The Map of My Life

Springer has just published an autobiography of Goro Shimura, entitled The Map of My Life. Shimura’s specialty is the arithmetic theory of modular forms, and he’s responsible for a crucial construction generalizing the modular curve, now known as a “Shimura variety”. The book has a long section at the beginning about his childhood and experiences during the war in Japan. The rest deals mostly with his career as a mathematician, including often unflattering commentary on his colleagues. One of those who comes off the best is André Weil, who encouraged and supported Shimura’s work from the beginning. They both ended up at Princeton, with Weil at the Institute, Shimura at the University.

The book contains extensive discussion of the story of what Shimura calls “my conjecture”. This is the conjecture proved by Wiles and others that implies Fermat’s Last Theorem. In the past, it has conventionally been referred to by various combinations of the names of Shimura, Taniyama and Weil, although more recently the convention seems to be to refer to it as the “modularity theorem”. Shimura also claims credit for conjecturing the “Woods Hole formula” that inspired Atiyah and Bott to prove their general fixed-point theorem.

To get a flavor of the unusual nature of the book, here are some extracts from one section:

Jean-Pierre Serre, whom I had met in Tokyo and Paris, was among the audience, and kept asking questions on the most trivial points, which naturally annoyed me…. Somebody told me that he had become frustrated and even sour. Much later I formed an opinion that he had been frustrated and sour for most of his life. As described in my letter to Freydoon Shahidi, included as Section A2 in this book, he once tried to humiliate me, and as a result gave me the chance to state my conjectures about rational elliptic curves. I now believe that his “attack” on me was caused by his jealousy towards my supposed “success” — my conjectural formula and lectures — at Woods Hole….

In spite of the fact that my mathematical work was little understood by the general mathematical public, I was often the target of jealousy by other mathematicians, which I found strange. I can narrate many stories about this in detail, but that would be unpleasant and unnecessary, and so I mention only one interesting case…

(he then describes an encounter in which Harish-Chandra compares favorably Apery’s result on the irrationality of ζ (3) to Shimura’s work.)

Clearly he [Harish Chandra] thought he finally found something with which he could humiliate me: To his disappointment, he failed. Did he do such a thing to other people? Unlikely, though I really don’t know. But why me? To answer that question, let me first note an incident that happened in the fall of 1964. As I already explained, Atiyah and Bott proved a certain trace formula based on my idea. Bott gave a talk on that topic at the Institute for Advanced Study. In this case he clearly acknowledged their debt to me. In the talk he mentioned that Weyl’s character formula could be obtained as an easy application. Harish-Chandra, who said, “Oh, I thought the matter was the other way around; your formula would follow from Weyl’s formula.” Bott, much disturbed, answered, “I don’t see how that can be done.” After more than ten seconds of silence, Harish-Chandra said “It was a joke.” There was half-hearted laughter, and I thought that his utterance was awkward and did not make much sense even as a joke.

It is futile to psychoanalyze him, but such an experience may allow me to express some of my thoughts. He was insecure and hungry for recognition. That much is the opinion shared by many of those who knew him. He did not know much outside his own field, but he was not aware of his ignorance. In addition, I would think he was highly competitive, though he rarely showed his competitiveness. From his viewpoint I was perhaps one of his competitors who must be humiliated, in spite of the fact that I was not working in his field. Here I may have written more than is necessary, but my concluding point is: He did so, even though I did nothing to him.

The book contains quite a few other unpleasant characterizations of other people, together with assurances that everyone else shared his view of the person in question. I know for a fact that in at least one case this is untrue:

A well known math-physicist Eugene Wigner was in our department, and so I occasionally talked with him. He was pompous and took himself very seriously. That is the impression shared by all those who talked with him.

Wigner was still around when I was a student at Princeton and often came to tea. My impression of him was not at all that which Shimura claims to have been universal.

: An exchange between Shimura and Bott about the Woods Hole story can be found here.

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25 Responses to The Map of My Life

  1. chickenbreeder says:

    Interesting. I will probably buy a copy of the book if it’s not expensive.

    A book like this is not unprecedented. Andrei Sakharov’s memoir has a lot of moments when he pointedly accused his colleagues of character flaws. Those include at least one for Zeldovich, who had been supportive of him most of the time and was considered by AS as a friend. In fact, I think this is exactly what a good memoir should be: Honest recollection of one’s thoughts and feelings, at the end of one’s career when there’s nothing more at stake. This also serves as a release, or else one would have to bring those thoughts and feelings alone to the grave.

    (In the revised version of his memoir, Sakharov mentioned that he and Zeldovich eventually reconciled.)

  2. Coin says:

    Maybe not the most appropriate question to ask, but I cannot help but wonder– does Shimura’s book have anything of detail to say about Taniyama, or attempt to offer any insight into his suicide?

