It took one semester of studying physics before he shifted to the field of his fascination, sending him on a path of brilliant discovery, including proving the notion that he could, actually, “do much in mathematics.’’
Dr. Tate, who explained fundamental ideas in the theory of numbers, many of which now bear his name, died Oct. 16 in his Lexington home. 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 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 an + bn = cn 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 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 Wiles’s proof, beginning on the second page.
For his work laying the foundation for a wide range of abstract but fundamental mathematics concepts, Dr. Tate was awarded the prestigious Abel Prize, the field’s equivalent to the Nobel Prize. Many of these concepts now bear his name, among them the Tate module, the Tate curve, the Tate cycle, the Hodge-Tate decompositions, the Tate cohomology, the Serre-Tate parameter, the Lubin-Tate group, 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.”
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.
“I was in my last year of secondary school in December 1941 when Pearl Harbor was bombed,” Dr. Tate recalled in the EMS Newsletter.
He attended Harvard College, where he volunteered for a naval officer training program in which he learned meteorology and did mine-sweeping research. “I was in the Navy for three years and never aboard a ship,” he said in the newsletter interview. “It was frustrating.”
Dr. Tate graduated from Harvard in 1946 with a bachelor’s degree in mathematics and was discharged from the Navy the same year.
After one term of graduate studies in physics at Princeton, he switched departments, completing his doctoral degree in mathematics 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,” 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 other 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 and was a foreign member of the French Academy of Sciences.
Dr. Tate married Carol Perpente MacPherson in 1988. She survives him, as do three daughters, Jennifer Tate, Valerie Clausen, and Amanda Tine; six grandchildren; and one great-grandson. His first marriage, to Karin Artin, ended in divorce.
According to information his family placed with the DeVito funeral home in Arlington, funeral arrangements were private.
Dr. Tate relished what he called the “artistic aspect to mathematics” but thought it wasn’t something that could be easily shared with those outside the field.
“Unfortunately it’s only beautiful to the initiated, to the people who do it,” he said in the EMS Newsletter 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,” he added. “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.”
Nevertheless, he said, “the happy thing is that mathematics does have applications which enable us to earn a good living doing what we would do even if we weren’t paid for it. We are paid mainly to teach the useful stuff.”
Material from The New York Times was used in this report.
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