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