A book about mathematician Grigory Perelman is being published in Russia. Forbes publishes several excerpts from it

In 2002-2003, Russian mathematician Grigory Perelman published on the Internet a proof of the Poincaré conjecture that had not been given to any of his colleagues for almost a hundred years. Perelman was awaited by fame, numerous awards and a $1 million prize awarded for solving this problem by the charitable Clay Institute. Perelman, however, refused both honors and money, and a few years later he left mathematics altogether. Deputy editor-in-chief of the Snob project Masha Gessen wrote a book dedicated to the mathematician. The book was originally published in English in the USA, now a translation of the book “Impeccable Rigor. Grigory Perelman: genius and the task of the millennium” is published in Russian by CORPUS publishing house (translated by Ilya Krieger). Forbes publishes excerpts from the book, including the chapter “How Not to Become a Millionaire.”

From the prologue

In 2000, the world's leading mathematicians gathered in Paris to assess the state of their field. This was an event of exceptional importance. Scientists talked about the beauty of mathematics, about each other's merits and - most importantly - together they dreamed about the future. The Millennium Meeting was organized by the Clay Institute, a nonprofit organization founded by Boston businessman Landon Clay and his wife Lavinia to promote and encourage mathematics. Within two years of its existence, the Institute acquired an impressive office near Harvard Square in Cambridge (Massachusetts, USA) and presented several awards for outstanding research.

Now the Clay Institute set out to propose an ambitious plan for the development of mathematics. According to Andrew Wiles, the British scientist who proved Fermat's Last Theorem in 1995, the scientists gathered in Paris were supposed to come up with a list of the most difficult mathematical problems of the 20th century that we would most like to see solved: “We do not know how or when they will be solved.” these tasks. This could take five years, or maybe a hundred. But solving them will open up completely new possibilities for mathematical discoveries, new horizons.”

In order to make the mathematical fairy tale come true, the Clay Institute identified seven “millennium problems” (seven is the magic number in many cultures around the world) and offered a fantastic reward - a million dollars - for solving each of them. The “Kings of Mathematics” gave a series of lectures in which they recalled the essence of these problems.

Michael Francis Atiyah, one of the greatest mathematicians of the 20th century, began with a hypothesis formulated by Henri Poincaré back in 1904 and which became a classic of topology: “Many famous mathematicians struggled with this problem, but did not solve it. Sometimes they found mistakes themselves. Sometimes others did it.” The audience - among them at least a few people who had failed with the Poincaré conjecture - laughed...

...None of the mathematicians gathered in Paris imagined that a solution would be found so quickly. Many mathematicians who work on famous problems prefer to keep it secret (as did Wiles, incidentally, when he was working on Fermat's theorem), but they usually keep an eye on what others are doing. And although new versions of the proof of the Poincaré conjecture were published almost every year, the last significant success was achieved back in 1982. Then the American Richard Hamilton proposed a solution plan (mathematicians call such plans programs). He found, however, that this plan was too difficult to follow, and no one could offer an acceptable alternative. Poincaré's conjecture could remain forever unproven...

...Since it was believed that none of the “Millennium Problems” would be solved in the foreseeable future, the Clay Institute established a clear procedure for awarding the prize. The solution to the “Millennium Problem” must be formalized in the form of a publication in a peer-reviewed scientific journal (this is what mathematicians usually do). Over the next two years, the international mathematical community must check the proposed solution and come to an agreement on its correctness and author's priority. Finally, following the recommendation of the award committee, the Clay Institute will award the winner a million. Wiles suggested that a solution to the first Millennium Challenge might not be available for at least five years, if it ever appears at all. In general, the procedure did not look very complicated.

However, just two years later, in November 2002, a little-known Russian mathematician published a proof of the Poincaré conjecture on the Internet. He was not the first to claim a solution to this problem. He was not even the first Russian to publish a proof of this hypothesis on the Internet that year. But only his solution turned out to be correct.

