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# Goro Shimura, 89, Mathematician With Broad Impact, Is Dead

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 on May 3 at his home in Princeton, N.J. He was 89.

The death was announced by Princeton University, where Dr. Shimura had been a professor from 1964 until his retirement in 1999.

In 1955, Yutaka Taniyama, a colleague and friend of Dr. Shimura's, posed some questions about mathematical objects called elliptic curves. Dr. Shimura helped refine Dr. 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 *a*^{n} + *b*^{n} = *c*^{n} 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 — *a*^{2} + *b*^{2} = *c*^{2} — has many solutions where all of the numbers are integers. For example, 3^{2}+ 4^{2}= 5^{2}.)

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.

In 1986, Kenneth Ribet of the University of California, Berkeley, proved an intriguing connection: If Fermat's Last Theorem were wrong, and there indeed existed a set of integers that fit the equation, that would generate an elliptic curve that violated the Taniyama-Shimura conjecture.

Thus, a proof of a form of the Taniyama-Shimura conjecture would also prove Fermat's Last Theorem. In the 1990s, Andrew Wiles, then also at Princeton, figured out how to do just that, and Fermat's Last Theorem had finally been proved true.

From The New York Times

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