By KENNETH CHANG
New York Times News Service
Goro Shimura, a mathematician whose insights provided the foundation for the proof of Fermat’s Last Theorem and led to tools widely used in modern cryptography, died May 3 at his home in Princeton, New Jersey. He was 89.
The death was announced by Princeton University, where Shimura had been a professor from 1964 until his retirement in 1999.
In 1955, Yutaka Taniyama, a colleague and friend of Shimura’s, posed some questions about mathematical objects called elliptic curves. Shimura helped refine Taniyama’s speculations into an assertion now known as the Taniyama-Shimura conjecture.
But no one knew how to prove it.
The conjecture appeared unconnected to Fermat’s Last Theorem, a seemingly simple statement made by the French mathematician Pierre de Fermat in 1637: 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. (If n is equal to 2, the statement becomes the Pythagorean theorem, which says that the squares of the lengths of two sides of a right-angled triangle equal the square of the length of the hypotenuse; this equation — a2+ b2 = c2 — has many solutions where all of the numbers are integers. For example, 32+ 42= 52.)
In his writings, Fermat claimed that he had figured out a proof but that he did not have enough room to write it down. For centuries, mathematicians sought unsuccessfully to figure out what Fermat was referring to.
Shimura is survived by his wife, Chikako; a daughter, Tomoko Shimura; and a son, Haru.
Shimura’s awards included wa Guggenheim Fellowship in 1979, the Cole Prize for number theory in 1976, the Asahi Prize in 1991 and the American Mathematical Society’s Steele Prize for lifetime achievement in 1996.