Professor
Sue Geller
of Texas A&M
University
will be
speaking 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.
