [[35], [36], [37], [38]] has revolved around highlighting the countless benefits for our sciences that emerge from systematic deprivations of resources, the reason being that under such materially deprived conditions our brains are forced to think imaginatively to compensate for this lack of resources and many great things happen thereby. When the second and the longest reigning world chess champion, Emanuel Lasker noted in his widely praised Manual of Chess that “in a city well supplied with water I should feel very little interest in an effort to discover an Artesian spring; in the desert such a search would captivate all my attention” [39], it was an iteration of this standpoint, according to which shortages of resources are to be welcomed openhandedly rather than being avoided at all costs.

Finally, although the aesthetics of chess are artistic in essence, the analytical nature of the game allows for these aesthetics to be analyzed deeply. Tentatively, the aesthetics of chess could be divided into a couple of distinct elements, including (a) effectiveness (Fig. 1a), (b) sacrifice (Fig. 1b), (c) technical correctness, (d) preparatory subtleness, (e) disguise (Fig. 1c), (f) paradox (Fig. 1d), (g) bold and inventive goings against the textbook advice and prescripts, (h) cooperative unity of distinct pieces, and (i) originality [40]. This classification can form the basis for studying the theory of aesthetics in any other domain of life, science included.

Fig. 1.

(a) Chessmaster 2100 vs. Uskoković V., Belgrade, 1993, 0–1. In this position, Black must find 50 … h1 = Q, which would force White to take the promoted queen, and only then play 51 … Rb6 if White takes with the rook (51.Rxh1) or 51 … Rf2 followed by … Rc2 and … Rc1 if White takes with the king (51.Kxh1). Playing 50 … Rb6 right away instead of 50 … h1 = Q would have been an error because White would not take on h2, but rather play 51. Kh1, which would lead to a draw by stalemate after 51 … Kd4 52.Rxb2 Rxb2. (b) Uskoković J. vs. Uskoković V., Belgrade, 1991, 0–1. In this position, Black sacrifices the queen with 26 … Qxd4 and the checkmate is unavoidable after 27. Rxd4 Rxa3+ 28. bxa3 Bxd4#. (c) Uskoković V. vs. Colossus Chess 4.0, Belgrade, 1991, 1–0. In this position, White played 26.Kh2, a quiet but crucial move in disguise, preparing for a pawn and bishop sacrifice in the two moves that followed: 26 … Rfd8, 27. e4 Rxd4 28. e5 Rxd3. The push of the white pawn to e5 enables the white knight to reach f6, which after 29. Nf6+ Bxf6 30. exf6 leads to checkmate in four. With the king on g3, this maneuver would not have been possible because after 26. e4 Rxd4 27. e5 Rxd3+ 28. Kh2 fxg4, Black would gain a winning advantage. (d) Uskoković V. vs. Uskoković D., Belgrade, 1991, 0–1. In this position, Black finds 18 … Qd6, tempting White to take on f7 and force the black king to move toward the middle of board after 19. fxg6 hxg6 20. Bxf7+ Kh7 21. Qg2 c5 22. dxc5 Qxc5 23. Bxg6+ Kxg6 24. Qe4+ Kxg5, which, paradoxically, does not threaten its safety, but works greatly to improve the activity of black pieces, as indicated by the Stockfish 14+ evaluations of +0.4 before 18 … Qd6, −0.6 after 20. Bxf7+, and −2.3 after 24 … Kxg5.

4.2. The principle of activity

One principle instructive to students in natural sciences in search of the recipe for creativity is that demanding an incessant activity from the sentient agent acting as a researcher. In chess, winning advantages are routinely being squandered simply because the winning side lost a tempo or two in the attack and allowed the opponent to be back in the game. This principle goes hand-in-hand with that demanding from the player to maintain an active plan in each stage of the game. Although positional play is often such that it leads to the improvement of the positions of the pieces without a particular strategic or tactical idea in mind, a number of active plans collide in the head of a chess master and a choice between them determines the course that the game would take. For novices, however, the conception of these plans comes hard and this writer's block and a sense of being idealess and lost in space and time symptomatically befalls newcomers to the world of scientific research, too. Allowing well-defined research goals to guide our decisions in the lab, in the field or in the theoretical domain while resisting the urge to passively sit and wait for something to fall from the sky and save us is what this chess principle may teach students very well.

Moreover, not only should every move in a game of chess have a purpose, but this purpose must encompass the entirety of the chessboard, spanning many moves ahead. If it were to be said that decisions in the sphere of science, in analogy, must account for the entire world, this might sound utopian, but a healthy holistic attitude would be lurking from within this saying. For, through this striving for the impossible, horizons that would have otherwise remained out of reach could become attainable after several tries. Nurturing this holistic worldview would also make the scientist aware of the countless contexts hovering over and determining the fate of one's science: political, socioeconomic, psychological, metaphysical, and so on. The awareness of these contexts, needless to add, tends to make the scientist's view of science wiser than the views of it that are pervasive in this digital age, often being clueless about anything lying outside of the immediate limits of one's scientific interests and area of specialization.

Exceptions notwithstanding, the pursuance of these active plans usually implies that advancements on sections of the board over which our pieces have most control are most desired. In science, likewise, we should play to our strengths, be they experimental, theoretical, solitary, collaborative, paradigm-shifting, paradigm-amending, and so on. This principle may also instruct students to resist the passive attitude of submitting to distractions that conflict with the goals that they have decided to pursue and where their strengths lie, remembering all the while, of course, that life-changing ideas may come from the least expected corners. It should be understood, however, that there are positions in chess that are salvageable only by exhibiting patience and passivity. To build a fortress in the endgame or to resist opening up a position in the middlegame when this opening would only benefit the opponent are oftentimes the only means to drawing a losing game, meaning that rules, starting with this one, should never be followed literally and independently on the circumstances because not only are there exceptions to every rule, in chess, science and life alike, but exceptions, in truth, confirm the rules in question by their being exceptions and not rules per se. One example of this sensitivity to the subtlest environmental signals and the liberty to modify our approaches by 180° if needed may come from the 4th world chess champion, Alexander Alekhine's switching the focus from the kingside to the queenside based on a single, 21.a3-a4 move of the white pawn at the edge of the board by Efim Bogoljubov in a game played at the tournament in Hastings, England in 1922, exactly a century ago (Fig. 2). With this switch of the focus, Alekhine did not hesitate to perform the traditionally forbidden return of a piece back to its prior position with the 20 … Nc6-e7, 21 … Ne7-c6 maneuver before winning the white a4 pawn that initiated this whole change of the plan and sacrificing no less than two rooks and three queens in order to end up with a single pawn advantage in a king and pawn endgame and, naturally, win it.

Fig. 2.

Bogoljubov vs. Alekhine, Hastings 1922, 0–1. Position on the board before 20 … Ne7 21.a4 Nc6. Black returned the knight to c6, having recognized that now it could penetrate White's position via b4 and d3 squares.

4.3. Complicating things to emerge as a victor

Another guiding principle Lasker held onto in his play was as follows, in the words of Richard Réti: “With the perfect technique in chess that is dominant today, a peaceful, correct play almost always leads to draw. To avoid that, with theoretically wrong moves, Lasker would draw himself onto the very edge of a cliff. However, owing to his exceptional strength, he succeeds in clinging onto this edge while tossing the opponent down the abyss” [41]. Decades later, the 8th world chess champion, Misha Tal would rearticulate this principle pioneered by Lasker by advising his protégés to “take the opponent to a deep dark forest where 2 + 2 = 5 and where the path leading out is only wide enough for one” [42]. Later on, the 13th world chess champion, Garry Kasparov would build his entire style of play around the proclivity to deviate from textbook variants at the cost of producing moderate positional weaknesses in one's position, albeit open for more tactical possibilities. In other words, the making of an error is needed to create a state of asymmetry and circumvent a drawish position by giving a slight advantage to the opponent, but such that it is not clearly convertible to a winning one, at which point complications ensue and the more skilled or inspired player is the one to usually emerge as a winner. Tal would later comment on this drawing of the parallel between him and Lasker: “Lasker is the greatest player of all time – he made miracles on the chessboard. They compare me to Lasker, which is an exaggerated honor. He made mistakes in every game and I make them only in every other one” [43]. David Bronstein, the contender for the world champion title in a match against Botvinnik in 1951, built a whole method around this principle, which he christened “the dynamic handling of positions with formal but unexploitable weaknesses” [44]. This method, like that pursued by Lasker and Tal and virtually every super-grandmaster today is based on two key premises: (a) insistence on perfection leads to passivity; (b) deliberate deficiencies can be invaluable assets if they succeed in distracting the opponent from his plans.

Indeed, whenever we have a perfectly balanced and thus inherently infertile situation in front of us, be it as a position that leads to a predictable draw in chess or a status quo in the sphere of scientific research, the only way forward is to step out of balance while accepting all the risks that this distancing from order and temporarily entering a realm of chaos entails. This guideline is particularly quintessential in situations in which one starts off as an outsider. As the basics of the chess strategy imply, when one hung a piece or gradually accrued a material or positional disadvantage, but still harbors hopes for the win or at least a draw, one has no other approach but to complicate, to force the opponent into complex positions and consciously tiptoe around the edge of the cliff, all the while displaying unpredictability by making stylistically different moves from one moment to another, keeping tensions from petering out and allowing surprises to be constantly ready to jump out. When one starts off from a materially advantageous position in chess, the correct way of playing is to simplify the position, force the opponent into exchanges and eliminate any tensions, but when one finds oneself on the other side of the board, materially weakened and out of theoretical favor for the win or perhaps even a draw, one should have no other plan before oneself but to enter that dark forest where “2 + 2 = 5”.

4.4. Chess dispels the ideal of perfection

In science, an erroneous ideal often gets perpetuated, according to which anything that has passed peer-review and become a piece of published literature must be fully correct. In fact, accounting for experimental approximations, if not flat errors, interpretative inaccuracies and fundamental mistakes latent in the premises, no more than 50% of facts in any given paper or a textbook are correct, I tell my students, and everything, therefore, everything must be doubted. Probing unanswered questions and probing unquestioned answers, in other words, can lead to equally groundbreaking discoveries.

