Shimura, Goro Taniyama, Yutaka (1961), Complex multiplication of abelian varieties and its applications to number theory, Publications of the Mathematical Society of Japan, 6, Tokyo: The Mathematical Society of Japan, MR 0125113 Later expanded and published as Shimura (1997).

The Story of Imari: The Symbols and Mysteries of Antique Japanese Porcelain is a non-fiction work by Shimura published by Ten Speed Press in 2008. His hobbies are shogi problems of extreme length and collecting Imari porcelain. His Collected Works have been published, in five volumes.

Shimura dryly commented that his first reaction on hearing of Andrew Wiles's proof of the semistable case of the theorem was 'I told you so'.Īmong many honors and awards, Shimura received the Cole Prize for number theory in 1976 and the Steele Prize for lifetime achievement in 1996, both from the American Mathematical Society. He is known to a wider public through the important modularity theorem (previously known as the Taniyama-Shimura conjecture before being proven in the 1990s) Kenneth Ribet has shown that the famous Fermat's last theorem follows from a special case of this theorem. In that sense his work is now 'mainstream-for-Princeton' but this assimilation (through David Mumford, Pierre Deligne and others) hardly includes all of the content. The central 'Shimura variety' concept has been tamed (by application of Lie group and algebraic group theory, and the extraction of the concept 'parametrises interesting family of Hodge structures' by reference to the algebraic geometry theory of 'motives', which is still largely conjectural). He also argues for a 'romantic' approach, something he finds lacking in the younger generation of mathematician. Shimura himself has described his approach as 'phenomenological': his interest is in finding new types of interesting behaviour in the theory of automorphic forms. Even to define in general a Shimura variety is quite a formidable task: they bear, roughly speaking, the same relation to general Hodge structures as modular curves do to elliptic curves. It equally brought out the concept, in general, of Shimura variety which is the higher-dimensional equivalent of modular curve. This work (and other developments it provoked) provided some of the 'raw data' later incorporated into the Langlands program. Shimura then wrote a long series of major papers, extending the phenomena found in the theory of complex multiplication and modular forms to higher dimensions (amongst other results). They wrote a book (the first book treatment) on the complex multiplication of abelian varieties, an area which in collaboration they had opened up.

Shimura was a colleague and a friend of Yutaka Taniyama.

The Map of My Life by Goro Shimura