My Take on Perelman

My American friends often ask me for insights into why Grigory Perelman refused the one million dollar Clay prize for his proof of the Poincaré conjecture. They are right to ask me: my life experience was very similar to Perelman’s.

I went to a high school for children gifted in math. I was extremely successful in competitions. I got my gold medal at IMO and went to college without entrance exams. I received my undergraduate and graduate degrees in one of the best math academic centers in Soviet Russia. Perelman traveled a similar path.

Without ever having met Perelman, I can suggest two explanations of why he might reject the money.

First explanation. To have it publicly known that you have suddenly come into money is very dangerous in Russia. Perelman’s life expectancy would have dropped immediately after accepting the million dollars. Russians that have tons of money either hide their wealth or build steel doors way before they make their first million. In addition to being a life hazard, money attracts a lot of bother. He would have been chased by all types of acquaintances asking for help or suggesting marriage proposals.

Second explanation. We grew up in a communist culture where money was scorned and math was idolized. The goal of research was research. Proving the conjecture was the prize itself. In his mind, receiving the award money might diminish the value of what he did. I understand this way of thinking, but I am personally too practical to follow such feelings and would accept the prize.

My first explanation has a flaw. Though valid, it doesn’t explain why he rejected the Fields medal. So I reached for the book abour Perelman, Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century by Masha Gessen. I like Gessen’s explanation of why he rejected the Fields medal:

His objection to the Fields Medal, though never stated as clearly, seemed to have been twofold: first: he no longer considered himself a mathematician and hence could not accept a price intended for the encouragement of midcareer researchers; and second, he wanted no part of ICM, with all the attendant publicity, speeches, ceremony, and king of Spain.

The reasons are specifically related to the medal, so the Clay prize rejection might not be connected to the medal rejection. This argument slightly rehabilitates my first explanation.

Perfect Rigor

I liked the book. It is a tremendous undertaking — writing about a person who doesn’t want to talk to anyone. After reading it, I have one more possible explanation of his refusal of the prize.

Perelman is a loner. One of the closest people to him was his math Olympiad coach. The coaches tend to understand the solutions on the spot, mostly because they already know them. If in his mind Perelman expected all mathematicians to be like his coach, then he might have expected a parade in his honor the day after he solved the conjecture. Instead, he got silence and attempts to steal the prize from him.

Can you imagine doing the century’s best math work without receiving congratulations for many years? The majority of mathematicians waited for the judgment of the experts, as did Perelman. The experts were busy and much slower than Perelman expected. The conjecture was extremely difficult, and it was a high-profile situation — after all, $1 million was attached to its solution. So the experts were very cautious in their pronouncements.

Finally, instead of congratulating Grigory, they said that the proof seemed to be correct and that they had not yet found any mistakes. If like Perelman, I was certain of my proof, I would have found this a painfully under-whelming conclusion.

Perelman expected to feel proud, but instead he probably felt unappreciated and attacked. Instead of the parade he may have hoped for, he had to wait for a long time, only to face disappointment and frustration. This reminds me of an old joke:

A genie is trapped in a lantern at the bottom of the sea. He vows, “I will give one million dollars to the person who frees me.” One thousand years pass. He changes his vow, “I will give any amount of money to the one who frees me.” Another thousand years pass. He ups the ante, “I will give any amount of money and two more wishes to the person who frees me.” Another thousand years pass. He promises, “I will kill the one who frees me.”

Third explanation. Perelman was profoundly disappointed in the math community. Unlike the genie, Perelman didn’t want to kill anyone, but he did want to express his disillusionment. Perhaps that is why he rejected a million dollars.



  1. Jason Polak:

    I think even if your first explanation is not the full story (what paragraph really ever is?) but I think the burden of being rich certainly had something to do with his rejection. I can imagine that even in North American suddenly coming into possession of such a large sum of money would certainly have some burdens. Mathematicians especially need a lot of intellectual space, and I can imagine myself getting caught up in the best way to invest it, etc, etc.

    Of course, I wouldn’t reject the money, as I feel the benefits far outweigh the costs.

  2. ObsessiveMathsFreak:

    I think you overlooked the most important thing about Perelman. He left to go the the US in 1991, did very well, but then went back to Russia in 1995.

    I suspect that the key to Grigori Perelman lies in that decision.

  3. I. J. Kennedy:

    Thank you for your interesting and informed perspective on Perelman and why he refused such a prestigious award and nice sum of cash. I think it’s worth noting that he also refused the EMS prize back in 1996, before proving Poincaré. And at the risk of coming off disrespectful to a great intellect, isn’t it possible his odd behavior is caused by his being just a little crazy?

  4. Tanya Khovanova:

    IJK: He might be a little strange, but I do not think he is insane.

  5. WakeMeUpWhenTheCloudsAreFarBehind:

    He rejected it because he didn’t feel like being a part of people’s circus.

    People and their institutions can be very disappointing. Oftentimes shallow. Erratic. Impulsive. Vain. Driven largely by the pursuit of fame and status and social standing, in turn driven by our biology and evolution. And this seems to apply to most institutions and most people, even in academia (perhaps especially in academia?). This may sound far-fetched, but just think about what we do every day to impress others, have our names in the limelight, and be at the top of the pyramid, whether at school reunions or at academic conferences. And then think about why we do it.

    I suspect that to a mind like Perelman’s this (biological) pursuit of glory, authority, and fame in society, whether within an academic institution or even in simple daily interactions, was repulsive or at least a waste of time.

    And that may explain why he has withdrawn from people as a whole so much. He isn’t “insane”, unless by insane we mean that he has stopped caring about the ridiculous rituals and social games that constitute our interactions.

    I wish I could do that sometimes.

  6. Juan Carlos:

    Desde el lejano Paraguay, mis saludos y admiración para Tanya

    Juan Carlos

  7. Lukasz:

    I ask kindly to place the following modified version of my post.

    I have read the article (in Polish): Jozef H. Przytycki, “Grigorij Perelman, Poincare’s hypothesis and rejected Fields’ Medal”, Wiadomosci Matematyczne (Annales Societatis Mathematicae Polonae Series II), vol. 46, No. 1, 37 – 61 (2010), where among others, there has been written that Prof. Perelman has said that Fields’ Medal has not been of interest for him and everyone has understood that if the proof is correct, then no other form of applauding is necessary.

    Well, the authors of the paper: T. J. Stępień, Ł. T. Stępień, „On the Consistency of the Arithmetic System”, Journal of Mathematics and System Science, vol. 7, 43 (2017), arXiv:1803.11072, have not any problems with an excess of fame. The proof of the consistency of the Arithmetic System published there and done within this system, is correct, and this apparently must be sufficient for them…

  8. Peter:

    Perelman does not care about your petty green paper and whether or not it’s “his” or “yours”. Petty things like whether or not something is his or yours is irrelevant and meaningless to his great mind.

    It’s the same reason why Dumbledore doesn’t care about your petty gold and political power.

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