The Pursuit of Mathematics

Amy Sullivan, guestblogging at Washington Monthly, notes an article about mathematics teaching methods which seem to improve girls' participation and performance. So far, so good; but then she tries to tie it to the issue of academic representation, saying "More evidence to combat the idea of innate aptitude." In doing so, she betrays an unfortunate lack of understanding about what mathematics is like for its real practitioners.

These are masses of students, sitting together, working on problems within the reach of all, and holding up their answers when they are done. They bear as much resemblance to the research of a Ribet or an Atiyah as a rubber-band vehicle does to a space shuttle. And they are almost as dissimilar when contrasted with the activities of the top young mathematicians and future scholars, even as teenagers.

I have had the good fortune to meet some of these people, and the misfortune to on occasion compete with them. Even as teenagers, they are forging ahead into deep and counterintuitive realms, moving away from the workaday world of concrete numbers to other systems and formal languages.

Mathematics is perhaps the most solitary of occupations. Even the most prolific and sociable practicing mathematician, for every step in every published proof, will have mentally explored hundreds of alternate avenues. The talent and interest for this may be present, or not, in a fifteen-year-old; but holding up answers to arithmetic problems will not create, enhance or detect it.