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. 'synopsis' may belong to another edition of this title.Shimura was a colleague and a friend of Yutaka Taniyama. He is the author of Elementary Dirichlet Series and Modular Forms (Springer 2007), Arithmeticity in the Theory of Automorphic Forms (AMS 2000), and Introduction to the Arithmetic Theory of Automorphic Functions (Princeton University Press 1971). Steele Prize for Lifetime Achievement from the American Mathematical Society.

Goro Shimura is Professor Emeritus of Mathematics at Princeton University. Such luminaries as Chevalley, Oppenheimer, Siegel, and Weil figure prominently in its anecdotes. Every page of this memoir contains personal observations and striking stories. He describes his survival of American bombing raids when he was a teenager in Japan, his emergence as a researcher in a post-war university system that was seriously deficient, and his life as a mature mathematician in Princeton and in the international academic community. In this book, the author writes freely and often humorously about his life, beginning with his earliest childhood days.

The Map of My Life by Goro Shimura