[1] Tate taught at Harvard for 36 years before joining the University of Texas in 1990 as a Sid W. Richardson Foundation Regents Chair.

[4][5][6] Tate's thesis (1950) on Fourier analysis in number fields has become one of the ingredients for the modern theory of automorphic forms and their L-functions, notably by its use of the adele ring, its self-duality and harmonic analysis on it; independently and a little earlier, Kenkichi Iwasawa obtained a similar theory.

In the decades following that discovery he extended the reach of Galois cohomology with the Poitou–Tate duality, the Tate–Shafarevich group, and relations with algebraic K-theory.

His students include George Bergman, Ted Chinburg, Bernard Dwork, Benedict Gross, Robert Kottwitz, Jonathan Lubin, Stephen Lichtenbaum, James Milne, V. Kumar Murty, Carl Pomerance, Ken Ribet, Joseph H. Silverman, Dinesh Thakur, and William C. Waterhouse.

In 1956, Tate was awarded the American Mathematical Society's Cole Prize for outstanding contributions to number theory.

In 2010, the Norwegian Academy of Science and Letters, of which he was a member,[13] awarded him the Abel Prize, citing "his vast and lasting impact on the theory of numbers".

According to a release by the Abel Prize committee, "Many of the major lines of research in algebraic number theory and arithmetic geometry are only possible because of the incisive contributions and illuminating insights of John Tate.

"[14] Tate has been described as "one of the seminal mathematicians for the past half-century" by William Beckner, Chairman of the Department of Mathematics at the University of Texas at Austin.

One of his grandchildren, Dustin Clausen, currently works as a mathematics Professor at Institut des Hautes Études Scientifiques.