Chess can illustrate this inevitability of inaccuracies and errors in every model with a couple of simple analogies, one of which may be a comparison of two hypothetic white pawn structures in the center: c4-d4-e3 (Fig. 3a) and c5-d4-e3 (Fig. 3b). Even though the former pawn structure does not form a chain and is less stable of the two structures, it allows White to better control the center. As White converts to the more stable c5-d4-e3 structure (Fig. 3b), he simultaneously diminishes the control over the center and enables Black to occupy squares along the a8-h1 diagonal, which he may use to infiltrate White's position. Apart from the fact that with c4-c5 White may lock the position or allure Black into an offense that could, depending on the position, turn out to be a paper tiger or a trap, this comparison harks back to the principle educed by the chief samurai in Kurosawa's classic, Seven Samurai [45]: to stabilize one's structure is to lose grip of the position and create opportunities for the opponent to take over the control, when only an inherently unstable structure can remain in charge of the position. Needless to add, a masterful strategist recognizes that a weakness is always present in the opponent's position, even when it appears immaculate and indestructible on the surface. Very often, these weaknesses are exposed by the most counterintuitive of means, which is where one of the major aesthetic elements of chess lies. In a game played at the 2022 US Women's Chess Championship between Gulrukhbegim Tokhirjonova and Rochelle Wu, for example, White deliberately sacrificed a crucial tempo in the opening to force the development of a Black's piece, but also to achieve a broader strategic goal (Fig. 4), proving the point that every developing move, regardless of how immaculate it may seem, always creates a weakness somewhere in one's position.

Fig. 3.

Structurally similar, but strategically distinct central pawn structures: c4-d4-e3 (a) and c5-d4-e3 (b).

Fig. 4.

Tokhirjonova vs. Wu, 2022 US Women's Chess Championship, Saint Louis, MO, 1–0. Position on the board after 1.e4 c5 2.Nc3 d6 3.f4 g6 and before 4.Bb5+ Bd7 5.Bc4. White willingly loses a tempo by moving the light-squared bishop twice and provokes the development of Black's light-squared bishop with the idea that after the moves played in the game, 5 … Bg7 6.Nf3 Nc6 7.d3 e6 8.f5: (i) any fxe6 capture by White cannot be left unattended to because the white pawn on e6 will be attacking the black bishop on d7; (ii) a move such as Bf4 would attack the black d6 pawn, now undefended by the black queen because the bishop on d7 stands in the way; (iii) Black's main counterplay involving the opening of the center with … Nge7 and … d5 is not feasible because the d5 square is no longer supported by the black queen.

4.5. Chess and science both liberate the egotist from ego

One misconception that outsiders to the world of chess have had is that chess can only be played, when, in fact, viewing and studying chess games is far more aesthetically rewarding on average. Just as many more people read books than write them, so should watching and reading games from the chess literature be more common than playing them, especially if the goal is to grasp principles and points translatable to science and life. This transition from chess as a playing activity to chess as a form of visually rich literature, if ever conducted on the mass scale, would soften the competitive character ascribed to the game and bring about a greater awareness of its aesthetic elements, which are instructive from many different angles.

Meanwhile, a constant trap in the career of a scientist is that of a toxic ego, given that one's name and recognition are attached to individual discoveries, papers published and awards and accolades received, adding to the false power-boosting effect that acting as an academic authority to students has. Liberation from the ego is therefore an ongoing effort in the life of every humble scientist and teacher. Chess can aid in this effort, but only when it is played for the sake of creating a beautiful game, regardless of who wins it. The 5th world chess champion, Max Euwe noted that “whoever sees no other aim in the game than that of giving checkmate to one's opponent will never become a good chess player” [46]. To advance from the level of a coffeehouse player to a true master is to see the game in a bigger, more selfless light, as an emanation of magnificent creativity and craving for beauty rather than a petty desire to win at all costs, even with the cheapest of means if needed. But when our goal in chess becomes the co-creation of a beautiful game in togetherness with our formal opponent, regardless of who the winner is, and we play the game as an objective search for truth in a position, we should know that we have reached a stance that is, indeed, something special. This is when any competitive thirsts to checkmate the opponent right away vanish and the focus on simply playing the best possible or the most creative move in each position gets instilled in our heads. The same applies to well thought-out science, the immersion in which extinguishes the ego very well and builds a sense of humility before the wonders of the physical world. All the petty destinations tying to the rewards for our career thus disappear and enjoyment of the intellect in studying scientific phenomena at a most fundamental level, if not for the practical benefit of the world, begins to take hold in our minds. Chess, therefore, can be a good guide in this exercise in humility in the practice of science, which is increasingly needed in these days when it has gotten harder and harder amidst the many temptations for the ego of the scientist to stay grounded and selfless.

Hence, each game of chess we play should ideally proceed with our finely balancing the attempt to find the best possible moves for one's position and the desire to produce a wonderful piece of art out of the game, paying no attention to who the winning side will be. From this stance, where self-centered inclination to win a game mingles with the selfless aspiration to produce an objective piece of art, a “middle ground” concept for education can be derived, taking the form of pedagogic instruction that is neither teacher-centered nor student-centered, but focused on enriching the way between the two [47,48]. Moreover, this empathizing with the player on the other side of the chessboard to the point of caring little as to who will win leads naturally to the boycotting of the rat race for the win that the obsolescent, carnivorous shades of humanity impose on us. Here, an ideal worth learning from is that of Misha Tal, who strived to make each of his games “as inimitable and invaluable as a poem” [49] and who, according to his autobiography [50], took as much pride in earning the game beauty prizes at tournaments as winning them. Garry Kasparov once described Tal as follows: “Tal was an artist, he deemed any game worthy if it was interesting … He wasn't contentious. Chess is very contentious game by its nature, and he wasn't … He did not even seek the truth in chess, he sought beauty. It was a concept completely different from most of ours” [51]. Tal could be said to have shared a lot with the masters of the primal, Romantic era from the chess history, to whom style was more important than winning [52], which is, en passant, the very same priority that we could assign to our scientific engagements too, if we only wish to take science away from its today's entrepreneurial, materialistic stage into something more spiritual. If so, chess could help science slide from the peak of prosaic positivism on which it finds itself today and drop down to humbler and more beautiful grounds.

4.6. Volatility of style and its adjustment to personality in the postmodern era

There are lessons in chess and beyond that one could learn from the playing styles of some of the notable chess players from the history of the game. As far as the three players who influenced me most throughout my career are concerned, from Alexander Alekhine, “a poet who creates a work of art out of something that would hardly inspire another man to send home a picture postcard” [53], as Euwe described him, I learned the art of creating and navigating the grandeur of profoundest positional play; the skills of the 11th world chess champion, Bobby Fischer convinced me in the latency of the potential to crush every opposition into pieces through a laser focus of the intellect, which emerges best from an uncompromising search for truth in a position; Misha Tal showed me how anything in life, including chess, could be turned into dazzling emanations of artistic beauty, of sacrificing all that one has and gaining the whole world in return, proving thereby that spirit ranks higher than matter on the scale of significance of things in life. In fact, the most famous players from the history of chess can be said to have had highly distinct chess personalities, that is, playstyles. Thus, if we proceed mostly chronologically, we could evoke the romantic outpours of heroic emotion and energy by Paul Morphy; methodological bohemianism cherished by the first undisputed world chess champion, Wilhelm Steinitz; the tactical elegance and brusqueness on the board by Lasker and, later, Fischer; the hypermodern ingenuity and strategic wizardry of Alekhine; the endgame-enforcing combinatorial clarity of Jose Raul Capablanca; the pensiveness and prioritization of the aesthetic over the practical by David Bronstein; the monumentality and grandiosity of unprecedentedly methodical and principled Mikhail Botvinnik; Tigran Petrosian's positional patience and slow-moving cornering of the opponent, as if he was a boa constrictor; the sacrificial, dying-in-beauty style of the bard and the gambler called Misha Tal; Boris Spassky's serving the role of a precursor for the sharp, aggressive style rooted in puzzling positional sacrifices performed to secure and/or preserve the initiative, which would later be mastered by Garry Kasparov; the defensive timidity of the king of prophylaxis, Anatoly Karpov; Kasparov's delving in complexities where atomic chess energies lie latent; Vladimir Kramnik's solid and principled, “draw-with-me-or-lose” style; Vassily Ivanchuk's transmuting erratic mood swings into exciting positions on the chessboard; Vishy Anand's maintaining the calm of a Bengal tiger focused on its prey in the midst of self-initiated tactical storms; and so forth. One interesting trend to observe here is how the progression from one dominant world chess champion's style to another followed a sinusoidal path, such that the methodical, principled lineage spanning from Steinitz to Capablanca to Botvinnik to Petrosian to Karpov to Kramnik was intercepted by the unorthodox, dynamic lineage connecting Lasker to Alekhine to Tal to Fischer to Kasparov to Anand, before the current era of universality of style, aka Magnus era, was reached, largely with the help of computers.

Individual players' styles have further often been reflections of their cultural milieus, if not stereotypes. Bobby Fischer's style of play, for example, sharp, succinct, direct, in-your-face, favoring practicality over poetry, is as American as the American literature, serving as a paradigmatic example of how sociocultural traits of a player tend to become reflected in his moves on the chessboard. It is a statement of fact, however, that modern times have made this quest for one's own authentic chess language at the top level difficult because it is demanded from the most competitive chess players to excel in every single aspect of the game and apply different styles in response to different situations on the board and different proclivities of the opponent. This explains why the era of Magnus Carlsen, the reigning world champion since 2013, will go down in history as the one during which the uniqueness of style among the world's best chess players has finally vanished and the universality of the style has become a rule without an exception, echoing the Polish-Argentinian chess grandmaster, Miguel Najdorf's description of Bobby Fischer: “Perfection has no style” [54]. The early hint that perfection across every facet of a given art is equivalent to bleak impersonality, in fact, came from the style of Mikhail Botvinnik, who is usually regarded as the “patriarch” of chess because of the completeness of his skill in every segment of the game, but who never left as much of an inspirational footprint among chess novices and artists as the likes of Misha Tal or Bobby Fischer did. Other notable players from the past who may be said to have been devoid of distinct style and who may have served as precursors for today’s era of pure pragmatism in chess include Carl Schlechter, Vasya Smyslov, Reuben Fine and, last but not least, Max Euwe, the chess player whom Fischer considered not normal because of being, ironically, “too normal”. Expectedly, however, none of these players or their likes get to be cited, not even occasionally, as sources of inspiration for players at either amateur or professional levels. Therefore, one of the major concerns as chess heads into the future is if the game will cease to inspire because of the implicit demand from the players to adopt a universal style if they want to compete at the top level, so that each move will be subdued to the objective needs of the position rather than made so as to conform to the player's unique personality. Indeed, although ambiguity as to what constitutes a correct move in any given position gives players the opportunity to show their affinity for more dynamic or more solid choices, the success at top tournaments, especially in the last decade, appears to have correlated directly with this versatility of style, as players who tend to risk more and play unorthodoxly, to amuse the audience and the muses, so to speak, tend also to get punished for their risks taken. Historically, this can be exemplified by the limited success of the chess daredevils such as Rudolf Spielmann, Rashid Nezhmetdinov, Ljubomir Ljubojević or Alexander Morozovich at the highest level and, more recently, by the poor scores of Richard Rapport and Alireza Firouzja at the 2022 Candidates Tournament in Madrid. One commonality shared by the top players in the world from the mid-2010s onwards, therefore, is that they could all be seen forcing the transitions to dynamic positions brimming with countless tactical possibilities, but could also play solid positional chess depending on the circumstances. If expedience has overcome great moral ideals in today's world, then the reflections of this disheartening state of affairs can be readily glimpsed in modern chess, which makes it a mirror of global social trends and signs of the times, just as every art has been since its inception.

