On Fecundity

A letter in the 3 June 2010 issue of Nature addresses "The role of mentorship in protégé performance". That sounds sort of interesting. I'd like to know ".. the extent to which protégés mimic their mentors' career choices and acquire their mentorship skills".

Those are two very different things, though. I can see how you could determine whether protégés follow the same career path as their advisers, but you need some assumptions to go from those data to interpretations about acquisition of mentorship skills (or lack thereof).

To address these issues, the authors (Malmgren et al.) used a large database that has tracked mathematicians and their academic "genealogy" for centuries. Despite the massive database going back to 1637, the authors analyzed only the years 1900-1960 because these data were deemed "most reliable" and this range allows the tracking of a few generations.

More recent data would be interesting to consider as well, if possible, particularly to see if the culture of academic math departments has changed. Or perhaps nothing changes the culture of math departments; the authors concluded that, despite the occurrence of some world wars etc. in the 20th century, there were "no systematic historical changes" evident in the database.

The research was designed to evaluate whether protégés "acquire the mentorship skills of their mentors". This is done by studying mentorship fecundity. I am not sure that fecundity necessarily relates to "mentorship skills" or "mentorship success", but that's how it was defined.

A brief aside: This may be a seminal paper, but I wish there were a different term that could be used than fecundity to represent the number of protégés a mentor trains. I also wish there were a better term than "protégé", although I know that technically the word is used appropriately in this paper. Advisee and mentee aren't great words either, but somehow they seem more professional to me. Or, if protégé must be used, can I be called a patron rather than a mentor?

Anyway, what we all want to know is:

Can you predict the fecundity of a mathematician?

Well, it's complicated, but you can write an equation! Also, you can make an analogy with parents (= mentors) and children (= protégés), such that a protégé's graduation date is their "birth date". I'm not sure why this new terminology was introduced, as the original concepts of mentor, protégé, and graduation date are not that complicated, but so it goes.

The results, which aren't actually explained in the paper, are "three significant correlations in mentorship fecundity", which I will condense into two:

1. Protégés of mentors with low fecundity (< 3 protégés) had more protégés than "expected".

2. The protégés of early-career mentors are themselves more fecund than "expected" and are more fecund than protégés who are advised by these same mentors later in their careers; i.e., fecundity might be influenced by the adviser's career stage.

The first interpretation did not surprise me, although one has to be clear about what the "expected" fecundity of protégés is before deciding if the result is greater or less than expected. The second one is more surprising, but whether it has any meaning depends, of course, on the methods and assumptions of the study.

It's a rather strange study and we can pick away at it, but is there anything to be learned from it about the influence of mentors on the later careers of their mentees? I doubt it, although I think the motivating question of the study is an interesting one, and perhaps impossible to study in a meaningful and quantitative way. To be relevant to modern mentorship, such a study would also have to track career paths that veer from math to engineering, or to any of various other interconnected disciplines.

And, because being a successful mentor doesn't have to mean that we clone ourselves and produce academic children who mimic our careers, perhaps there would need to be a different way of measuring the quality and success of mentorship than simply counting up the numbers of academic children and grandchildren and great-grandchildren.