Professor
Sue
Geller
of Texas A&M
University
gave a presentation Friday, Nov. 15, 2019, at 1 PM in GAB 104,
UNT on
Fermat's Last Theorem: History, Attempts,
Unsolved Issues.
The
talk
is open to all UNT men and women and is appropriate for
undergraduate students interested in mathematics as well as
graduate students, postdocs, and faculty. Dr. Geller is a Professor of
Mathematics, a Professor of Veterinary Integrative Biosciences,
and Director of Honors Programs in Mathematics at Texas A&M.
Abstract:
After
Pythagoras proved that A^2 + B^2 = C^2 for right triangles
with hypotenuse C, many mathematicians asked if there were
nonzero integers such that A^n +B^n = C^n for n>2. By the
third century, it was a common conjecture that no such
solution was possible for any n>2. In 1637, Pierre de
Fermat wrote in his copy of Diophantus's Arithmetica ``I have
discovered a truly remarkable proof which this margin is too
small to contain." This ``result" became known as Fermat's
Last Theorem, yet no proof of his was ever found, only a
correct proof for n=4. In 1993, corrected in 1995, Andrew
Wiles proved something much stronger from which the truth of
Fermat's Last Theorem came as a corollary. There still is no
direct proof of Fermat's Last Theorem.
This talk will
focus on the history of attempts to prove Fermat's Last Theorem,
some of the fields of mathematics which started in this pursuit,
a common proof technique with roots in Fermat's proofs for low
n, and conclude with a modern example of an attempt to prove a
special case using only what Fermat knew, where it went
deceptively wrong, and how to find such mistakes yourself. The
talk will be accessible to undergraduates, graduate students,
and faculty. All are welcome.