Nevertheless, the multiple number of correct moves playable in most positions where one side has an advantage that is nil, minimal or moderate allows players to showcase the affinity for more dynamic or more solid options. Moreover, the exposure to various styles during chess education eventually leads to their blending and making of a style of one's own. This style, as chess instructs us, must always conform to one's personality, which is another iteration of that “be who you are” principle, so important to youth of every generation [55]. This is particularly so because all the world chess champions had distinct styles and for a long time it was thought that without a unique style, no significant achievements in chess could be made, a principle readily translatable to scientific research as well as to art. Or, as John Neal, the pioneer of the American literary nationalism of the 19th century put it, “to succeed, I must imitate nobody, I must resemble nobody, I must be unlike all that have gone before me” [56]. On the other hand, style, especially in the postmodern age, is volatile and this can be demonstrated by how Kasparov managed to stay in his first match as the world champion contender, against Karpov in Moscow in 1984/85, only because he was ready to abandon his authentic, aggressive style of play and adopt passivity for the first time in his career. Namely, after only nine games of a match played up to six wins and the result being 4–0 in Karpov's favor, Kasparov's goal changed from that of winning the match to prolonging it for a bit longer and losing at least honorably, and so he began to play in a closed and cautious style that mirrored that of his opponent at the time. With this strategy, he managed to draw the following seventeen games, before losing another one, thus bringing himself a game away from losing the match. However, things then dramatically changed in Kasparov's favor, as he scored the first win in Game 32, which was followed by two more wins and fourteen more draws in the sixteen games that followed, at which point the match was abandoned and replayed six months later. The replayed match Kasparov won, which marked the beginning of his long reign as the world chess champion and an instructor in decision-making [57] using none other but this example of mirroring the opponent's style to score a win against it. A concordant example may be that of Vlatko Kovačević’s winning a game as Black and as the 260th best player in the world and a complete underdog against the World No.1 at the time based on Elo ratings, Bobby Fischer, in Round 8 of the tournament in Rovinj in 1970. In this game, Kovačević, to begin with, opted for the very same Winawer variation of the French defense that had been played in Round 6 of the same tournament by Wolfgang Uhlmann, whom Fischer defeated relatively effortlessly by resorting to his usual Winckelmann-Riemer gambit, the same tool he employed in his game against Kovačević. More importantly, however, Kovačević played in the style of Bobby Fischer, himself, that is, boldly and aggressively, sacrificing three pawns before move 20 to open up the kingside, attack the white king and prompt Fischer's resignation on move 30. In fact, a fellow Yugoslav, Bora Ivkov, who played at the same tournament, commented after the game that if anyone had watched it live and knew not which of the two players was White and which was Black, they would be certain based on the styles of play, let alone the world rankings, that the winning black pieces were Fischer's and the losing white pieces were Kovačević’s [58], but their guesstimate would have been very much incorrect.

4.7. Chess and science both demand patience and long-term efforts

Emanuel Lasker, in the abovementioned Manual of Chess, states the following: “In Life a tension within Society always leads to a revolutionary political act, a great tension in the sentiments conduces to a revaluation of established values, and it cannot surprise us if in Chess a tension brings about a combination… For if a great advantage is the necessary and sufficient condition for the existence of a combination, this longed for but seldom attained goal, the laborious search for it can be methodically made and thereby facilitated. Therefore, in the beginning of the game ignore the search for combinations, abstain from violent moves, aim for small advantages, accumulate them, and only after having attained these ends search for the combination – and then with all the power of will and intellect, because the combination must exist, however deeply hidden” [39]. Indeed, since a game of chess could be seen as a metaphor of the human life and of battles waged figuratively in its course, as it was depicted in Ingmar Bergman's movie The Seventh Seal [59], whenever we are uncertain about what moves to make and what strategy to adopt, we could turn to the strategic principles in chess, such as those outlined by Lasker in his classic manual. For example, the students' eagerness to conceive of actions that would bring immediate results bears a resemblance to the rather inexperienced way in which novices open games of chess, that is, by seeking a winning combination from the very start instead of patiently developing pieces and improving the position gradually, in a solid, principled and methodical manner. There are also those who try to trick their opponents by contriving a fast combination or catching them in their sleep, hoping that they would blunder a piece or a checkmate. However, one such intrinsic lack of respect for the opponent oftentimes takes the form of a boomerang that they throw in the air in hopes of catching the prey, only to realize that it is returning towards them to slam them in their face. For, by expecting that blunt errors will be committed by the opponent and then punished as opposed to focusing on the proper development of one's own pieces first, these players leave inevitable and gross weaknesses in their positions, which an experienced player would know easily how to take advantage of. Hence, the advice I give to students who foolishly rush forward and dream of making grand discoveries in extraordinarily short periods of time and with minimal effort is to pay attention to the way in which a game of chess is to be played scholastically: not by looking after materializing one's intellectual efforts as soon as possible, but by patiently placing pieces to influential squares on the board and developing solidly, with style, sensitivity and strength, while being prepared to sacrifice the material at the right moment to establish the decisive dominion on the board.

The stronger the opponent in chess, the more patience is needed to establish a positional advantage and then convert it to a material advantage or a mating attack. If the scientist were to be envisaged through an analogy as a chess player, having on the other side of the board the physical reality with all its wonders and quirks, it would be a partner as challenging to play with and against as one could imagine, meaning that patience in science has to be equally imperative as in chess. Of course, once a positional advantage has been accrued through persistence and patience, its conversion to a material advantage or a decisive attack can happen rather quickly, but how much more important the positional advantage is than the material can be illustrated by countless chess games involving appealing sacrifices by the winning side or by a game such as Svetozar Gligorić’s win against Medina Garcia in Palma de Mallorca in 1968, when the Serbian grandmaster forced his Spanish chess colleague to resign in a closed Spanish game without capturing any of his pieces nor giving away any of one's own.

Impatience feeding on ultrashort attention spans, as it must be known to virtually every instructor and mentor in natural sciences, has gained epidemic proportions among students in today's educational institutions [[60], [61], [62]]. However, in times such as these, when brevity and expedience of information presentation and acquisition are norms and seeking rewards in as short-term of periods as possible is an attitude held onto like a holy grail by scientists and engineers in the high-tech business world, young people cannot be held liable for nurturing these impatient stances. Rather, as ever, they hold to us, the instructors, the mirrors in which wider social truths and trends are reflected. That this is the current drift is no secret, yet chess teaches the complete opposite of it. Because deep down, in a game between two grandmasters who are equally skilled at assessing positions, the one who sees farther down the variations, deeper into the future toward which the game evolves, is more likely to emerge as a winner. Chess, as such, is an endless assembly of lesson after lesson in holistic thinking and long-range planning, which scientists and technologists from the current era, with attention spans that have never been lower than today, could have a lot to learn from. Chess, from this viewpoint, presents a convenient tool for teaching students how to think of the horizons in their disciplines and deduce their critical decisions with these broader pictures in mind.

4.8. Chess is intrinsically collaborative, but it favors the auteur approach

Many times games were organized where grandmasters would play against the world in terms of tens of thousands of chess players democratically voting for each move in real time, and the outcome has almost always been the same: the win of the individual grandmaster (Fig. 5a-b). This is a reminder that individual creativity in science and the following of one's personally zested dreams comes with a lot more advantages than diluting these dreams via their forced collectivization. This is, however, not to say that we should remain closed to the input of other people's ideas, which would be dangerous, to say the least, in the increasingly collaborative and interdisciplinary milieu of modern science. Besides, chess is intrinsically a co-creative art, where the creative input of a pair of players is needed to create a single work of art in the form of a chess game. What this principle does say, however, is that the most outstanding creative work in science springs from powerful individual visions and from following them in accordance with one's unique personality and style.

Fig. 5.

(a) The World vs. Karpov, Internet, 1996, 0–1. Position on the board before 32 … Rc1, the move with which Karpov sacrificed the rook and prompted the world to resign in its first game against a single chess player in history. (b) The World vs. Kosteniuk, Internet, 2004, 0–1. Position on the board before 33 … g5, the move with which Kosteniuk, the former women's world chess champion, gave away the passed pawn on e3, having assessed that the rook endgame with two passed pawns on g and h files was winning for Black.

4.9. Learning to recognize blunders

Perhaps most unpleasantly to students of all breeds, the art of chess teaches its players how dangerous blunders are. Modern chess computers classify moves into a number of different categories, including the correct, the inaccurate, the mistakes and, worst of all, blunders, moves which instantly lose a game against a strong opponent. It is essentially defeatist to think how a series of superbly played moves followed by a single blunder could seal our fate, but such is the nature of life, where a single wrong act can cast a shadow over hundreds of immaculate decisions and lead to one's lifelong downfall. Correspondingly, what makes an expert in sciences stand out from amateurs is exactly this consistency of making solid moves over prolonged periods of time, even when on average they may not be as stellar as those produced by a creative genius. Conversely, herein lies the reason why the tops of the scientific pyramids are devoid of such geniuses, namely that fact that they make their moves from higher-risk standpoints relative to the grounds on which conformists stand, which makes every series of extraordinary moves of theirs prone to be followed by a gross inaccuracy, misjudgment or blunder. And as chess instructs us, to be consistent in delivering solid and principled moves provides for a more effective approach than that of making ten moves of an out-of-this-world virtuoso followed by a single blunder. In fact, being familiar with the major and minor errors we commit in our sciences prompted the Danish quantum physicist, Niels Bohr to define the scientific expert as a person who knows what common errors in his profession are and how to avoid them [63]. Bobby Fischer, correspondingly, is said to have memorized strictly the losing moves from the chess games from the literature and based his play on avoiding them [64]. Similarly, failed projects and forlorn hypotheses can be considered as significantly more meaningful than their successful counterparts to a mind aspiring to become scientifically superior, and chess, again, is a solid route for learning about this principle. Mistakes, all in all, are to be befriended as key signposts in our striving for extraordinary scientific insight [65], just as well as proneness to blunders should not discourage chess aficionados from continuing to nurture love for the game and rejoicing in its aesthetics.

