Andrei Yafaev is in New York and he thought I might like to watch a Russian television documentary about Grisha Perelman, which you too can watch on YouTube. It’s in Russian but English subtitles have been added. It has so far been viewed 268,517 times, so I’m probably not telling you anything most of you don’t already know; but it has a few provocative moments.
The documentary insists repeatedly that Perelman was “impeccably honest,” [безукоризненно честен] even as a child. And this is depicted, for the Russian audience, as a characteristic of mathematicians. Perelman’s “teachers insisted that mathematics is not only the Queen of the Sciences, but also the most moral science.” Alexander Danilovich Alexandrov, Perelman’s thesis advisor, is quoted (at 32’02”) as saying “I’m not interested in geometry, I’m interested in morality [нравственность].” Anatolii Vershik follows with a claim (at 32’12”) that mathematicians “have a very clear sense of right and wrong.” Here “right and wrong” is a translation of истинность; this should ring a bell for those of you who have seen Ed Frenkel’s Rites of Love and Math, where the love-making and seppuku are both performed under the sign of истина, which is translated “truth.” So we see Mikhail Gromov claiming (at 34’51”) that “mathematicians don’t care about money and prizes” — though he admits that money is convenient: if you break your glasses you can replace them.
Perelman — a “national hero,” according to Fyodor Bogomolov — is unusual only for taking his impeccable honesty, his attachment to истинность, to extreme lengths; his refusal of the Fields Medal and of the Clay Millenium Prize are the best-known examples of this. But the documentary takes a strange detour near the end: having spent 40 minutes depicting Perelman as a supreme exemplar of mathematical morality, suddenly the narrator remarks (at 39’17”) on how “strange” it is that he “rejects an ethical rule [главное этическое правило] of mathematics” [even a “main ethical rule” in the Russian original] in insisting that Richard Hamilton was equally deserving of the Prize. And here Jim Carlson, speaking for the Clay Mathematical Institute, informs the viewer that “according to an unspoken rule the prize goes to the one who crosses the finish line.” (The Russian version has Carlson attributing this to “mathematical sociology” — questionable translations in both directions.)
This is weird in more ways than I can count, but I’ll just mention a few of them whose weirdness is independent of the Russian context. Most obviously, the Clay Mathematical Institute is giving out its own prizes, and surely it can make up its own rules. Next, the idea that there are “unspoken rules” governing the awarding of prizes in mathematics is completely new to me. It’s hard, of course, to apply the methods of sociology to the study of “unspoken rules,” since by definition nobody is talking about them — but even if (as is likely) Carlson used “unspoken” as a poetic synonym for “hardly ever spoken,” or “spoken about in whispers,” one wonders: how high up do you have to be in the hierarchy (oppressive or not) to have heard the faint whispering about these unspoken rules?
And then there is the principle itself, which seems to me to leave little scope for formal appreciation of those who point out where there are finish lines, so that others can exemplify an ethical rule by collecting prizes for crossing them. I have a few people in mind, mathematicians whose names are most familiar in adjectival form. Does anyone know where one might fruitfully whisper about this principle, and to whom?