Gerhard Frey

Gerhard Frey (German: [fʁaɪ]; 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's proof of Fermat's Last Theorem.[1][2]

This article is about the mathematician. For the politician, see Gerhard Frey (politician).

Gerhard Frey
Gerhard Frey at Oberwolfach in 2004
Born	1944 (age 75–76)
Nationality	German
Alma mater	University of Heidelberg
Scientific career
Fields	Mathematics
Institutions	Saarland University University of Duisburg-Essen
Doctoral advisor	Peter Roquette
Doctoral students	Tanja Lange

Education and career

He studied mathematics and physics at the University of Tübingen, graduating in 1967. He continued his postgraduate studies at Heidelberg University, where he received his Ph.D. in 1970,[3] and his Habilitation in 1973. He was assistant professor at Heidelberg University from 1969–1973, professor at the University of Erlangen (1973–1975) and at Saarland University (1975–1990). Until 2009, he held a chair for number theory at the Institute for Experimental Mathematics at the University of Duisburg-Essen, campus Essen.

Frey was a visiting scientist at several universities and research institutions, including the Ohio State University, Harvard University, the University of California, Berkeley, the Mathematical Sciences Research Institute (MSRI), the Institute for Advanced Studies at Hebrew University of Jerusalem, and the Instituto Nacional de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro.

Frey was also the co-editor of the journal Manuscripta Mathematica.

Research contributions

His research areas are number theory and diophantine geometry, as well as applications to coding theory and cryptography. In 1985, Frey pointed out a connection between Fermat's last theorem and the Taniyama-Shimura Conjecture, and this connection was made precise shortly thereafter by Jean-Pierre Serre who formulated a conjecture ${\displaystyle \varepsilon }$ and showed that Taniyama-Shimura+${\displaystyle \varepsilon }$ implies Fermat. Kenneth Ribet proved soon after enough of conjecture ${\displaystyle \varepsilon }$ to deduce that the Taniyama-Shimura Conjecture implies Fermat's last theorem.[4] This approach provided a framework for the subsequent successful attack on Fermat's last theorem by Andrew Wiles in the 1990s.[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.[6]

Awards and honors

Frey was awarded the Gauss medal of the Braunschweigische Wissenschaftliche Gesellschaft in 1996 for his work on Fermat's Last Theorem.[7] Since 1998, he has been a member of the Göttingen Academy of Sciences.[8]

In 2006, he received the Certicom ECC Visionary Award for his contributions to elliptic-curve cryptography.[9]

See also

• Fermat's last theorem
• Elliptic curves
• Trace zero cryptography

References

1. Helen G. Grundman (21 October 1999). "Are mathematicians finally satisfied with Andrew Wiles's proof of Fermat's Last Theorem? Why has this theorem been so difficult to prove?". Scientific American. Retrieved 21 August 2016.
2. Keith Devlin (21 July 1999). "Beyond Fermat's last theorem". The Guardian. Retrieved 21 August 2016.
3. Gerhard Frey at the Mathematics Genealogy Project
4. Odifreddi, Piergiorgio (2006). The Mathematical Century: The 30 Greatest Problems of the Last 100 years. Princeton University Press. p. 87. ISBN 0-691-12805-7.
5. Bernstein, Richard (November 28, 1997). "Following a Proof of Fermat's Theorem to the Far Horizon of Pure Reason". New York Times. Retrieved January 24, 2010.
6. Hankerson, Darrel; Vanstone, Scott; Menezes, Alfred J. (2004), Guide to Elliptic Curve Cryptography, Springer, pp. 170–171, ISBN 9780387952734..
7. Die Gauß Medaille (in German), Braunschweigische Wissenschaftliche Gesellschaft. Accessed January 24, 2010
8. "Member list" (PDF). Göttingen Academy of Sciences (in German). Retrieved January 24, 2010.
9. "Certicom ECC Visionary Award" (PDF). Code and Cipher. 3 (1): 1. 2006. Retrieved January 24, 2010.

External links

• Gerhard Frey's webpage at University Duisburg-Essen