Why do many mathematicians go crazy?

Math: why is this genius giving up a million?

There are many legends surrounding the Russian mathematician Grigory Perelman. Around ten years ago, the genius proved the so-called Poincaré Hypothesis - one of the greatest, hitherto unsolved problems in mathematics.

But the bearded man from St. Petersburg rejected both the Fields Medal, which is considered the Nobel Prize in Mathematics, and the one million dollars awarded as part of the so-called Millennium Prize. This had been abandoned by the Clay Mathematics Institute for the proof of the conjecture formulated by Henri Poincaré a good 100 years ago.

The American-Russian author Masha Gessen wrote a biography about Grigory Perelmann that clears up some myths. In any case, after reading it, it is clear to the reader that Perelman would loathe this book.

Dramaturgy of a criminal case

He would undoubtedly find it presumptuous to call his proof of Poincaré's Conjecture, which was posted on the Internet in 2002/03, as “proof of the century”. He would consider it dishonest to assume that a similarly significant - or possibly even greater - mathematical breakthrough could not be achieved in the course of this century.

But Perelman is unlikely to read his biography. Masha Gessen wrote it without having met the Russian mathematician. The eccentric man from Saint Petersburg has not spoken to anyone for years - with the exception of his mother, with whom he lives. By the way, she is also a mathematician.

The dramaturgy of this biography is similar to the investigation of a criminal case. Masha Gessen, who also wrote books on the Russian intellectual scene after the collapse of communism and published a highly acclaimed portrait of Vladimir Putin last year, spoke to the people Perelman met in Russia, America, France and Israel.

Phantom image of a lonely genius

From this she drew a phantom picture of Grigory Perelman, which probably would not have been any different if she had been able to talk to Perelman personally.

A man who solves one of the greatest problems in mathematics and then harshly rejects the one million dollar prize money that is offered, arouses the curiosity of people who are not interested in mathematics.

The story fits into the cliché: An unworldly genius who lives in an imaginary mathematical cosmos and not only neglects personal hygiene in this world, solves an unimaginably difficult problem.

Perelman was only interested in math

In fact, Perelman's behavior is similar to Asperger's disease, that special form of autism that enables those affected to think exceptionally well, but dramatically reduces their social skills. It is well known that mathematicians have a particularly high number of people with Asperger's Syndrome.

However, Gessen does not claim that Perelman is one of them. But it can be said without a doubt that all his life Perelman was only interested in mathematics, not in women, not in good food, not in what goes on in other people's minds.

The story of Perelman, as told by Gessen, offers more than the usual clichés of unworldliness and ingenious loneliness. Gessen takes a historical approach: she traces the conditions under which science was carried out in the Soviet Union and explains why the country was not a good place for someone who cared a lot for predictability and logic. Mathematics, however, opened up the possibility of living in a parallel world.

Parallel world in the Soviet Union

Perelman immersed himself in it at the age of ten - and never left it again. He owes the fact that he was able to complete a course of studies and do a doctorate in mathematics to a fascinating series of happy circumstances. Because he came from a Jewish family, there were a number of anti-Semitic restrictions.

As a teenager, Perelman probably did not notice these obstacles, which his sponsors tried with great dedication to remove. With admission to Leningrad University, it would probably not have worked if Perelman had not won a gold medal for the Soviet Union at the Mathematics Olympiad in Budapest in 1982 with 42 out of 42 possible points.

One can read Masha Gessen's book at a profit without having to know what the conjecture formulated in 1904 by the French mathematician and physicist Henri Poincaré actually means.

Money is not a substitute for recognition

Nonetheless, in a chapter Gessen outlines what it is all about in a way that is understandable for mathematical laypeople: the topological properties of three-dimensional manifolds in four-dimensional space.