After this, events began to develop completely differently from the plan of the Clay Institute and, in general, any plan that an ordinary mathematician might consider acceptable. Grigory Yakovlevich Perelman, the Russian I mentioned above, did not publish his results in a reputable scientific journal. He refused to check or even read explanations of his solution published by other mathematicians. He rejected offers from the world's best universities for cooperation. He did not accept the Fields Medal, the highest honor in mathematics, which he was awarded in 2006. Finally, he withdrew from communication not only with fellow mathematicians, but also with almost all other people...

Chapter 11. How not to become a millionaire

Jim Carlson became director of the Clay Institute in the summer of 2004, when the scandal surrounding Perelman's evidence and the million-dollar prize began. I suspect that Carlson became what he became and did what he did, with difficulty overcoming his incredible shyness and modesty. He spoke quietly and shyly and was unusually polite; this is the last person you would imagine at the center of a scandal.

Fortunately, when Carlson took over as director of the Clay Institute, he did not anticipate the media uproar the story of Perelman's evidence would cause. “I heard the news,” Carlson told me, “and I remember thinking, ‘Oh my God, this is great—we might have a proof of the Poincaré conjecture!” And of course, I thought about the prize. Isn't this wonderful? Most likely, this will be the only award that I will be given. Nobody knows in advance. I would compare it to an earthquake - you only know when it happens. You can, of course, see that stress is building in the rocks, but no one can successfully predict earthquakes. Likewise, no one knows when or who will come up with the breakthrough idea that will lead to a solution.”

This happened a few months after Carlson took over the Clay Institute. By this time, he already knew that Perelman had published his preprints on the arXiv website. This was not unusual: many mathematicians do this before publishing their papers in journals, to spark discussion before the peer review process ends. The catch is that Perelman did not publish his materials in the form of an article. He didn't intend to do this at all. What previously seemed a completely harmless and self-evident condition for presenting the Millennium Prize has become a stumbling block.

Jim Carlson came out of the situation with dignity. He organized seminars on the work of Perelman and the explications of Kleiner, Lott, Morgan and Tian. In a conversation with me, Carlson compared Perelman’s work to “a flash that illuminated the path through a dark forest”: “Of course, we need to do even more work, cut down a lot of trees, get through boulders and various rubbish, get around obstacles, but thanks to this we saw a new difficult the road. If we hadn't found her, no matter how much work we'd done before, it would all have been for nothing. But now, thanks to Perelman, this is not the case.”

The scientists who reconstructed Grigory Perelman's reasoning and explained his proof did not expect any reward. This also caused Jim Carlson to admire both the mathematicians and the system, which was able to adapt to the unusual conditions set by Perelman and provide a high-quality test of the solution to the problem...

…The time leading up to the International Congress of Mathematics in Madrid, marked by the publication of the paper by Cao and Zhu, as well as unusually intense media attention [to mathematics and mathematicians], turned out to be quite nervous. Nevertheless, Congress put everything in its place, and evidence of plagiarism that emerged in the fall of 2006 deprived the question of authorship of any meaning. The publication of Morgan and Tian's book on the proof was approaching. The Clay Institute could now begin the two-year review period required by the Millennium Prize rules. Then a committee should be appointed that could prepare recommendations by the fall of 2009. Barring the possibility of an error in evidence or other unforeseen and unlikely problem, the committee could make a recommendation: award the Millennium Prize to Grigory Perelman. There was only one question left: what then?

If Perelman's rule about when to take prizes and bonuses and when not to take them remained constant, then he should have taken a million. The refusal of the European Prize was due to the fact that it was going to be awarded to him for work that he himself did not consider complete. The same could not be said about the proof of the Poincaré conjecture: it was completely ready, and Perelman knew very well that it was his work.

His objection to the Fields Medal, although not clearly articulated, appears to have been twofold. First, he no longer considered himself a mathematician, so he could not accept an award intended to reward mid-career researchers. Secondly, he had absolutely no need for the International Mathematical Congress with its fuss, speeches, ceremonies and the Spanish king to boot.

