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Russians, Americans and Chi-Coms all squared off against each other. Organized deception, intrigue, insults, reclusive personalities ... another day in international politics? Not this time. It's mathematicians. You think physicists are strange? Try to figure out mathematicians some time.*
It starts with a bit of mathematical fluff called the Poincaré conjecture, encompasses certifiable silliness in the name of string theory and ends with a million dollars. You just don't get more intrigue than that.
Forget for a moment the big picture issue here, namely that string theory has become popular among people trying to get gullible civilians excited about science and a hundred years from now it will only be remembered by nostalgic history students who will regard it with the same quaint fondness that medical students have for skull drilling and leeches. Mathematicians think this issue is important and mathematicians, like shrill harpies bleating about global warming or evangelists wearing signs telling you the end of the world is next week, only feel important if they are impacting the game. And getting grants.
To be fair, while there are some bad things about mathematicians there are good things about math. What do we like about math? First, math believes in induction. A math whiz will agree with my statement that every even number is divisible by two even though neither of us have actually tested every even number - so induction is good enough for Faraday and good enough for ( insert name of a famous mathematician here, if there is one.) It's nice when the sciences work together like that. Second, math takes a hypothesis and uses logic to arrive at a conclusion. If the logic is good the hypothesis gets promoted to theorem. If a theorem is to become a proof, it goes under anonymous review and if it's published, it's passed the test. A proof of a theorem is definitive so, unlike law or science, there isn't a lot of qualification and revision. When it is finished, it is finished.**
It all sounds very elegant and it is, because life is easy for mathematicians. Math results from people having to do other things and not having a current way to do them. Take Newton, for example. He didn't want to invent calculus, he wanted to know why apples fell on his head and the mathematics of his day couldn't help so Newton created the math to do it. Math guys never have to worry about falling apples.
This lack of consequence is why mathematicians have pretty much claimed every other year for the past hundred plus years that they have solved the Poincaré conjecture. In the real world, if scientists are wrong, rockets blow up. In math theory, if you are wrong ... you have bad topology. Oooooooooh, bad topology. How does this all relate to string theory? Well, without topology and manifolds you can't have string theory, so you can see how the science community needed a win in order to maintain its bull@!$%# quota.
So first, what is the Poincaré conjecture? Physicists like to believe we can condense most anything to a form a 12-year old can understand but math doesn't always work that way. So the closest I can get is to tell you that if you take a connected three-dimensional space and it's enough like a sphere that each loop in the space can be tightened to a point, then it really is just like a three-dimensional sphere. Sounds like more bull@!$%#, right? Well, yeah, but the math guys have a point on this one. Without the kind of 'rubber-sheet' geometry topology brings, there are a lot of simulations physicists couldn't do.
Anyway, back to the drama. When a reclusive Russian math whiz, Grigory Perelman ( the Russian), put up a paper on the internet that seemed to solve Poincaré ( the dead French guy), all hell broke loose. For one thing, he violated the normal process and just went ahead and published it without that whole anonymous review process that makes math elegant. Plus, the Poincaré had become such a famous problem with so much money being thrown at it that it would be better for some mathematicians if it were never completed. And if it would be completed, it would be completed by the right person. The right guy, to some in China and certainly to himself, was Shing-Tung Yau (the Chinese guy.) Yau had been working on this for years, mostly with his good friend Richard Hamilton ( the American), with no results to-date. Having been handed a lot of money to analyze the newly-published papers of the Russian, he got two fellow Chinese to begin work. In April of this year they ( the Chinese guys ) submitted their finished paper but instead of affirming the work of Perelman ( the Russian) they stated that they had to re-do it all - which meant it was now their work ( the Chinese) not his ( the Russian.) They were gracious enough to credit Perelman ( the Russian - try to keep up ) with having "brought in fresh new ideas to figure out important steps to overcome the main obstacles that remained in the program of Hamilton ( the American)" but that was all. Shady? Yeah, a little.
The Russian was disgruntled enough to turn down a major award for his 'fresh new ideas' - I don't know the guy but I am betting he is pissed that the award is the kind of concession prize someone dangled to make him feel better when he loses credit for the proof, and immortality - but he's not so disgruntled he will turn down the one from the Clay Institute that pays a million dollars for solving the unsolvable problem. Especially if it turns out the Chinese team will get it instead.
Is Yau a crook? Like proofs, claims about who solved Poincaré should be treated with skepticism while mathematicians have a chance to review the circumstances thoroughly.
Until then you can believe Yau but, as he once said, without proof, "it's not math—it's religion."
Since I know this is all complicated and a little silly, I created the handy graphic above ( see it in glorious full size here )so you can follow along. You're welcome.
Paranoid conspiratorial tone and condescension lifted, in part, from this article in The New Yorker.
* Told you I would give biologists a break and pick on mathies just this once.
