“Pure” Mathematics

In case you havent heard, these are exciting times in the otherwise media unfriendly domain of mathematical research. A month ago, Grigory Perelman refused to attend the International Congress of Mathematicians (held in Madrid this time) in order to collect his Fields medal, the mathematical equivalent of the Nobel Prize. While Perelman was holed up in his mothers apartment in St.Petersburg, the worlds of gossip and geometry were intersecting at faster than light speeds. One of the pioneers in the field of geometric analysis, S.T.Yau, sued the New Yorker as well as Sylvia Nasar and David Gruber for writing this article about Perelman’s proof of the Poincare Conjecture.

I am not going to dwell any longer on the controversies surrounding Perelman and his proof, since the webuniverse has plenty of material to whet your appetites (including the New Yorker article cited above), but here is a juicy titbit of my own: while I was a graduate student at MIT in the late 90’s and early 2000’s, I lived in a one bedroom apartment owned by you know who: Mr Yau himself. We finally left the apartment after living there for five years after a traumatic week of no water, preceded by a shower that refused to work and a million cockroach infestations. Boy was it a slum! Mr Yau clearly has many avatars and being a Cambridge slumlord is one of them.

Anyway, this post is really about the following quote in the New Yorker article, from Mischa Gromov, one of my favourite mathematicians, where Mischa says

“To do great work, you have to have a pure mind. You can think only about the mathematics. Everything else is human weakness. Accepting prizes is showing weakness.” Others might view Perelman’s refusal to accept a Fields as arrogant, Gromov said, but his principles are admirable. “The ideal scientist does science and cares about nothing else,” he said. “He wants to live this ideal. Now, I don’t think he really lives on this ideal plane. But he wants to.”

Here’s what I want to say: Mathematicians and scientists use the word pure to mean moral qualities rather different from what other people mean. When for example, I say that St Francis of Assisi was a pure soul, I might highlight virtues like: he led an exemplary life of devotion, he cared for the weak and the poor, his love for animals, and his speaking truth to power. In other words, he led a supremely virtuous life in this world, fully aware of the weaknesses of humanity and nevertheless tolerant of those weaknesses. Mathematicians on the other hand, seem to think that purity involves shutting yourself off from society, caring only about abstract problems and disdaining any appreciation by others (after all, who are they to judge your pure heaven?).

I was a mathematician myself, so I am quite aware of the seductiveness of this kind of purity, which is often manifested in its “purest” form in South Indian Brahmin mathematicians. Just go to the TIFR maths department and check it for yourself. However, as I grow older, I am more and more worried by these abstract, intellectualized notions of purity. When Gandhi in Hind Swaraj talks about the evils of mechanized societies he didnt have mathematics in mind, but one look at a computer should convince you that according to the mathematicians norms, a computer is an ideal mathematician: it doesnt care for rewards, it is stuck in its own syntactically circumscribed universe and it will keep crunching away at a problem until and unless you pull the plug. In other words, not only are computers better at calculating your taxes, they are also morally superior to us.

Isn’t there something disturbing about this inescapable moral judgement? And what does it mean that within the natural sciences, the most valued, the most celebrated disciplines like string theory and higher mathematics presuppose a morality that priveleges mechanisms over humans and other animals? Perhaps we should rename physics autistic metaphysics.