News Release
ONE OF THE CENTURY'S GREAT
MATHEMATICAL QUESTIONS IS RESOLVED
CONJECTURE HAS LINKS TO
FERMAT'S LAST THEOREM
Embargoed for release on November 10, 1999
For further information, contact:
Professor Henri Darmon, McGill University
e-mail: darmon@math.mcgill.ca
telephone: (514) 398-2263
fax: (514) 398-3899
November 10, 1999
PROVIDENCE, RI---Recently mathematicians succeeded in resolving one of the most
important questions to arise in number theory in this century. The achievement
represents a major advance in the field and provides compelling evidence in a
far-reaching research program that lies at the heart of modern number theory.
The Shimura-Taniyama-Weil conjecture, as the question is known, was a central
ingredient in Andrew Wiles's celebrated proof of Fermat's Last Theorem. Wiles
proved a special case of the conjecture, which was sufficient for his proof of
Fermat.
The Shimura-Taniyama-Weil conjecture is as mysterious as it is profound, for it
links two seemingly unrelated areas of mathematics: elliptic curves and modular
forms. For decades mathematicians studied these two areas, uncovering
mysterious connections between the two without being able to pin down the exact
relationship. Just as astronomers linked the heavens and earth through the
discovery that stars are made up of the same elements found here on earth, so
the proof of the Shimura-Taniyama-Weil conjecture provides a bridge between two
very different mathematical worlds, that of elliptic curves and that of modular
forms.
The proof of the conjecture provided mathematicians with plenty of reason to
cheer, but there is more. The Shimura-Taniyama-Weil conjecture is part of what
is known as the "Langlands Program", a vast mathematical edifice formulated by
the mathematician Robert Langlands. As the central paradigm for modern number
theory, the Langlands Program provides a bold and sweeping vision uniting whole
areas of mathematics. The proof of the Shimura-Taniyama-Weil conjecture, as
well as Wiles's work on Fermat's Last Theorem, provide intriguing insights into
the Langlands Program and promise to keep number theorists busy well into the
new millennium.
"The Shimura-Taniyama-Weil conjecture, and its subsequent, just-completed
proof, stand as a crowning achievement of number theory in the twentieth
century," writes number theorist Henri Darmon in the article "A Proof of the Full
Shimura-Taniyama-Weil Conjecture Is Announced". The article will appear
this week as a special Research News item in the December 1999 issue of the
Notices of the AMS.
Founded in 1999 to further mathematical research and scholarship, the
30,000-member AMS fulfills its mission through programs and services that
promote mathematical research and its uses, strengthen mathematical education,
and foster awareness and appreciation of mathematics and its connections to
other disciplines and to everyday life.
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