Four mathematicians have offered a proof of the Taniyama-Shimura conjecture, extending the earlier work that led to a proof of Fermat’s last theorem by Princeton’s Andrew Wiles.

Knapp, A.W. 1999. Proof announced of Taniyama-Shimura-Weil conjecture. Notices of the American Mathematical Society 46(September):863.

Conrad, B., F. Diamond, and R. Taylor. 1999. Modularity of certain potentially Barsotti-Tate Galois representations. Journal of the American Mathematical Society 12(April):521. (See http://www.ams.org/jams/1999-12-02/.)

Peterson, I. 1994. Fermat’s famous theorem: Proved at last? Science News 146(Nov. 5):295.

______. 1987. Closing in on Fermat’s last theorem. Science News 131(June 20):397.

Singh, S. 1997. Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem. New York: Walker.

A technical description of the Taniyama-Shimura conjecture can be found at http://www.treasure-troves.com/math/Taniyama-ShimuraConjecture.html.

Brian Conrad
Department of Mathematics
Harvard University
1 Oxford Street
Cambridge, MA 02138-2901

From Science News, Vol. 156, No. 14, October 2, 1999, p. 221. Copyright © 1999, Science Service.