Gerhard Frey

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This article is about the mathematician. For the politician, see Gerhard Frey (politician).
Gerhard Frey
Gerhard Frey (matematico).jpg
Gerhard Frey
Born 1944 (age 71–72)
Nationality German
Fields Mathematics
Institutions University of Duisburg-Essen
Alma mater University of Heidelberg
Doctoral advisor Peter Roquette
Doctoral students Tanja Lange
Hans-Georg Rück
Stefan Wewers
Anne-Monika Spallek
Annegret Weng
Roger Oyono
Xavier Taixés i Ventosa

Gerhard Frey (German: [fʀaɪ]; 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.

Education and career[edit]

He studied mathematics and physics at the University of Tübingen, graduating in 1967. He continued his postgraduate studies in Heidelberg University where he received the Ph.D. degree in 1970[1] and his Habilitation in 1973. He was assistant professor at the Heidelberg University from 1969–1973, professor at the University of Erlangen (1973–1975) and at the Saarland University (1975–1990) and until 2009 held a chair for number theory at the Institute for Experimental Mathematics at the University of Duisburg-Essen, campus Essen. He was a visiting scientist at several universities and research institutions, including Ohio State University, Harvard University, University of California, Berkeley, the Mathematical Sciences Research Institute (MSRI), the Institute for Advanced Studies at the Hebrew University of Jerusalem, and IMPA in Rio de Janeiro.

Frey was co-editor of the Manuscripta Mathematica.

Research contributions[edit]

His research areas are number theory and arithmetical 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 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 the 1990s.[3]

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.[4]

Awards and honors[edit]

Frey was awarded the Gauss medal of the Braunschweigische Wissenschaftliche Gesellschaft in 1996 for his work on Fermat's Last Theorem.[5] Since 1998 he has been a member of the Göttingen Academy of Sciences.[6]

In 2006 he received the Certicom ECC Visionary Award for his contributions to elliptic curve cryptography.[7]

See also[edit]


  1. ^ Gerhard Frey, Mathematics Genealogy Project. Accessed January 24, 2010
  2. ^ 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. 
  3. ^ 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. 
  4. ^ Hankerson, Darrel; Vanstone, Scott; Menezes, Alfred J. (2004), Guide to Elliptic Curve Cryptography, Springer, pp. 170–171, ISBN 9780387952734 ..
  5. ^ Die Gauß Medaille (in German), Braunschweigische Wissenschaftliche Gesellschaft. Accessed January 24, 2010
  6. ^ "Member list" (PDF). Göttingen Academy of Sciences (in German). Retrieved January 24, 2010. 
  7. ^ "Certicom ECC Visionary Award" (PDF). Code and Cipher 3 (1): 1. 2006. Retrieved January 24, 2010. 

External links[edit]