To circumvent blunders on the chessboard and the scientific arena alike, one of the two essential principles derived by the Austrian-American constructivist and second-order cyberneticist, Heinz von Foerster comes handy, namely “if you desire to see, learn how to act” [66]. This principle can be used as a precautionary measure against an oft-observed phenomenon, which is that blunders become visible to their maker as soon as they are being played [67], despite the tedious calculations preceding the move. This phenomenon illustrates how separate the world of thinking is from the world of doing and is well-known to any student in sciences who has thought that ideas on what to do research-wise were all nailed down, but only to witness these very ideas fall flat on their face after they are being practically tested. The remedy here, of course, is to nurture a balance between abstract conceptualization and empirical experimentation, just as well as chess players must both think hard and practice hard to succeed in elevating their game to the next level.

Moreover, the critical effect of blunders on the result of the game is a consequence of the fundamental fact that in an equal or nearly equal position, there are no winning moves, but there are moves that can instantly lose the game for a player who makes them against a solid opponent. Playing by this principle liberates the player from any aspiration for an immediate accomplishment of a goal and immerses her instead into the road, not the destination, so to speak, with countless ensuing benefits for the thinking process. The same approach could be prolifically implemented in science as well as in every segment of life. If so, an infantile mindset constantly seeking rewards gets to be replaced by the one playing patiently, diligently, cautiously and humbly, with eyes kept on distant horizons and views broad and generous, knowing that such a frame of mind is particularly conductive to making big discoveries in the province of science.

4.10. Chess can be illustrative of fundamental scientific concepts

The use of analogies between phenomena on microscopic scales probed by natural sciences and phenomena in more accessible realms of human experience is a tool instructors can use to help promote the sticking of the knowledge about the former phenomena to the memory [68]. One of the many situations where chess can come handy as an illustration of scientific effects is that where a state of balance is being explicated. For example, one common misconception that chemistry students even at the highest, postgraduate educational level have is that there is a clear-cut division between ionic and covalent bonds, when in reality each ionic bond has a degree of covalency ascribable to it. This is readily relatable to the frequent division of chess styles to strictly positional and strictly tactical ones, which is equally wrong because every chess player by default must employ both of these elementary skills to be successful. Therefore, the only classification that does make sense is that of assigning a degree of positionality to a chess style, just as we do to the chemical bonds.

Another example may be that of illustrating the necessity of considering the entire environment around physical objects to correctly assess their energy states, an approach intrinsic to an atomistic framework such as that of the quantum field theory [69]. A common misconception here is that the energy of a physical object is independent on its physical surrounding, when, in reality, the energy of the object, be it kinetic or potential, can only be assessed relative to its environment. Just as the material value of a chess piece must be supplemented with its positional value, which is dependent on the overall position on the board, before the real value of the piece can be derived, so is it with any physical entities, for their exact physical qualities can be inferred only after taking into account the total state of their environment at the moment of the measurement. This is where we arrive at the practical impossibility of accounting for the entire physical environment and all the potential combinations on the chessboard. In the first published paper on computer chess [70], Claude Shannon, namely, estimated the total number of possible combinations on the chessboard at around 10¹²⁰, which is greater than the estimated number of atoms in the Universe (∼10⁸⁰) and is the digit that is still cited as a good ballpark approximation [71].

Yet another example may be that of correlating the division of a chess game to its strategic and tactical aspects with the balance between the holistic and the reductionist thinking in sciences. Here, whereas the strategic aspects refer to the general and long-term ideas implementable in a game, the latter are related to immediate and short-term maneuvers on the board. Whereas the former predominantly take place during the middlegame and during the transition from the opening to the middlegame, the latter typically occur as the middlegame matures and as it transitions to the endgame. Thus, whereas it makes sense to consult an openings book or a tablebase to find a specific move for an opening or an endgame, respectively, the most we are left with in the early middlegame are strategic, general rules. Whereas the strategic views of the game span many moves ahead, the tactical elements cover only a couple of them. Hence, strategic perspectives in chess are reminiscent of the holistic views that keep their eyes on the forest and are authentically human. In contrast, the tactical ideas are oriented towards resolving fine and immediately perceptible characteristics of individual trees and computers display an unprecedented mastery in spotting and executing them on the chessboard. Needless to add, both of these modes of thinking act as bases for effective scientific reasoning and one without the other could not exist. Limiting approaches in chess and science alike only to the goal of attaining immediate gains without any long-term plans born in mind is as fruitless as neglecting fine tactical maneuvers while keeping an eye on the wider scheme of things.

This balance between strategy and tactics in chess can be fairly well linked to the scientific method of explaining the physical reality. Namely, just like the prospect of finding the solution to a perfectly played game of chess is an ultimate but hardly attainable ideal in the minds of chess theoreticians and enthusiasts, a similar belief that equations for a perfectly consistent deterministic description of the physical reality and fulfillment of the ideals of Laplace and his demon would someday be derived exists alive in the minds of many natural scientists. However, the complexity of calculations required to predict the effects of each chess move or physical cause are beyond the grasp of the computational capabilities of the current day. Hence, pure tactics and elementary particle physics do not seem to be able to provide reliable answers to these fundamental questions. Rather, holistic views, in terms of chess strategy and philosophy of physical sciences with all their intrinsic indeterminacies, are invited over to fill these gaps in our knowledge. The nature of human thought, after all, is such that discerning the features of physical reality down to its finest detail and keeping an eye on the way of the whole are both required to summit the sublime vistas of truly sagacious semantics. Through this duality, the resolution of the human probing of natural systems, enabling an ever more precise manipulation with the substrate of physical reality, and the evolution of the understanding of the contexts in which these activities are placed can be developed in parallel. Only with one such progress on parallel planes can the conditions for the evolution of science and humanity be reached.

Moreover, just like having the answer to the ultimate question of chess – namely, if both Black and White played perfect moves, would the game end as a draw or as a win for White? - would make any further playing fundamentally nonsensical, the same can be said for being hypothetically in the possession of the equations of what is colloquially known as the theory of everything. If humans were able to predict all the natural events and if everything could become known in advance, the meaning of life, crucially dependent on perpetual questioning, searching and evolving thereby, would cease to exist. In the context of the game of chess where ignorance with regard to the best possible move we could make in the opening and the middlegame is what keeps the evolution of our knowledge of the game going and sustains our joy of playing it, the Serbian chess writer, Dragoslav Andrić, noted in the final sentence of one of his popular books that “chess exists only due to mistakes” [72]. The same can, of course, be said for the evolution of higher forms of life and our scientific knowledge and expressional aesthetics: they all depend on ignorance, entropy and stochastic chaos in our physical and mental worlds. Entropy, for one, is a pivotal prerequisite for any automatism established in our brains to be interrupted and our synaptic connections to dance their way toward new semantic attractors. Only insofar as they pervade every corner of the space of our minds can our knowledge and being evolve into higher forms, further up the vertical extending from the animalistic to the angelical.

4.11. Dual purposefulness of the classiest class of chess moves

The principle of two weaknesses is one of the classic strategic principles in chess. According to it, as the attacking player starts to suppress the opponent around one weak point in his position, he should look for the right moment to shift partially the focus of the attack to another weak point in the opponent's position, which may or may not appear as a consequence of imperfect defending. Or, as summed up by Danny Rensch of chess.com, “you often see amateurs misplay endgames precisely because they get so obsessed with their one advantage that they forget to look for the principle of two weaknesses ideas as a way to gain winning chances” [73]. Chess, in other words, offers us a great lesson as to how banging the head against the wall of a well-defended weakness does not provide for a best way to overcome an obstacle, be it over the board or in life or on the science lab bench.

With this principle in mind, moves made by a chess master are said to be such that they usually serve multiple roles on the board and, at their most effective, expose multiple weaknesses in the opponent's position and pose multiple threats to it. Modern chess, in fact, necessitates a tireless search for moves that would be simultaneously offensive and defensive, combinational and positional in their character, and can be translated to the glorification of ambiguities and semantic multiplicities intrinsic to the most captivating expressions in any form of art. Historically, the emphasis on such moves with a dual character began in 1910s with the third world chess champion, Jose Raul Capablanca, who is often said to be great “because he understood the power of two”, that is, “of doing two things at once” [74]. One out of myriads of such moves pulled out from the repertoire of games by the Cuban grandmaster can be his pawn move as Black, 15 … c5-c4, from the game played against Ossip Bernstein in Moscow in 1914 (Fig. 6a), a minimalistic gem that was to serve as a stylistic inspiration for Bobby Fischer half a century later. With this simple move, Capablanca destabilized his hanging pawn structure in the center, but simultaneously blocked and threatened the white b2 pawn, opened space for the attacking slide of the black bishop from e7 to b4, and limited space for White by seizing the d3 square. In contrast to his being able to pose multiple threats with this move, the weaknesses in his own position thus created were not exploitable in a similar manner, he correctly recognized, as the white rook's attack on the undefended pawn on d5 and the hopping of the white knight onto the opened d4 square to gain positional advantage excluded each other. A more recent example may come from the legendary king-march game of Tigran Petrosian against Mikhail Botvinnik from their world championship match in 1963, where Petrosian as White engaged in the daring repositioning of his uncastled king from e1 all the way to g7, behind a couple of black pawns, where it found safety in the midst of a mating net. In this game, Petrosian focused on creating double weaknesses in Botvinnik's position, the first one being the lone pawn on e6 and the second one being the lone pawn at c4 [75], which he exploited with a knight in the middle of the board (Fig. 6b), a piece he had preferred throughout his career over bishops precisely because of the multiplicity of squares that it could attack or defend around it. An even more recent example may be that of the 24th move of Game 9 of the semifinals of the Candidates Tournament in 1974 played between Anatoly Karpov and Boris Spassky: Nc3-b1 (Fig. 6c). With this move, Karpov returned the white knight to its starting square, from which it would go on a hunt in a different direction, posing threats and weakening Spassky's pawn structure in the center and on the kingside, while also fortifying the stalwart rook on d2, opening the room for c2-c3 to chase away Black's best positioned piece and, all in all, laying path for an effective offense by seemingly withdrawing from it, the style so typical for the Uralian grandmaster that today it deserves the colloquial epithet “Karpovian”. The last example to be mentioned here is the final, fortieth move in the win of Vladimir Kramnik against Loek van Wely in Wijk aan Zee in 2007, e4-e5 (Fig. 6d). With this move, the b8-h2 diagonal was closed and the b1-h7 diagonal opened, the former of which blocked the coordinated attack of the black queen and the rook on the h2 pawn guarding the white king and the latter of which allowed the launching of an indefensible assault on the black king, meaning that this one move served both a defensive and an offensive purpose, being a part of the dream play of every modern chess player. Other notable multipurpose moves from the chess history may include Clemenz's 21.Ba1-a3 from the game against Eisenschmidt played in Tartu in 1890, Najdorf's 11.Qd8-e8 from the game against Glucksberg played in Warsaw in 1929, Spassky's 9.Nc3-e4 from the game played against Bronstein in Saint Petersburg in 1960 and later immortalized in the James Bond movie, From Russia with Love, Petrosian's 30 … f5 from Game 7 of the world championship match against Spassky in Moscow in 1966, Fischer's 29.Qh3-g3 from Game 6 of his world championship match against Spassky in Reykjavik in 1972, Topalov's 46 … Rf5-f4 from the game against Kharlov played in Tripoli in 2004, and Carlsen's 18 … Ne8-c7 from Game 9 of the match against Anand that decided the world champion in Chennai in 2013.