However, the Clay Institute Prize is awarded for a specific achievement and does not require the recipient to continue to study mathematics. In addition, the award does not imply any ceremony at all: the mathematician is honored by fellow mathematicians, and not by the kings of the outside world. The Millennium Prize differed favorably from both the European and Fields Prizes in that it celebrated a specific single achievement of Perelman; he has not been compared to any of his contemporaries or predecessors, and, moreover, it is likely that no living person will witness the presentation of another Millennium Prize.

“Perhaps he has a plan,” suggested Alexander Abramov, Perelman’s former coach at the Mathematical Olympiad. “Maybe when he gets the Clay Award he'll accept it.” This will be a symbol of complete recognition. Moreover, after that he will be able to live the way he wants, and not depend on anyone.” He paused and added: “But [I assume this only because] there must be some reasonable hypothesis.” Those who care about Perelman cannot help but worry about him. Abramov told me: “I’m afraid that all this will end badly. It's too crowded and too lonely. You never know what comes into his head.”

Abramov was one of those with whom Perelman stopped talking on the phone. Before this happened, Abramov called him one day and offered help, moral and financial. Perelman could, for example, write an article for Kvant, the popular science magazine founded by Kolmogorov and edited by Abramov, and receive a fee for it.

Perelman rejected all offers, including Abramov's offer of friendship. “He told me,” recalls Abramov, “that one of his principles is not to force his friendship on anyone...

...Jim Carlson called Grigory Perelman from the hotel on the day of his arrival in St. Petersburg. He introduced himself and outlined the situation (what Perelman already knew): two years must pass after publication in a peer-reviewed publication; the publication of Morgan and Tian's book can be considered a starting point; The composition of the award committee could be determined by May 2009, and by August the committee could make a decision.

Perelman listened to him politely.

Carlson did not ask whether the Russian mathematician would take the money if he was offered it. “The direction our conversation took,” Carlson later explained to me, “was inappropriate.” Perhaps the shyness of the president of the Clay Institute showed itself at the wrong time. Or maybe he didn’t dare ask the question about the money in order to give himself another year of faint hope that Perelman would still accept the award. “I didn’t feel like the path was cut off,” Carlson told me.

At the end of the conversation, Perelman remarked: “I don’t understand what the point of our conversation was”...

…Carlson admitted that many mathematicians criticize the practice of awarding cash prizes because they consider it superficial. Some find this offensive. Even Carlson’s friend Vershik published an article in which he criticized the Millennium Prize from these very positions. But Carlson told me that students often ask him what kind of problems they are offering millions to solve. The Millennium Prize brought an unexpected benefit: “Getting the public interested in mathematics without spending a dime on it is a good result,” Carlson told me proudly. Perelman became his involuntary assistant: “The public is interested in a person who is not interested in money.”

Carlson wasn't just trying to pretend that everything was fine. He felt that in this clumsy way he was able to attract everyone's attention to an achievement that deserved it. During my conversations with Carlson, he never showed any irritation towards Perelman. This makes him stand out from other mathematicians I've talked to. Unlike Kleiner, for example, Carlson’s professional pride did not suffer because of Perelman’s victory. Unlike Tian, Carlson did not feel ignored by Perelman. Carlson did not understand Perelman and did not try to do so. All he felt for him was respect.

The only person who not only claimed to understand Perelman's way of thinking, but also seemed to still be in contact with him, was Mikhail Gromov [ famous mathematician. - Forbes ]. — Do you think Perelman will agree to take a million? — I asked.

“I don’t think so,” Gromov answered.

- Why?

- This does not correspond to his principles.

- Which one?

“From his point of view, Clay is a nonentity.” Why take his money?

“But Perelman’s colleagues decide,” I objected.

“These people are playing along with Clay!” - Gromov got angry. - They decide! Perelman has already proven the theorem - what else can be solved?

Grigory Perelman. How not to become a millionaire