  3. Pingback: Shimura’s “Map of my Life” « Math on the Street

  4. Neville says:

    It sounds like a rather sad book. Life should be a happy adventure.

  5. mathematician says:

    Is there any reason to doubt the general picture portrayed by Shimura of a not always pleasant sociology. I would tend to take him at his word (with an appropriate grain of salt). Surely there are at least others in that circle who could confirm the existence of this kind of negative atmosphere.

    I know nothing of this group, but I have seen and experienced negative things in my own circles, and I am acutely aware of how much people resent being informed of it.

  6. anonymous says:

    One is obviously reminded of Grothendieck’s “Recoltes et Semailles”, where similar “score settling” sadly occurs.

    When I’ve got a grudge against someone, I take it up with him/her, not with the general public.

  7. MathPhys says:

    I know that Grothendieck’s accusations of a certain person in R et S were completely unfounded.

    Grothendieck was a very great man, but when he wrote R et S, he was too angry to see that others may have perfectly valid explanations for their actions.

    In any case, the people that he attacked were all still around and active when R et S was distributed.

    In Shimura’s case, the situation is different as many of the people that he talks about are no longer in a position to defend themselves.

  8. Peter Woit says:


    There’s a bit in the book about Taniyama, no insight into the reason for his suicide.


    I gave one reason to doubt Shimura’s portrayals of other people’s failings, based on my own personal experience. I’ve never met Serre personally, but Shimura’s claim that he was jealous because of the Wood’s Hole conjecture is hard to believe. The currency of renown among mathematicians is theorems, not conjectures….

  9. Per says:

    If the text above is true, then it is a bit sad that excellence in mental achievements does not imply growth of other aspects of personality.

    Egomaniacs seem to roam the halls of famous mathematics institutions also.

  10. mathematician says:

    Peter, okay you have a point that Shimura’s claims of the form “everyone agrees with me” are easily refuted by people disagreeing with him.

    But his claims of the form “person X has certain negative characteristics” are not so easily refuted by people disagreeing with him. People may not like hearing such things, but if they know nothing of the people involved they should just remain agnostic on the issue. I object to people automatically rejecting his claims, just because they are negative.

    I have personal experience of being severely mistreated by someone who is viewed positively by many people and who has received awards and recognition for being something completely different to what I am describing. Several years ago I was almost driven to suicide by this person, and I believe there is another case where the word “almost” does not apply. And yet I just have to keep my mouth shut about it, because of the backlash that there is to such negative claims.

  11. st says:

    The academe in previous decades was not nearly as open-minded as it is today. I am sure as a foreign Japanese scholar working in the US back then, he must have felt at least some form of subtle prejudice or discrimination. From the excerpts and letter to the AMS, it appears that Shimura has felt that his ideas were often ignored or belittled and would like proper credit for his work. Although he may come across as a bit paranoid in his writing, that doesn’t mean his observations about his colleagues were inaccurate or baseless, though the assertion that “all” agree with his opinion is exaggerated.

  12. woit says:


    If Shimura felt discriminated against by anyone for being Japanese, he doesn’t mention that in his book.

  13. st says:


    I mentioned discrimination because it was well known at the time. For example, in his paper A History of Mathematics at Princeton University (available here), Michael Seip writes:

    Gian Carlo Rota was an undergraduate mathematics major at Princeton in the early 1950’s, a period marked by growth of the department and political upheaval in academia. He describes another, more ugly, notion of the times; nationality prejudices in academia. Many notable professors from Europe and the Far East were allowed to visit American universities, but not many were granted tenure. This bias was expressed at Princeton in several notable instances. The geometer Kunihiko Kodaira, from Japan, was appointed to a six-year term but was not awarded tenure. Though Kodaira, “whose work in geometry was revered by everyone in the Princeton main line”, (Rota, p. 226) was an accomplished and productive researcher, several members of the Princeton faculty were opposed to his award of tenure on the basis of his nationality and he was voted down.

    On a different note, the paper continues with this observation:

    “Bias also existed towards those men who studied subjects considered intangible at the time…”

    This type of bias, unfortunately, is still pretty much alive today.

  14. Kea2 says:

    Over the years, Shimura has increasingly isolated himself from other mathematicians. Like Grothendieck, he can write very well about nonmathematical things — for example, his memoir on Taniyama (BLMS 1989) is very moving — but I wouldn’t give any more credence to his characterizations of other mathematicians than I do to Grothendieck’s.

  15. Jean-Paul Billon says:

    Whatever the domain, to push one’s ideas leads to be shot at will by people you were trusting to be fair great minds. Mathematicians are not outside of the current universe under this aspect. Having been a mathematicinas in a former life, I was hurt by the buzz that a very obvious fundamental theorem I was using to base on a new method of theorem proving was wrong. No luck for my detractors, it was a well known theorem proven by Shannon. Since I have been moving to industry and now to politics. Same game. But you learn how to get a thick skin. Whoever believes that fundamental science is clean from any blow under the belt is a naive. Novertheless, sciens is moetimes progressing, which is great. BTW, did you know that Einstein was barred from tenure in France when seeking asylum…?

