Fermat's Last Theorem is one of the most famous theorems in the history of mathematics.

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 of mathematics.

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 theorem.

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.

 

Central Michigan University, CMU, gets chance at math challenge
October 14, 2006. Source: 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 years.

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 now."

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.