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 important 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 state in general what a Shimura variety is (should be) is quite a formidable task.

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 Mumford, Deligne and others)hardly includes all of the content.

He is known to a wider public through the important Taniyama-Shimura conjecture, which implied the famous Fermat's last theorem as a special case. The conjecture was finally proven in 1999.

His hobby is shogi problems of extreme length.