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NMSU professor unearths manuscripts revealing first female research in mathematics

Thanks to New Mexico State University mathematics professor David Pengelley, pioneering 19th century female mathematician Sophie Germain is getting the recognition she deserves.

Research by NMSU mathematics professor David Pengelley has shed new light on the work of pioneering female mathematician Sophie Germain. (NMSU photo by Darren Phillips)

As reported by Science News Online, by examining hundreds of pages of notes housed in the Bibliotheque Nationale in Paris, Pengelley, along with Virginia Polytechnic and State University professor and former NMSU professor Reinhard Laubenbacher, found that Germain's contribution to mathematics, particularly the legendary mathematical problem known as "Fermat's Last Theorem," was much greater than previously known.

Pierre de Fermat, a 17th century mathematician and founder of the modern study of number theory, knew from classical Greek mathematics that the square of a whole number can be the sum of the squares of two other whole numbers. For instance, 25 is the square of the number 5 and is also the sum of the squares 9 and 16. This is a fairly common occurrence in squared whole numbers.

Fermat wondered if something similar could happen for cubes or higher powers. He asserted that it was impossible; that no cubed number could be the sum of two other cubed numbers and the same was true for any power above 2. He claimed in the margin of his notes that he had developed a proof of this, but said the margin was not large enough for him to provide this proof.

"He was the kind of person who would leave it for other people to prove as true," Pengelley said of Fermat's choice to not supply his evidence.

Fermat's proof was never found and for 350 years his theorem baffled mathematicians around the globe.
Finally, in 1994, Fermat's assertion was demonstrated to be correct. It is one of the most sophisticated and complicated proofs in the history of mathematics.

It seems, however, that despite the discrimination toward women during the 1800's, Germain was "the first person to develop a realistic plan to prove Fermat's Last Theorem," according to the Science News Online article.

In the two-part series available at www.sciencenews.org the author describes the circumstances surrounding Germain's work.

It was not accepted for women to participate in higher education and Germain's parents unsuccessfully attempted to snuff out her interest in mathematics early in her life. Women weren't allowed to attend the universities in France at the time, so in order to pursue her work, Germain assumed the identity of a male student. Eventually her true identity was revealed but due to the impression her work had made on noted mathematician Joseph-Louis Lagrange, she was granted limited access to the academic community.

Still, she did not receive the acclaim or credit that contemporary male mathematicians enjoyed and her work remained largely unknown until Pengelley and Laubenbacher reviewed her notes. It was then revealed that whereas most people studying the problem at the time only attempted to solve the problem for individual powers, Germain had developed a system to solve the equation for any possible power, a revolutionary concept.

"I personally believe that she intended to submit (one of her manuscripts) to the French academy for the prize for Fermat's Last Theorem," Pengelley is quoted as saying in Science News Online.

Even though Pengelley says the proof Germain created is incomplete, it was far ahead of its time and had it been created by a male mathematician, he believes a position at a university and publication of the material would have been guaranteed. However, due to her marginalized status, her work may never have even been recognized for what it was.

"She was the first woman in the world who did important original mathematical research," Pengelley said. "Other women had been students, teachers and writers of mathematics, but not researchers."

Pengelley presented his work at the Joint Mathematics Meetings in San Diego. He intends to publicize Germain's work as much as possible, including producing French-language articles for publication in France.

"I hope it will increase the inspirational nature of Germain's work," Pengelley said, "especially for women."

More information on the work of Sophie Germain and the research of Pengelley can be found at www.math.nmsu.edu/~davidp.