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# Gerhard Frey

Gerhard Frey (born: 1944) is a German mathematician, known for his work in number theory. His Frey curve, a construction of an elliptic curve from a purported solution to the Fermat equation, was central to Wiles' proof of Fermat's Last Theorem.

He studied mathematics and physics at the University of Tübingen, graduating in 1967. He continued his postgraduate studies in Heidelberg where he received the Ph.D. degree in 1970[1] and his "Habilitation" in 1973. He was assistant professor at the University of Heidelberg from 1969-1973, professor at the University of Erlangen (1973-1975) and at the University of Saarbrücken (1975-1990) and currently holds a chair for number theory at the Institute for Experimental Mathematics at the University of Duisburg-Essen, campus Essen.

His research areas are number theory and arithmetical geometry as well as applications to coding theory and cryptography. He was a visiting scientist at several universities and research institutions, including The Ohio State University, Harvard University, University of California at Berkeley, the Mathematical Sciences Research Institute (MSRI), the Institute for Advanced Studies at the Hebrew University of Jerusalem, and IMPA in Rio de Janeiro.

In 1985 Frey pointed out a connection between Fermat's last theorem and the Taniyama conjecture, and this connection was made precise shortly thereafter by Kenneth Ribet, who proved that the Taniyama conjecture implies Fermat's last theorem.[2] This approach provided a framework for the subsequent successful attack on Fermat's last theorem by Andrew Wiles in 1990s.[3]

Frey was co-editor of the Manuscripta Mathematica. He was awarded the Gauss medal of the Braunschweigische Wissenschaftliche Gesellschaft in 1996[4] for his work on Fermat's Last Theorem. Since 1998 he has been a member of the Göttingen Academy of Sciences.[5]

In 1998, Frey proposed the idea of Weil Descent Attack for elliptic curves over finite fields with composite degree. As a result of this attack, cryptographers lost their interest in these curves.

In 2006 Frey was received the Certicom ECC Visionary Award for his contributions to Elliptic Curve Cryptography.[6]

See also

* Fermat's last theorem

* Elliptic curves

* Cryptography

* Elliptic curve cryptography

References

1. ^ Gerhard Frey, Mathematics Genealogy Project. Accessed January 24, 2010

2. ^ Piergiorgio Odifreddi, The mathematical century: the 30 greatest problems of the last 100 years. Princeton University Press, 2006. ISBN 0691128057; p. 87

3. ^ RICHARD BERNSTEIN, BOOKS OF THE TIMES; Following a Proof of Fermat's Theorem to the Far Horizon of Pure Reason. New York Times, November 28, 1997. Accessed January 24, 2010

4. ^ Die Gauß Medaille (in German), Braunschweigische Wissenschaftliche Gesellschaft. Accessed January 24, 2010

5. ^ Member list, (in German) Göttingen Academy of Sciences. Accessed January 24, 2010.

6. ^ Certicom ECC Visionary Award, Code and Cipher, vol. 3 (2006), no. 1, p. 1. Accessed January 24, 2010

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