Fermat's Last Theorem is one
of the most famous theorems in the history of
Despite how closely the problem is related to the
Pythagorean theorem, which has infinite solutions and
hundreds of proofs, Fermat's subtle variation is much
more difficult to prove. Still, the problem itself is
easily understood even by schoolchildren, making it all
the more frustrating and generating perhaps more
incorrect proofs than any other problem in the history
The 17th-century mathematician Pierre de Fermat wrote in
1637 in his copy of Claude-Gaspar Bachet's translation
of the famous Arithmetica of Diophantus: "I have a truly
marvelous proof of this proposition which this margin is
too narrow to contain."
For over 350 years, the
proof or disproof of this conjecture occupied the minds
of mathematicians. In fact, several more important or
useful theories were derived in the effort to prove this
It was finally proven using
very deep methods by Andrew Wiles in 1995 (after a
failed attempt a year before). Wiles, a mathematician
from Princeton, proved this theory in a work consisting
of more than 200 pages.
Michigan University, CMU, gets
chance at math challenge
October 14, 2006.
The Mourning Sun by Ian Patrick Gray
Mathematics forms the basis of nearly every
higher human endeavor including science,
architecture, music and technology.
There are some problems in mathematics, however,
that defy easy answers, such as Fermat's Last
Theorem, which defied solution for nearly 350
A $500,000 National Science Foundation grant
will put a few of those difficult (if less well
known) problems to the test of 30 Central
Michigan University undergraduates.
"They will be doing research in basic
mathematics, exploring the open problems in
math," said mathematics professor and
co-organizer Ken Smith. "This program is modeled
somewhat after some programs in the sciences,
where students begin to explore open questions
in chemistry or physics.
"What makes this novel is working with the
students on these problems for two years. As far
as I know, we are the only institution supported
by NSF for a long-term program for mathematics."
Beginning in June 2007, teams of three
undergraduate researchers and a faculty member
will begin to explore the boundaries of
mathematical understanding in the "Mentoring
Critical Transition Points" program. The grant
money will pay for stipends and housing for
students and student conferences, faculty summer
stipends and publishing research results.
"We're not after a giant problem," Smith said,
referring to Fermat's Last Theorem. "But we will
take students to the frontiers of mathematics,
where they will solve problems that have not
been solved before. They will get to contribute
to the field of mathematics. I hope they will be
excited by that and want to go on to graduate
studies in mathematics."
Each four-person team requires $25,000 each
year, Smith said.
Smith said there would be six fellowships
awarded in the spring to begin that summer. The
program targets freshmen and sophomores to
commit to the two-year program.
The NSF's grant is designed to help develop
mathematics in the United States by aiding
students at critical points in their careers.
"We are focusing on the development of college
students as they transition into professional
scientists and mathematicians," Smith said. "Our
grant will focus on undergraduate students doing
genuine mathematical research under the
mentoring of CMU math faculty. We will be
focusing on students at our own university and
helping CMU students become outstanding
professional scientists and mathematicians."
All together, the NSF authorized $1.5 million to
four schools, including CMU. The other schools
include the lead school, The University of
Richmond in Virginia ($500,000), Coppin State
University in Maryland ($250,000) and Olin
College in Massachusetts ($250,000).
The whole program will run 10 teams over four
years, Smith said.
"I just got back from a conference on
undergraduate research and the leaders of the
conference were saying that they want to see
more year-long research programs," Smith said.
"I started smiling because that's exactly what
we are doing here."
Smith said that part of the motive behind the
NSF grant was to create a model for multi-year
mathematics research programs that could be
duplicated at other universities.
"Hopefully, this will be the national model,"
Smith said. "I think CMU has a lot to be proud
of. We're certainly in the national spotlight
Interested CMU students, who need not be math
majors but who must commit to a program of
mathematics study, should contact Ken Smith at
989-774-6521 or e-mail:
Ken.W.Smith@cmich.edu . Applications are due no
later than Feb. 16, 2007.