Fig. 6.

(a) Bernstein vs. Capablanca, Moscow 1914, 0–1. Position on the board before 15 … c4. (b) Petrosian vs. Botvinnik, Game 5, World Championship, Moscow 1963, 1–0. Position on the board before 32.Kc4. (c) Karpov vs. Spassky, Game 9, Candidates semifinals, Saint Petersburg 1974, 1–0. Position on the board before 24.Nb1. (d) Kramnik vs. van Wely, Corus tournament, Round 13, Wijk aan Zee 2007, 1–0. Position on the board before 40.e5.

Two things relevant for this discussion tie to this search for chess moves with dual or multiple purpose. First, the most fascinating works of art are such that they combine mutually antipodal expressions, be it the ambiguousness of major and minor scales in Schubert's late piano sonatas, the simultaneous depth of perspective and directedness of expression in Degas' ballet dancers, the contrapuntal use of sound and vision in the avant-garde films of the Soviet film school from the 1930s, or the two tritons, the tranquil and the mad, of Fontana di Trevi. Second, it is not unconceivable that scientific works could deliver a similar degree of innovativeness at different levels, including the artistic and the analytical. In fact, the major component of my career as a scientist has gone into the effort of convincing the fellow scientists that this is possible and that a form of scientific expression, such as a paper or a lecture, could be both immaculately rigorous and original from the analytical standpoint and emotionally touching and conceptually innovative from the artistic point of view. Mingling science with art is often seen as a sign of blasphemous infidelity to science and as a descent into the muddy waters of pseudoscience, but this need not be so and scientific works could indeed be both unprecedentedly original in terms of their scientific content and also artistic in their form and expression. A few examples of this marriage from my personal oeuvre may suffice here, taking the form of different scientific papers released in a single year, 2022: (a) a paper demonstrating that, like the journey of Odysseus, the trip of a nanoparticle out of the eukaryotic cell is longer than that into the cell, while presenting the content in a stream-of-consciousness fashion as an homage to Joyce's Ulysses [76]; (b) a paper demonstrating an age effect of watchers of children at playgrounds on their mood and play, while giving a real-life account of children's play in a poetic triptych that occupies the central part of the paper [77]; (c) a paper showing that inter-individual distances between aquatic birds depend on whether they are being interacted with by solitary birdwatchers or by pairs of birdwatchers, while beginning and ending the paper with strings of diffuse and disconnected thoughts to veritably reflect the birth and the death of creative ideas in our heads [78]; (d) a paper presenting research in physics and chemistry of a newly discovered colloidal phenomenon in the form of a theatrical play, using coauthors as its imaginary characters and partially expressing the research through a dream [79]; (e) a “reality” paper written in the form of a diary, documenting the search for a research subject, performance of research and the interpretation of findings in real time [80]. Needless to add, all five of these examples provided forms of expression – e.g., stream-of-consciousness, a lyrical triptych, deliberately chaotic beginnings and ends, a theatrical play partially enacted through a dream, and self-reflective diary - that were artistic and completely new to the history of the given medium, in this case scientific paper.

Concordantly and very importantly, the personality of chess players naturally tends to live up to this juxtaposition of contrasting effects implementable on the chessboard. Or, as Alexander Alekhine deemed, “a master must envisage himself as a cross between an ascetic monk and a beast of prey” [81], holding “the sword in one hand and the olive branch in the other” [82], as his predecessor on the world champion throne, Wilhelm Steinitz maintained. This is what imparts immodest doses of complexities to the mindsets of chess players, which, like exceptional artists and scientists, require solid grounding to support them lest the mental structures in place collapse. This complexity at the personality level, however, is natural and not something to shun or hide away from, with chess being a good model for reminding scientists thereof.

4.12. Forced lines have nil creative potential

In chess, when sequences of moves are forced, there is no room for exhibiting creativity; likewise, whenever one is subjected to rigorous commands and orders, when doubts cede place to dogmas, when uncertainties and solecisms are banished like the plague, when laws are too many and freedom, entropy and chaos too little, when guardians of the gate of customs and norms prohibit the exhibition of the will to liberate the text from the cages of the syntax and, like here, produce sentences where words have been allowed to fly freely, beyond the bounds of full stops, creativity suffers and with it our ability to provide impetuses for the evolution of science and of the human race toward horizons beyond those where they stand today. Freedom, in essence, albeit a notion at fundamental odds with the academic tradition of authoritarianism and albeit capable of existing only within rigid frames defined by the rules of the game, provides the only means by which meaningful knowledge and creativity of independent thought can flourish. Here chess ties to the second of the two principles devised by Heinz von Foerster, namely “act always so as to increase the number of options”, which translates to the chess terminology as the principle recommending the piece with the least options to be moved first [83]. This guiding principle illustrates how the positional aspects of chess can be approached and studied through a technically infinite number of mental models and frameworks. Further, this iterates the possibility that each new player may invent a completely new way of viewing the game and performing the calculations, whether the game is chess or science. Insights like this expand the horizon of possibilities and are of an enormous benefit to any domain populated by perpetuators of standards and dogmas that work from within to restrict these infinite possibilities.

4.13. Creativity has no alternative

From science to chess to all aspects of life, freedoms of expression arise only because of the existence of constraints and rules enabling them. To play chess well, therefore, familiarity with opening and middlegame principles and with rules applicable to endgames is essential. Maintaining a good pawn structure; breaking through the center when the opponent delays castling; understanding that the side controlling pawn breaks in a closed position is the one having an advantage and also that being a mobile pawn up makes up for a greater advantage than being a blocked pawn up; attacking in the direction in which the pawn chains point; trading pawns and releasing pawn tensions when one is ahead in development; trading pieces other than pawns when defending in the middlegame; keeping rooks on the board when playing against the isolated queen's pawn; taking advantage of coordination between the queen and the knight and between the rook and the bishop; doubling rooks along open files (Fig. 7a); placing bishops on long and open diagonals (Fig. 7b); exchanging passive pieces for the active ones; exchanging in general when playing for a draw or when controlling less space in the middlegame; taking advantage of opposition in king and pawn endgames and of other forms of zugzwang in positions with a limited number of reasonable moves for the opponent (Fig. 7c); favoring knights over bishops in closed positions and in endgames when pawns are only on one side of the board; sliding knights away from the edge of the board and close to the center (Fig. 7d); and favoring endgame positions having lower pawn majority numbers on one side of the board are a few of the many thousands of such principles followed by grandmasters. However, in each stage of the game, middlegame in particular, clarion calls for creativity to be exhibited are being made for those who can hear them. These calls, of course, can be followed only insofar as one is ready to defy the classical principles in one's discipline and stun the peers with one's rule-breaking schemes. As far as scientific thought is concerned, this is where the paths for its progress are being lain: in preparedness to disobey the paradigm and go beyond its premises. This can be a reminder that solid knowledge of basic principles and foundations is needed for successful engagement in scientific activities, but so are the exhibitions of creativity. Without the ability to think in a creative manner, which is such that it constantly surprises, both oneself and others, a goodbye could be waved to a beautiful and inventively played game of chess and inventive lifetime in sciences alike.

Fig. 7.

(a) Uskoković V. vs. Chessmaster 2100, Belgrade, 1992, 1–0. Owing to the pressure exerted by the rooks doubled along the d file, the position on the board is evaluated as equal (0.0) by Stockfish 14+ even though White is a piece down. Moreover, in order to maintain equality or gain advantage, White must sacrifice another piece, that is, the bishop on g5, playing either 25.c5 or 25.R1d7, with possible continuations being 25.c5 fxg5 26.Bc4+ Kf8 27.R1d7 (+1.3) or 25.R1d7 fxg5 (if … Kg8, then 26.Bc1 is winning for White) 26.Rxe8 (0.0). (b) Uskoković J. vs. Uskoković V., Kumbor, 1991, 0–1. Position on the board before 27 … b5 28. cxb5 Qxg5+, where Black first gave away the b pawn to open up the a8-h1 diagonal for the light-squared bishop and then sacrificed the queen to create an indefensible attack on the white king, leading to either an immediate checkmate after 29. fxg5 Rh2+ 30. Kf3 Bd5# or checkmate in nine after 29.Kf2 Bxf4. (c) Uskoković D. vs. Uskoković V., Belgrade, 1991, ½ – ½. Position on the board before 50.h6. After this move, Black is in zugzwang and the game ends in a draw because after 50 … Bg8 51.Ke4 b4 52.Kf5, the black and a white pawn would promote simultaneously. If, however, it was Black's turn to move in this position, White would win because after 50 … Bg8 51. h6 Bh7, the light-squared bishop would cover the e4 square and force the white king to retreat and thus lose a precious tempo in the run toward g6 or f7 to help promote the g7 pawn. (d) Uskoković V. vs. Uskoković D., Kumbor, 1991, 1–0. Position on the board before White played 20. f5, thus removing the defender of the central d5 square so as to bring the knight to the center and create a passed pawn on the seventh rank after 20…Bxf5 21. Bxf5 exf5 22. Nd5 Qb7 23. Ne7+ Bxe7 24. Qxb7+ Kxb7 25. dxe7 Rde8 26. exf6, around which White would build his attack in the further course of the game.

