Goro Shimura - Life and Career

Life and Career

Shimura was a colleague and a friend of Yutaka Taniyama. 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 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). This work (and other developments it provoked) provided some of the 'raw data' later incorporated into the Langlands program. It equally brought out the concept, in general, of Shimura variety; which is the higher-dimensional equivalent of modular curve. 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.

Shimura himself has described his approach as 'phenomenological': his interest is in finding new types of interesting behaviour in the theory of automorphic forms. He also argues for a 'romantic' approach, something he finds lacking in the younger generation of mathematician. 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). 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.

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. Shimura dryly commented that his first reaction on hearing of Wiles's proof of the semistable case of the theorem was 'I told you so'.

Among 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. His Collected Works have been published, in five volumes.

His hobbies are shogi problems of extreme length and collecting Imari porcelain. 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.