Goro Shimura

"The Fourier expansion of an elliptic modular form has been fruitfully utilized in various arithmetical problems as well as in the study of the analytic properties of the form itself. The same can be said also for the Hilbert and Siegel modular forms."

"The maxim "A university professor is the next easiest profession after a beggar" really rings true."

"Though he was by no means a sloppy type was gifted with the special capability of making many mistakes, mostly in the right direction. I envied him for this, and tried in vain to imitate him, but found it quite difficult to make good mistakes."

"The subject that might be called “explicit class field theory” begins with Kronecker’s Theorem: every abelian extension of the field of rational numbers Q is a subfield of a cyclotomic field Q(ζn), where ζn is a primitive nth root of 1. In other words, we get all abelian extensions of Q by adjoining all “special values” of e(x) = exp(2πix), i.e., with x ∈ Q. Hilbert’s twelfth problem, also called Kronecker’s Jugendtraum, is to do something similar for any number field K, i.e., to generate all abelian extensions of K by adjoining special values of suitable special functions. ... Aside from some results of Hecke in 1912, the only progress on the twelfth problem was made by Shimura and Taniyama in the 1950s. They achieved complete results concerning the abelian extensions of number fields arising from abelian varieties, with complex multiplication, of arbitrary dimension n ..."

"Andrew Ogg:"