4.14. Chess hints at curious phenomena hidden even in the most lackluster of scientific expressions

One elementary aspect of the aesthetics of chess is that main lines in any given game are where only a portion of the instructive content lies. In reality, these main lines are akin to the tip of an iceberg, when a far greater content usable in enjoying chess and learning about it lies concealed in the unplayed variations. Every classic game from the history of chess, in fact, from Steinitz's victory over van Bardeleben in Hastings in 1895 to Kasparov's win versus Topalov in Wijk aan Zee in 1999 to Anand's victory against Aronian in the same Dutch town in 2013 to Hou Yifan's win against Ider in Gibraltar in 2017, amuses not only with the played lines, but even more so with the variations that could have been played had the game taken on a different turn. Studying these hidden variations is, in fact, a must for any chess player in training, simply because a success over the board comes from the precise calculation of responses along a multitude of variations at each point of the game. Finally, this resting of the greater and more informative chess content in variations that were never played in the game allows practically any game, even those played by players beyond their prime (Fig. 8), amateurish aficionados or total patzers, to be extracted for enriching ideas. Such ideas, of course, need not relate to the improvement of precise play per se, but may also bring about more poetic or survivalist insights, oftentimes bordering tarot-like oracles. One analogy with the world of science here is that regardless of how dull and lackluster a specific scientific expression, idea or model is, in it always lie hidden far more abundant insights than those visible on the surface. There is no such thing as a boring scientific paper, presentation or a model, as digging deep inside them will always yield fantastic insights to a keen eye. After all, chess is played on a 8 × 8 board, but to use it as an aid in solving the problems of science and life alike, like in the famous “thinking outside the box” problem, the lines of analogies must be extended beyond the board, far beyond what eyes could see, where only the scope of an imagination unbound could reach.

Fig. 8.

Uskoković D. vs. Uskoković V., Belgrade, 2022, 0–1. In an unplayed variation, Black was to find 27 … Kh8, the only move that preserves the attacking momentum for it according to Stockfish 14+, as after 28. Rd7 Black sacrifices the queen with 28 … Qxd7 and gains a decisive advantage after 29. Bxd7 Bd4, whereas after 28. Bf5 Black capitalizes on the bishop pair in an endgame after 28 … Rf3 29. Rd7 Rxg3+ 30. Qxg3 Bxg3 31. Rxg7 Kxg7 32. Rf1 Bf4. The way in which the retreat of the king to the edge of the board in the middlegame can act as the most attacking of moves - seemingly made to avoid the pin threat and loss of queen after 28. Rd7, but only for that very same queen to be sacrificed a move later - can be a definite source of amusement and inspiration. A scientist confining herself to a quiet corner to study her science can, likewise, be the most effective move in her attempt to save the world.

4.15. Chess is political

All those who may come forth and point out that science is unlike chess, tennis or any other sport where fair competition decides who would make it to the top because micropolitics is the strongest determinant of one's success as a scientist may be reminded that chess, despite this, is extraordinarily political, like any human affairs. The infamous splitting of the World Chess Federation (FIDE) and the Professional Chess Association (PCA) in 1993 and the detrimental effect this had on the popularity of the game may be an illustration of these powerful political streams that guide the evolution of the game. Rules of chess have also changed throughout the history and the proposals for change, such as Bobby Fischer's random chess aka chess960 or Capablanca's chess, have all been ignored by the official agencies, yet such changes could be implemented or resisted only by exhibiting a certain degree of political power. Finally, the world champion determination format has changed during the history too, in the most unexpected ways, which were, deep down, dependent on the politics of the era, and the chance is that the world champions that we know of today would have been different under different political umbrellas.

In the scientific multiverse, we have known since the work of Thomas Kuhn and the philosophers of science in the 1960s [84] that new scientific theories and models are not accepted when they satisfy the criterion of objective truth, but when they get accepted by the scientific community, a process that favors the politically conscious individuals more than it favors the apolitical ones or the dissidents. Concordantly, the entrance exams for higher education institutions are reserved for students alone, but not for their teachers, who are admitted based on the political powers of their prior affiliations and recommendations, undergoing virtually nil evaluation of their direct teaching skills or scientific knowledge. As a result, in just about the same way as careers of some chess prodigies, such as those of Bobby Fischer or David Bronstein, have been hampered by their political nonconformities, the careers of people at universities have been defined primarily not by the scopes of their imagination and creativity, but by how compliant they are with the academic establishment. Therefore, when exuberances of creativity are rejected as dangerously radical, trivial or suspected of fraud by the mediocre political powers that be in sciences, we may simply come to think of how a grandmaster's playing a simultaneous blindfold game exhibition would be similarly classified as an act of lunacy by amateur chess players rather than as a display of an extraordinary skill. We may also think of how two hypothetic humans playing a game of chess like that between the engines Arasan and Igel from the 2023 TCEC League 2 Igel Gauntlet [85] or that between the engines Koivisto and Stoofvlees from Round 14.2 of the 2023 TCEC Division P [102] would be likely denounced by ordinary chess players as drunken patzers, even though each of them could singlehandedly beat the world's best human player with a rook down.

Moreover, not only is the fate of individual scientists and theories determined by politics, but so is that of the entire fields of science sometimes, as exemplified by my alma mater major, physical chemistry, which was initially conceived as an independent scientific discipline that would strive to explain chemical phenomena using fundamental physical principles, but has now been reduced to nearly 100% computational chemistry at the research level, after fields such as chemical engineering, solid state chemistry, high-energy physics and biochemistry claimed their shares of the cake and stripped physical chemistry of nearly every last trace of empiricism. Similarly, there are disciplines in chess, the propagation of which is directly proportional to how influential the administrative and social voices advocating them are. Most notably, these disciplines include correspondence chess and chess problem solving and composition (Fig. 9), for which the very same titles, from the master to the grandmaster, are conferred as in classical chess, yet the interest in them, primarily among the young players [86], has waned over the years, coinciding with the stagnation of the number of delegates at the annual world congresses of chess composition since the 1990s and the fact that the times when the world-renowned grandmasters played correspondence chess, including the likes of Alekhine, Euwe, Fischer, Paul Keres, Igor Bondarevsky and Ulf Andersson, are long gone. As to how politics governs science at multiple other levels no words need be spent, but the central point here is that definite parallels exist between the universes of chess and science when it comes to the clouds of politics gathering, usually ominously, over them.

Fig. 9.

Vukcevich, duplex helpmate in 2, Bad Pyrmont, 1996 [solution: 1.Ng6 f8 = Q 2.Ne5 d8 = N#, 1.f8 = R Nf7 2.d8 = B Nd6#]. This exemplary allumwandlung chess problem created by my first cousin and the first American FIDE grandmaster in chess composition illustrates the versatility and scope of potential of pawns, which are such that they exceed those of any other pieces in chess despite the fact that they are least valued. Deemed so much weaker than other pieces that they usually do not even earn the attribute of a piece, pawns can transform to any of these stronger pieces in addition to defining the game structure (open vs. closed) and serving as the first line of protection for the king. The game of chess also begins with pawns and their struggle to occupy the center, while endgames invariably revolve around the coordinated effort of all the pieces to either enable or prevent their promotion. This intrinsically political point, inaugurating the least valued into the most valuable, like many other points, can be glimpsed on the chessboard, be it in real games or composed positions such as this one.

4.16. Chess is life

People's personalities are mirrored in their chess playstyles because, to put it simply, chess is a language of life, just as well as the styles in which one engages in science, physical sports and all other gestural forms of communication are. Bobby Fischer's proverb “chess is life” [87], Ingmar Bergman's aforementioned movie, The Seventh Seal, Eldon Tyrell's making replicants in Blade Runner grandmasters who play incessant correspondence chess with their maker [88], and Agent Cooper's nemesis', Windom Earle's saying that “all of life could be found in patterns and conflicts on the chessboard” [89] all illustrate this fundamental alikeness. Here, it may be worth recalling that although the most beautiful and worshipped games of chess tend to end in the explosive fireworks of an exciting middlegame, some of them do reach the endgame, the stage where the display of a mathematical precision in making moves is needed to ensure a good result. As this last phase of the game is reached, the period of a dizzying creativity reigning in the middlegame is over and prewritten rules could be referred to in order to bring the game to a successful end. Less pieces remain on the board and the range of both possible and correct moves is significantly diminished, which evokes the constructivist view of perception, as employed in the previously elaborated co-creational theory of cognition [[90], [91], [92]]. Namely, the frequency of repetitions of a priori assimilations of perceptive forms into objects in a juvenile mind is comparatively low, permitting through extreme calculations one to even believe that the fantastic and the otherworldly can become real. But as the perceiver gets older and more experienced and these perceptive assimilations necessary for the coordination of physical movements and sensations become more frequently reinforced, rigidity of the construction of the experiential world becomes higher, leaving one with a lessened capacity to recognize an astonishing variety of features in familiar objects and events. What this instructs the scientist is that the analytical mind is bound to perceive different things and think differently as it ages and as options get reduced with the transition from the opening to the middlegame to the ending.

4.17. Romanticism of modern chess engines

Art traditionalists continue to nurture an aversion to computers and all things artificial, but modern age has brought an overwhelming openness of art not only to computers, but to high technologies in general. Modern music, movies and architecture, for one, would be unthinkable without the reliance on these technologies and the same goes for science, where the most influential research today has been performed with the assistance of delicate instrumentation in empirical sciences and the assistance of supercomputers and novel algorithms in theoretical sciences.

Chess engines have tremendously influenced the style of the world's top chess players. There are two types of chess moves, in particular, diametrically opposite in nature, that computers have taught humans about: (a) completely passive moves, which keep the position in a status quo, neither improving nor aggravating it, and (b) incredibly dynamic moves, where simple mathematical calculations of the material value of individual pieces fail and piece sacrifices are made all over the board. Neither of these types of moves had humans considered as natural before the advent of computers. Still, they very well illustrate this breadth and universality of style in the modern era, the rise of which the computers have immensely contributed to.

In fact, a most interesting thing about state-of-the-art chess engines, such as Stockfish, Komodo or Ethereal, is not that their Elo ratings are by a 1000 points higher than that of the average grandmaster and by nearly 800 points higher than the world's strongest player and the current world champion, Magnus Carlsen. It is that they often play far more imaginatively than the world's strongest grandmasters, disobeying the classical principles and sacrificing the material in utterly mysterious ways. Stockfish's putting one's own queen first into confinement with 21. Qa4 and 22. Nb5 and then to the edge of the board with 30. Qa1 or deliberately entering a discovered check with 37. Kh2 (Fig. 10a) in the Season 7, Stage 2, Round 5 Top Chess Engine Championship (TCEC) game against the computer engine Jonny 6 [93] can be one of the examples. Another example may come from Houdini's playing cool and unfazed 23 … Kf7 after 22 … b4 23.cxb4 (Fig. 10b), thus sacrificing its third pawn in nearly the endgame against Rybka in their Round 1 TCEC match from 2011 [94], having correctly assessed that giving away three pawns would give it a solid positional advantage over the opponent, even without bothering to capture the free white pawn on b2 any time soon or move the central king's pawn from e7 until the 50th move of the game. Other notable examples may include Stockfish's developing not one, but both of its knights to the edge of the board in Game 46 of the TCEC Season 23 superfinal match against Leela (Fig. 10c), paying not even a slightest heed to that classical knight-on-the-rim-is-dim principle, as well as AlphaZero's sacrificing two pawns on the kingside to Stockfish [95] and offering the third, but then instead of launching a logical attack along the open g and h files with two rooks positioned on them, playing the calm and soothing sequence of Kb1-Rgg1-Ka1 (Fig. 10d), secluding the king and retreating with both rooks, shifting them away from the kingside without any concerns over losing precious tempi thereby, then giving away another pawn in the center with 30.d5 to gain more open space, and finally creating a decisive attack via the a1-h8 diagonal spearheaded by the bishop on b2, protecting all along the king on a1.

