He continued his postgraduate studies at Heidelberg University, where he received his PhD in 1970,[4] and his Habilitation in 1973.

Until 2009, he held a chair for number theory at the Institute for Experimental Mathematics at the University of Duisburg-Essen, campus Essen.

[5] This approach provided a framework for the subsequent successful attack on Fermat's Last Theorem by Andrew Wiles in the 1990s.

[6] In 1998, Frey proposed the idea of Weil descent attack for elliptic curves over finite fields with composite degree.

[7] Frey was awarded the Gauss medal of the Braunschweigische Wissenschaftliche Gesellschaft in 1996 for his work on Fermat's Last Theorem.