  16. N. Nakanishi says:

    My impression of E. Wigner is common to P. Woit’s one. In 1961, at Princeton I met him and reported that I had translated his famous essay entitled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” into Japanese. He was extremely polite to such a young Japanese as me.

  17. sz says:

    Mathematicians always behave like children, even great ones like Shimura are no exception. In this book Shimura portrayed himself more like an aged Tom Sawyer than a matured adult. I don’t see anything wrong about it, I believe his words are sincere and truthful.

    In my naive psycho-analysis, I think sometimes when a person describes another person, he unconsciously projects his own shadow over the others’ image. In Shimura’s opinion about Harish-Chandra, I very much see an image of Shimura himself.

    But I do think this is different from Grothendieck’s “Recoltes et Semailles”, because Grothendieck is not a traditional mathematician. What he did in mathematics is, in some sense, not mathematics at all, but rather like mythology of Ramanujan…it’s like he hits the weakness of standard mathematical thinking in some way. His anger towards the others maybe come from the fact that even those closest to him can not or would not follow his way of thinking.

  18. a.k. says:

    ..discrimination was not only ‘well-known at that time’, it certainly influenced the mathematical community not only in those days. In difference to any other subclass of society, the existence of discrimination by race, class or gender among mathematicians is not a ‘valid’ subject of discussion, is is assumed to be non-existent due to the general ‘level of civilisation’, which one presupposes for mathematicians. This is -without any doubt- the (conscious or subconscious) reason why Shimura did not explicitly mention the term of discrimination in his book, although it seems to be clearly implicit. It is a common phenomenon for people experiencing discrimination to react in a way which seems ‘paranoid’ to the observer, even or especially if the actual formulation of the term ‘discrimination’ is, for some reason, not an accepted way to choose for the person in case, for personal or ‘external’ reasons.

  19. former mathematician says:

    I can’t resist the opening to report a Shimura anecdote from the 50’s or 60’s, when it seemed that he was publishing at least one 45-page paper each month.

    A mathematician was browsing through typewriter ribbons ath the university store. Shimura approached him and said, “Don’t get that brand; get this brand. You will find it helps write better papers.”

  20. Peter Woit says:


    Funny, typewriter ribbons seem to be a big concern of Shimura’s. In his book, he describes one city in Japan where he worked as kind of a wasteland, with the main evidence being that he had trouble finding a place to buy typewriter ribbons.

  21. anonymous says:

    Jean-Pierre Serre was probably the greatest mathematician of the second part of this century. He remained very creative over the years. Of course there were very creative new comers, who started at the right time. But the fact that Jean-Pierre Serre lasted so long must be irritating to some…

  22. Betsy Devine says:

    What a strange characterization of Wigner, who was shy and so European-polite as to seem quite formal.

    I remember in the mid or late 1970s when the talk of Princeton physics was Wigner’s courting Pat Hamilton, the widow of another physicist who was soon to become his third wife. Joan Treiman told me that on summer evenings you could see them out strolling together, holding hands. I never saw this phenomenon, but it was a real pleasure to see them at physics parties looking both so, so happy. My impression was that Wigner’s colleagues loved as well as admired him.

  23. st says:

    I wonder whether mathematicians, in general, are always aware of how they come across to others especially in social situations. I would imagine that this awareness is probably below average as a group, although there are some with average to superb social skills. This is because we’re trained to be direct, specific, and honest in our communication. There’s little room for “spinning” when proving a theorem. As Gian-Carlo Rota once observed, mathematicians have “bad personalities,” make “terrible salesmen,” and are “totally devoid of common sense.”

    To give an example from my own experience, I’ve pointed out several relatively minor mistakes to a speaker in public without realizing at the time that that might have been offensive. For us, it is almost an instinct to correct. So I can understand how someone “asking questions on the most trivial points” might just be trying to understand the material rather than to intentionally annoy. What is “trivial” to one expert may be puzzling to others not directly working in the area. Coupled that with the extra-sensitivity of a person who might have experienced discrimination, it is easy to give birth to a “grudge” without the other party being aware of any wrongdoing. Such misunderstanding is unfortunate indeed.

  24. Anonymous says:

    Goro Shimura recently published this book too:

    Link can be found here:

  25. anon smith says:

    Professor Goro Shimura, one of the greatest mathematicians of our day, has written a wonderful book about something well outside of mathematics: an aspect of Japanese culture that should be of great interest for anyone interested in Japanese civilization. I congratulate him for writing so eloquently outside the field of mathematics and for showing his sincere passion for an art form that is unique to historic Japan and its tradition. This book will enlighten and delight any reader with interest in Japan, in fine porcelain, and in ancient traditions.

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