#### Many of his explanations of fundamental ideas now bear his name, a much-honored one among mathematicians.

John T. Tate, a mathematician who explained many fundamental ideas in the theory of numbers, many of which now bear his name, and who won the 2010 Abel Prize, a top math award modeled after the Nobels, died on Oct. 16 at his home in Lexington, Mass. He was 94.

His death was confirmed by Harvard University, where he taught for many years.

Number theory is, in large part, the study of finding solutions to equations that cast insight into the fundamental properties of integers. But instead of solving equations one by one, theorists like Dr. Tate look for underlying patterns in similar equations and develop tools to tackle them.

"Tate is really the person who laid the big bricks in that theory,"said Kenneth A. Ribet, a mathematician at the University of California, Berkeley, and a former a graduate student of Dr. Tate's.

For example, Fermat's Last Theorem, a seemingly simple statement made by the French mathematician Pierre de Fermat in 1637, is a problem of number theory. Fermat asserted that equations of the form a + b = c do not have solutions when n is an integer greater than 2 and a, b and c are positive integers.

Dr. Tate did not play a direct role in coming up with a proof. That was done in 1995 by Andrew Wiles, then at Princeton University.

"John would deny he had any role in it," said John H. Coates, an emeritus mathematics professor at the University of Cambridge in England who was a colleague of Dr. Tate's at Harvard in the early 1970s and who later served as Dr. Wiles's thesis adviser at Cambridge. "He was very modest, but nevertheless some of his ideas are lurking behind that."

Reference to Dr. Tate's results appear throughout Dr. Wiles's proof, beginning on the second page.

Dr. Tate laid the groundwork for a wide range of abstract but fundamental concepts that now bear his name, among them the Tate module, the Tate curve, Tate cycles, Hodge-Tate decompositions, Tate cohomology, the Serre-Tate parameter, Lubin-Tate formal groups, the Tate trace, the Shafarevich-Tate group and the Néron-Tate height.

"The list goes on and on,"the Abel Prize committee said in its citation honoring Dr. Tate in 2010. "Many of the major lines of research in algebraic number theory and arithmetic geometry are only possible because of the incisive contribution and illuminating insight of John Tate. He has truly left a conspicuous imprint on modern mathematics."

In an interview published in Notices of the American Mathematical Society after he won the Abel, Dr. Tate, as modest as ever, still talked of himself as unexceptional. He noted that he had initially studied physics in graduate school, because he had read a book about some of the great mathematicians in history and "I knew I wasn't in their league."

"I thought," he continued, "that unless I was, I wouldn't really be able to do much in mathematics. I didn't realize that a less talented person could still contribute effectively."

John Torrence Tate was born in Minneapolis on March 13, 1925. His father, also named John Torrence Tate, was a professor of physics at the University of Minnesota; his mother, Lois (Fossler) Tate, was a high school English teacher. While in college at Harvard, he volunteered for a naval officer training program in which he learned meteorology and did mine-sweeping research.

He graduated from Harvard in 1946 with a bachelor's degree in mathematics. He was discharged from the Navy the same year without ever having stepped on a ship.

He then started graduate school at Princeton. "Since my father was a physicist, that field seemed more human and accessible to me," Dr. Tate recalled in the American Mathematical Society interview, "and I thought that was a safer way to go, where I might contribute more."

After one term he realized that his true interest was mathematics and switched departments, completing his doctoral degree in 1950. In his thesis, Dr. Tate recast a 1920 finding by the German mathematician Erich Hecke, and though it did not prove a new result, it opened up new avenues of inquiry for other mathematicians.

"Tate gave it an entirely new spin," said Benedict Gross, a mathematician at the University of California, San Diego, and another of Dr. Tate's graduate students. "It was really a fundamental reformulation."

Dr. Tate published relatively few papers, but the ones he did publish were clear and concise and held fundamental findings. "When he finished thinking about a subject, it was understood," Dr. Gross said. "There were no loose ends lying around."

After completing his doctorate, Dr. Tate worked as a research assistant and an instructor at Princeton and then as a visiting professor at Columbia. He became a professor at Harvard in 1954 and remained there for 36 years. He moved to the University of Texas in 1990 and retired in 2009. He returned to Harvard as an emeritus professor.

Dr. Tate's honors included the American Mathematical Society's Steele Prize for Lifetime Achievement in 1995. In 2002, he shared the prestigious Wolf Prize in Mathematics. He was a member of the National Academy of Sciences.

Dr. Tate's first marriage, to Karin Artin, ended in divorce. He married Carol Perpente MacPherson in 1988. She survives him, as do three daughters from his first marriage, Jennifer Tate, Valerie Clausen and Amanda Tine; six grandchildren; and one great-grandson.

Dr. Tate relished the beauty of mathematics but realized it was not something that could be easily shared with those not in his field.

"Unfortunately it's only beautiful to the initiated, to the people who do it," he said in the American Mathematical Society interview." It can't really be understood or appreciated much on a popular level the way music can. You don't have to be a composer to enjoy music, but in mathematics you do."

"That's a really big drawback of the profession. A non-mathematician has to make a big effort to appreciate our work; it's almost impossible."

**Kenneth Chang**

Oct. 19, 2019 © The New York Times