An Irishman's Diary

Those depressing Leaving Cert results took some of the gloss off what has been a very exciting week for mathematics, with the news - I still hardly dare believe it myself - that a Russian academic may finally have solved the "Poincaré conjecture".

We'll come back to that in a moment. But first, in an apparently casual aside that will later turn out to have been a cheap literary device, I would like to echo the proposal by the CEO of the Irish Chambers of Commerce, made in this paper yesterday, to "actively incentivise" potential third-level maths students through funding. This would help get the message across, as he wrote, that "the Leaving Certificate does not represent a finishing line, but rather the starting gun for maximising one's skills and earning potential". Anyway, back to Poincaré's Conjecture, which has defied mathematicians, including the great Poincaré himself, since it was first posed in 1904. As I'm sure I don't need to tell Irish Times readers, the conjecture conjects, in short, that "a certain condition suffices to make a manifold homeomorphic to a sphere". But for those of you sniggering at the back of the class, I probably need to simplify this.

So, in the words of the New York Times, which reported its possible solution, the conjecture asserts "that if any loop in a certain kind of three-dimensional space can be shrunk to a point without ripping or tearing either the loop or the space, the space is equivalent to a sphere". Or in other words, to put it in layman's terms altogether: "Anything without holes has to be a sphere".

Simple as it sounds, the conjecture had for a century eluded all attempts at proof and its solution was long regarded as a holy grail in the study of three-dimensional space. So there was a mixture of excitement and scepticism when, in 2003, the Russian prodigy Grigori Perelman announced he had solved it. He posted a few heavily summarised papers on the internet, expanded on these during a short lecture tour of the US, and then promptly returned to St Petersburg, leaving experts to flesh out his ideas and decide if he was right.

Three years later, the verdict is tentatively in. As the NYT reports, the evidence is now circulating among academics in the form of three book-length papers comprising "about 1,000 pages of dense mathematics and prose". And although scholars are still not certain, there is "a growing feeling, a cautious optimism that they have finally achieved a landmark, not just of mathematics but of human thought".

Now 40, Perelman was already well known in academia. A brilliant high school student, he won a gold medal with a perfect score at the International Mathematical Olympiad in 1982, and after completing his doctorate, joined the prestigious Steklov Institute in St Petersburg. Before his latest breakthrough, he had also solved the so-called "Soul conjecture", with what scholars called "a surprisingly short argument".

The International Mathematics Union meets in Madrid next week and is expected to award him the Fields Medal, its equivalent of the Nobel Prize. The problem is, nobody knows if he'll turn up. Described as friendly but shy, and "not interested in material wealth", he has gone to ground since returning to Russia. His non-mathematical interests include "hiking in the woods near St Petersburg looking for mushrooms" - and maybe that's what he's at now. At any rate, he is not returning e-mails.

It goes without saying that a man who is as indifferent to money as Perelman seems to be could make a fortune in the US. Apart from anything else, a mathematics institute in Boston has a standing offer of $1 million for the first published proof of the conjecture. But his appeal would extend well beyond the academic community. According to one mathematician who met him in the US, "he looked like Rasputin, with long hair and fingernails". They have a hyphenated word for that in the States.

Box-office.

I suspect that if he returns to America, he could be in a grave danger of having a Hollywood film made about him. And you'd think that a man who likes spheres as much as he does might be tempted by the prospect of a Golden Globe. But he may be indifferent even to that.

Despite being massively incentivised, Mr Perelman seems to have fallen into the trap of practising mathematics for the love of it. In the chamber of commerce CEO's terms, he has jumped the starting gun, overshot the finish line, and fled the stadium, still running. He has run so far (presumably to the woods near St Petersburg) that his earnings potential cannot possibly catch him. He is, in short, a cautionary tale. As we attempt to persuade more Irish students to study third-level maths, it's as well to be aware of the risks.