Fig. 10.

(a) Stockfish vs. Jonny 6, TCEC 2014, 1–0. Position on the board before 37.Kh2, which threatened the sacrifice of the second white rook with Rd1 so as to distract the black queen from the a3-f8 diagonal at the cost of allowing the seemingly dangerous pinning of the knight on e5 with 37 … Ng6. (b) Rybka vs. Houdini, TCEC 2011, 0–1. Position on the board before 22 … b4 23.bxc4 Kf7. (c) Stockfish vs. Leela Chess Zero, TCEC 2022, 1–0. Position on the board after 13.Nh3. The knight will eventually be sacrificed on g6 to distort the pawn structure in front of the uncastled black king. (d) AlphaZero vs. Stockfish, AlphaZero – Stockfish match, London, 2018, 1–0. Position on the board before 21.Kb1 g6 22.Rgg1 a4 23.Ka1 Rg7 24.e4 f4 25.c5 Qe7 26.Rc1 Nf6 27.e5 dxe5 28.Rhe1 e4 29.Bxe4 Qf8 30.d5 exd5 31.Bd3.

These, of course, are excerpts from only a few out of many games that have dispelled the traditional belief that computers could not play wittily and creatively. In the 1990s, the decade during which chess engines made a stride from uncompetitive to superior at the grandmaster level, it was customary to perceive them not only as a nuisance because of their purely tactical, calculative nature at the time and the inability to conceive of creative strategic ideas, but also as a threat because it was deemed that human interest in chess would rapidly diminish at the point when humans start losing to computers. What has happened instead is that the engines have been continuously expanding our awareness of the breadth and the beauty of the game, unceasingly surprising us with discoveries. Through robust calculations they have rediscovered romanticism of chess that lay buried under the carpet of prosaic play for a long time, thus inspiring the top players in the world to become more audacious and less materialistic in their play. In that sense, the way computers revolutionize chess as these lines are laid may bring about a paradigm shift in our understanding how machines and artificial intelligence will change every other human discipline, science included.

Common sense has told us that computers, emotionless as they are, without any ability to abstract artistically, could boost productivity, but would inevitably dehumanize everything they touch. In the opening theory we see this distinctly: novelties introduced over the board, in real games, used to be the inventions of individual chess players and were traditionally assigned the names or countries of people who played them first. After the advent of the chess engines, however, any revolutionary new ideas in the openings could be traced to computer preparation, so that the inventors are no longer the creative and imaginative players, but those with the biggest memory capacity and time on their hands. For example, Sam Shankland’s castling cold-bloodedly straight into a pin and then giving away the pinned piece with a lost tempo after 18…Qxb2 19.Qxc4 Bxf2+ 20.Kh1 to win the game against Sergey Karjakin in Round 12 of the 2022 Tata Steel Masters tournament in only 26 moves would have earned accolades for inventive play a few decades ago, but today it represents only an instance of outsmarting the opponent through an exhaustive opening preparation aided by the computer. The corresponding concern in the scientific domain is that very soon computers will be programmed not only to perform calculations based on the preexisting concepts, but also to invent new ideas, at which point it would make no sense anymore for human researchers to earn laurels for proposing them. Further, one could argue that computer engines and databases do play a finite role in dehumanizing the social aspects of chess, for the very same reason that computer technologies dehumanize relationships between humans per se. To put it simply, in the days preceding the digital revolution and internet technologies, people had other people as communication partners and sources of information to a greater extent than today. People in a direct contact were thus naturally considered as holders of greater assets to each other than it is the case today, when information acquisition, work search and performance, shopping and entertainment could all be done over the computer, creating a situation where the purpose of a fellow human may get questioned. Depersonalization under such circumstances takes on epidemic proportions, empathy hits the rock bottom and people begin to drop other people with ever greater ease down the cliffs of life, the inklings of which can be sensed in today's online chess world as well. Playing chess online can thus be denounced as a diluter of the human component of the game, even when it is played entirely by two human beings, without any input from the computers. This latter input has been more difficult to avoid the longer the chess games last, which prompted the International Correspondence Chess Federation to conclude that it is impossible to prevent humans from cheating by consulting computers in the course of correspondence games, the length of which is typically over a year [96], and to allow the use of engines in correspondence chess [97]. This association of computers with dishonest play in the competitive context can be added to the list of effects by which the engines tear the fabric of cordiality and communion buildable around the chessboard.

Henceforth, choosing computers as partners or media for chess games over real humans in over-the-board settings has allowed players to be more efficient in playing and studying the game, but the cost has come in the form of thinning the links of intimacy between people and the overall dehumanization of the social network. In support of this dehumanization, one could cite today's notable grandmasters and YouTube/Twitch streamers who often comment on playing against mere Elo ratings - e.g., 1500s or 1900s - during their live broadcasts, showing how easily humans can be stripped of their personalities and reduced to triple or quadruple digits as their sole identities, evoking in the far distance the prisoner numbers in concentration camps as historical synonyms for dehumanization. Another example of this thinning of the links of humanness may come from the widespread acceptance of flagging the opponent in an inferior position among the younger players who learned chess solely as a computer game, which is a way of winning that is generally considered unethical by the older generation of chess players [98]. Also, many online chess platforms today either do not implement takebacks or allow the users to turn them off as an option in their games. Takebacks, of course, are logical actions under the assumption that the goal is to create a beautiful game, a work of art as it were, rather than win pettily, and granting the request for them is also always a sign of good sportsmanship, for which reason their vanishing from the contemporary chess culture can be taken as yet another sign of its dehumanization. Needless to add, mutual requesting and granting of takebacks is likely to be more pervasive in a casual over-the-board setting than when games are played over the internet, given that studies in psychology have shown that weaker interpersonal ties do tend to make virtual social groups more vulnerable to conflict as compared to their face-to-face/on-site counterparts [99]. In fact, if anything has been learned from the Milgram experiment of 1961 [100], it is that not seeing a fellow human being makes people in charge more prone to make a move that hurts and humiliates than a move that blesses and beautifies. In view of this, it becomes exceedingly surprising to witness the ongoing reversal of this dehumanization paradigm and renaissance of the dominant chess playstyle under the influence of the supposed dehumanizers, i.e., the computer engines. Indeed, that machines would humanize what has been dehumanized by humans - who could have expected that?

In broader frames, this may inspire humanity to consider the ways by which computers could humanize fields and disciplines that have become dehumanized by none other but the very humans. It is unforeseeable how science, currently reigned by stiff egotism, commercial self-interest and uninspired technicality instead of free-spirited altruism and inspirational lyricism, could be reborn with the aid of none other but computers, but the most recent progress in chess tells us that this is very much possible. For the sake of following the corresponding computer-assisted progress in science, education and other social enterprises toward more humanistic directions, there would be a great merit of weaving the relationship between chess and science and tracing it scrupulously by the scholarly minds more often than this is done these days.

In this intellectual adventure, exciting questions pertaining to chess will likely always be there to amuse the muses and the explorers. For example, if computers do restore the era of romanticism in chess, would they ever be able to teach humans how to think and play with such brilliancy or the excavation and decipherment of these enlightened pathways of thought would require even more sophisticated algorithms and computer programs and may remain a sweet mystery conforming to the premises of Gödel's incompleteness theorems? Besides, as computers embark more ambitiously on the quest to solve chess, is it possible that they would get tangled in Russell's paradox underlying Gödel's theorems, where perfection is needed to reach perfection, which becomes unattainable as such? Because if the prerequisite for the derivation of a perfect game that would solve chess is perfect play to start with, then the solution to this problem may be as impossible to reach as perpetuum mobile. These fundamental limits notwithstanding, what if the single best moves turn out not to be practically derivable for the opening positions or the very early middlegame even with the best capabilities for calculation? Clearly, illuminating aspects of answers to these questions requires rigorous analytical efforts and the perception of chess as science, the road toward which is being paved by this discussion.

In the end, projecting this indisputable and unexpected influence of computer engines on the chess game to various sciences is important not only from the standpoint of instructing scientists about the inevitability and immenseness of the effect of computers and artificial intelligence on every walk of life. It is also essential for the purpose of demonstrating how an art can be re-romanticized by computers teaching humans styles that have started vanishing under the sole human influence. Arthur C. Clarke's third and final law states that ‘any sufficiently advanced technology is indistinguishable from magic’ [101], but if this magic turns out to be the magic of skills and views left behind and buried in the sand of time by this whole human race for success, what then? Would that be sufficient to acknowledge that matter is mind and mind matter, once and for all? Would that be the beginning of the closing of the circle connecting the natural and the artificial, acknowledging that they are one and the same? And that rivers of science flow into the ocean of art, while the sublimated droplets of art feed the rivers of scientific thought at their source? If so, then this may be the most beautiful and relevant point for natural sciences that contemporary chess can convey and is the note on which this discourse deliberately ends.

5. Conclusion

Chess can provide a number of ideas instructive for students in natural and social sciences in search of the formulae for creativity in their newly entered fields. A handful of analogies were drawn here from chess and converted to lessons in creativity for students in these sciences. It is up to the reader to conceive of further steps in promoting this connection between chess and science, in accordance with his or her intellectual affinities and power of influence in the academic domain. In the recent years, the crafters of both K-12 and higher education curricula have understood the importance of converting STEM (Science-Technology-Engineering-Mathematics) to STEAM (Science-Technology-Engineering-Art-Mathematics) because of the essentiality of developing an artistic mindset for a productive scientific career. However, the clock is ticking and now may be an ideal time to think about including chess alongside arts in natural science curricula. Chess, as per arguments presented here, may be an efficient far-learning proxy for furthering the development of artistic skills among scientists and analytical, pattern-recognition skills among artists. It can also serve as a missing link between science and art in these curricula thanks to its finding itself halfway between the two.

