Shimura’s, said that his work “permeates modern-day cryptography.” Researchers use Dr. “His work encompasses laying the foundation to do things of this type in great generality.”Īlice Silverberg, a mathematician at the University of California, Irvine, who was a graduate student of Dr. “His works are fantastic,” Peter Sarnak, another Princeton mathematician, said in an interview. Shimura later expanded his work, and mathematicians now routinely talk about “Shimura varieties,” a fundamental concept in that area of mathematics. Wiles, now at the University of Oxford in England, wrote in an email that the Taniyama-Shimura conjecture was “a fundamental pivot in the proof of Fermat’s Last Theorem.” The proof also employed other key results of Dr. 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.ĭr. Thus, a proof of a form of the Taniyama-Shimura conjecture would also prove Fermat’s Last Theorem.

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. For centuries, mathematicians sought unsuccessfully to figure out what Fermat was referring to. In his writings, Fermat claimed that he had figured out a proof but that he did not have enough room to write it down. (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. 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. Taniyama’s speculations into an assertion now known as the Taniyama-Shimura conjecture. Shimura’s, posed some questions about mathematical objects called elliptic curves. In 1955, Yutaka Taniyama, a colleague and friend of Dr. Shimura had been a professor from 1964 until his retirement in 1999. The death was announced by Princeton University, where Dr. 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.

The Map of My Life by Goro Shimura