Figure 1 |. Relationship between mentorship fecundity and other performance metrics.

a, Cumulative distribution of the mentorship fecundity for NAS members (red) and non-NAS members (black). NAS members have an average fecundity of ${\langle k\rangle }_{\text{NAS}}=14$, which is far greater than the average fecundity of non-NAS members, ${\langle k\rangle }_{\text{non-NAS}}=3.1$, indicating that fecundity is closely related to academic recognition. Not all mathematicians in the non-NAS group were eligible for NAS membership, owing to citizenship and other circumstances. This fact makes the result in the figure all the more striking. b, Average number of publications as a function of the mentorship fecundity, for NAS members (red) and non-NAS members (black). NAS members have nearly twice as many publications on average as non-NAS members for all fecundity levels. Error bars, 1 s.e.