seven outstanding problems at the frontier of mathematics, to be known
as the "Millenium Prize Problems". For solving any of these in a
peer-reviewed journal, a mathematician would be awarded one million
dollars. Surprisingly, a reclusive Russian mathematician named
Grigori Perelman solved one of these, proving the Poincare Conjecture,
only three years later, in a series of articles published on the web.
In 2006, the reviews of this proof were complete, and the math
community came to agreement that Perelman had indeed solved the
problem. As a result, he was nominated for the Fields Medal, the math
world's equivalent of the Nobel Prize. But he refused this award.
The reasons for this form a sort of bizarre human drama in the
already odd world of mathematical research. Grigori Perelman had been
a math prodigy from a young age, and won a gold medal at the
Intenational Mathematical Olympiad as a teenager. In 1982, at the age
of 16, he entered college, and after earning his Ph.D., spent several
years at prestigious institutions in the United States in the early
1990's. He refused to abide by usual social conventions or
requirements; when asked by Stanford for a CV, he said, "If they know
my work, they don't need my C.V. If they need my C.V., they don't
know my work." Despite being recruited by institutions like Stanford
and Princeton, he returned to his old job in Russia in 1995, earning
less than 100 dollars per month. From there, he continued to work in
isolation, but used the internet to stay in touch with the math
community. In 2002, he began posting his proof of the Poincare
Conjecture, surprising some of his colleagues.
At the time, there had been a group of Chinese mathematicians
working on the same problem, led by former Fields medal winner
Shing-Tung Yau. Complicating matters, Yau apparently considered his
work more than just a mathematical accomplishment-- this also was a
step forward for the prestige of Chinese mathematicians. Yau's group
claimed that Perelman had made a contribution, but his proof was
incomplete-- and two of Yau's students, Xi-Ping Zhu and Huai-Dong
Cao, claimed to have completed the proof. They published a detailed
paper describing the full proof in the Asian Journal of Mathematics.
Was this paper necessary, or was Perelman's proof already complete?
It's hard to tell, since various mathematicians make competing claims,
and there are so few people around who are capable of understanding
this work overall. (By the way, I am not in that select group, in
case you were wondering!) Judging by the Fields Medal committee,
consensus seems to be that Perelman was indeed successful.
In any case, this situation apparently left a bitter taste in
Perelman's mouth. As he describes it, his choice was to raise a fuss
about the lack of integrity in the field, or to be "treated as a pet."
When asked whether he shouldn't stay in the mathematics world
and try to reform these issues, he angrily protested that he is not a
politican. He found another option: after refusing the Fields Medal,
he retired entirely from the world of mathematics. He is now jobless,
and lives with his mother in St. Petersburg.
My primary source for this podcast was an excellent article in the
New Yorker, which is linked in the show notes. I also included links
to the wikipedia articles on the Poincare Conjecture, Grigori
Perelman, and the Millenium Prize Problems.
And this has been your Math Mutation for today.