In view of this, it is advised that chess starts slowly infiltrating science curricula at both lower and higher education levels. How exactly this should be done and what exact adjustments to the traditional academic programs need to be made is, however, best left to the crafters of these programs to deliberate and decide on. The complexity of the chess coursework clearly needs to be adjusted to the level of chess literacy, which is currently highly variable across the nation and the globe and very modest to say the least. However, if chess education is introduced as mandatory early on in the K-12 system, then higher education courses on chess could cover more complex semantic grounds, which would extend beyond the fundamentals and be relevant through analogies such as those elaborated here for various creative scholarly engagements of the students. With a well-coordinated effort across all educational strata, such accomplishments are not impossible and a day may come when chess will inaugurate itself as an indispensable component of any academic programs aspiring to teach the balance between analytical and aesthetic reasoning and provide a powerful and versatile training in creative thought processes.

6. Author's glossary of selected chess terms

6.1. Algebraic notation

Conventional code in which chess moves are written, containing the move number, the piece moved (K for king, Q for king, R for rook, B for bishop, N for knight, and no symbol for pawn), the square to which the piece is moved, an action symbol (x for capture, + for check, # for checkmate, = for promotion), symbols for short and long castling, namely 0-0 and 0-0-0, respectively, the game score (1–0 for the win for White, 0–1 for the win for Black, and ½–½ for a draw), and other specifics.

6.2. Allumwandlung

German phrase meaning “complete promotion” and used to denote a type of chess composition where pawns get promoted to each of the four possible major and minor pieces, namely a queen, a rook, a bishop and a knight.

6.3. Blindfold chess

A game of chess played with at least one opponent not being able to see the board, having the moves read to and by him instead.

6.4. Blocked pawn

A pawn whose advancement up or down the board, toward promotion, is being hampered by a piece positioned on the square in front of it.

6.5. Blunder

A very poor move, usually annotated with a single or a double question mark. At the top level, it is almost invariably an oversight of a tactical maneuver giving the opponent a decisive advantage in the game.

6.6. Book

Normally refers to the book of chess openings containing thousands of opening lines and, occasionally, the explanation of their positional purpose.

6.7. Capture

A move by which a piece is moved to a square where an opponent's piece is located, removing the latter from the board.

6.8. Castling

A move by which the king and one of the rooks cross paths, usually made to relocate the king to a safer position by the edge of the board.

6.9. Check

An attack on the king, forcing the player to move the king, block the check or capture the piece giving the check.

6.10. Checkmate

The endpoint of every chess game – the king is in check, which it cannot escape. Players are allowed to announce the pending checkmate over the board by exclaiming “checkmate” and adding the exact maximal number of moves in which it will follow. For example, “checkmate in n” means that there is an indefensible checkmate in no more than n moves.

6.11. Closed game

A game opening with two queen's pawns, 1.d4 d5, but also a game with a lot of pawns on the board, involving crammed positions and little space for tactical maneuvers.

6.12. Coffeehouse player

A type of player setting cheap traps for the opponent in lieu of the principled play.

6.13. Combination

A tactical line usually, but not always, involving a sacrifice.

6.14. Correspondence chess

Chess where players send moves to each other through postal or electronic mail, taking approximately 1–2 months for each ten moves.

6.15. Development

A stage in the opening where pieces are placed closer to the center to make them more active and more coordinated than in the initial setup.

6.16. Discovered check

Putting the king in check by moving a piece other than the one giving the check.

6.17. Double pawn

A pawn surrounded by only one more pawn of the same color on a square directly above or below it.

6.18. Doubled rooks

Rooks of the same color on the same file.

6.19. Duplex

Two chess problems in one.

6.20. Dynamic play

A style of play leaning toward risky positions brimming with tactical possibilities and the potential for sudden gains or losses of advantage.

6.21. Elo rating

A number denoting the strength of a chess player based on his or her performance at competitions. Candidate masters have Elo ratings of at least 2000, masters of around 2300, grandmasters of at least 2500, top 40 players in the world of over 2700, while the Elo rating of top 100 chess engines, as per the CCRL 40/15 rating list, currently ranges from 3000 for the likes of Crafty 25.2, Gogobello 2.2 and Spike 1.4 to over 3500 for Fat Fritz 2, Dragon by Komodo and Stockfish 15.1.

6.22. Evaluation

Quantitative assessment of the position, today performed by engines, such that positive values indicate the advantage for white; negative values indicate the advantage for black; absolute values indicate the approximate extent of advantage in terms of individual piece values.

6.23. Exchange

A trade of pieces of equal value via mutual capture.

6.24. Exchange sacrifice

Trading a rook for a knight or a bishop.

6.25. Grandmaster

The highest title in chess. It has been earned by only around 50 players annually for the past 30 years and around 300 in total from 1950 to 1990.

6.26. Hanging a piece

Leaving a piece insufficiently defended and free for the opponent to capture.

6.27. Hanging pawns

Two pawns of the same color and on the same rank in the center, adjacent to one another and isolated from other pawns of the same color.

6.28. Helpmate

A type of chess composition where White and Black cooperate to give one side the checkmate.

6.29. Hypermodernism

A style of play that evolved in the early 1920s, allowing the opponent to occupy the center and then attacking it, usually from the flanks.

6.30. Endgame

One of three stages of the chess game, succeeding the opening and the middlegame and beginning when the number of pieces on the board has been significantly reduced so that positional play becomes superfluous and more precise calculations of variations must be performed instead.

6.31. Files

Eight vertical columns of the chessboard, annotated as a through h.

6.32. Flagging

Losing a game by running out of time on the clock. The term originates from the older generation chess clocks, which contained a flag lifted by the minute hand as the last few minutes rolled around and then dropped when the hand goes past the full circle.

6.33. Forced move

A move that either has no alternative according to the rules of the game or must be played lest a player give a considerable advantage to the opponent.

6.34. Fork

A move by which two or more pieces are being attacked simultaneously.

6.35. Fortress

The arrangement of the pieces by the materially weaker side, usually in the endgame, such that it blocks off the opponent's pieces and prevents them from entering it. If successfully set and appropriate for a given position, it leads to a draw.

6.36. Kingside

Half of the chessboard covering files e through h, named so because the starting squares for the two kings are e1 and e8.

6.37. Line

A sequence of moves that is played or only calculated, either during the game or later on, during analysis.

6.38. Lone pawn

A pawn isolated from other pawns of the same color. Known as isolani if on the d file.

6.39. Material

The value of a single piece or of many pieces, typically considered to be 9–10 for the queen, 5 for the rook, 3 for the bishop, 3 for the knight, and 1 for the pawn.

6.40. Material advantage

An advantage established solely based on the total value of one player's pieces on the board relative to the total value of the opponent's pieces. It does not always coincide with the positional advantage, and in specific positions the latter can prove the material advantage irrelevant.

6.41. Middlegame

The most creative phase of the game, succeeding the opening, but preceding the endgame, when pieces have been developed and positional concepts, broad strategic plans and tactical ideas can all be explored.

6.42. Open file

A file containing no pawns.

6.43. Open game

A game opening with two king's pawns, 1.e4 e5, but also a game with less pawns in the center and a plenty of open space, favoring tactical maneuvers.

6.44. Opening

The first phase of the chess game, where players develop pieces to increase their activity and coordination.

6.45. Opposition

Separation of two kings in king and pawn endgames by an odd number of squares, favoring the side whose turn is not to move.

6.46. Passed pawn

A pawn that advanced on the board to a higher rank, having no opposite color pawns in front of it.

6.47. Patzer

An amateurish chess player uncompetitive at any official competition level.

6.48. Pawn break

The push of a pawn in the center to enforce an exchange of pawns and opening of the position.

6.49. Pawn chain

Pawns of the same color positioned along a diagonal, so that each pawn except the one on the lowest rank is defended by another pawn.

6.50. Pawn majority

A greater number of pawns for one of the players on one of the flanks relative to that of the opponent.

6.51. Piece

Any object on the board. Pieces are divided to kings, pawns, major pieces, which include queens and rooks, and minor pieces, which include bishops and knights.

6.52. Piece activity

Qualitative estimate of the combined influence and mobility of a piece in a given position.

6.53. Pin

A move disabling the move of one of the pieces because of either a discovered check, as in absolute pin, or the hanging of another piece, as in relative pin.

6.54. Position

Arrangement of pieces on the board between two moves.

6.55. Positional advantage

Greater activity and better coordination of pieces around key strategic points in a given position.

6.56. Positional play

A style of play aiming to produce moves that reposition pieces to improve their activity, without any concrete tactical ideas in mind.

6.57. Promotion

Transformation of a pawn into a major or a minor piece upon reaching the eighth rank for White and the first rank for Black.

6.58. Queenside

Half of the chessboard covering files a through d, named so because the starting squares for the two queens are d1 and d8.

6.59. Ranks

Eight horizontal columns of the chessboard, annotated as 1 through 8.

6.60. Resignation

Admittance of a loss by one of the players before the game ends in a checkmate, usually accompanied with a handshake.

6.61. Sacrifice

Deliberately giving away the material in return for accelerated development, better piece coordination or a gain in the attacking momentum.

6.62. Semi-open file

A file containing pawns of one color only.

6.63. Skewer

A type of fork where one of the pieces is attacked indirectly, lying behind a piece that is being attacked and that is forced to move.

6.64. Solid play

A style of play aiming to find the safest and most conventional move in a position.

6.65. Solved position

A position known to result in a specific outcome, such as a draw or a win/loss, with the best play from both sides. All positions containing up to seven pieces are currently solved.

6.66. Stalemate

Draw elicited when the side to move has its king not in check, but no legal move to be made.

6.67. Strategy

A broad plan for play derived from general features of the position.

6.68. Super-grandmaster

An informal title reserved for grandmasters with Elo ratings of approximately 2700 and above.

6.69. Tablebase position

A type of endgame position found in tablebase reference books, for which the best possible moves by both sides are known to end in either a draw or a win/loss.

6.70. Tactics

Short and elegant sequences of moves involving forks, pins, skewers, discovered attacks and other tactical elements and requiring precise short-term calculation.

6.71. Take

Term synonymous with “capture”.

6.72. Takeback

Consensual undoing of a move, usually a blunder, and playing another move instead.

6.73. Tempo

Unit of time in a chess game, expressed in terms of the number of moves. Gaining a tempo implies being a move ahead in development or in implementation of a particular strategic plan or a tactical idea.

6.74. Tension

A type of position where one or more exchanges are pending, with the degree of tension being proportional to the width of ramifications extending along the variations proceeding from the point of exchange and from the point of delayed exchange.

6.75. Variation

A sequence of moves, nearly synonymous with “line” but usually applying to more theoretical sequences, such as those in the openings.

6.76. Zugzwang

A situation where every move one can play drastically weakens one's position and gives a decisive advantage to the opponent.

Author contribution statement

The author is the only contributor to the conceptualization, development and writing of this article.

7. Data availability statement

Data will be made available on request.

8. Declaration of interest's statement

The author declares that he has no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.