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![\"Germain_5\"](\"http:\/\/blogs.oregonstate.edu\/historyofscience\/files\/2014\/05\/Germain_5.jpeg\")
<\/a>On May 20, 2014, the OSU Department of Mathematics sponsored a history lecture by Dr. David Pengelley, of New Mexico State University. Dr. Pengelley presented an animated lecture on the French mathematician, Sophie Germain (1776-1831). Dr. Pengelley\u2019s interest in Germain was sparked by his use of primary historical sources in his teaching of mathematics. This led him to a store of Germain\u2019s original manuscripts at the National Library of France, which had not been studied in over two hundred years. Revisiting Germain\u2019s work as a mathematician, Dr. Pengelley found that Germain had developed a sophisticated plan for proving Fermat\u2019s Last Theorem, making significant contributions to number theory. Until recently, her work was known only via a footnote in another mathematician\u2019s treatise (Legendre, Essai sur la Th\u00e9orie des Nombres<\/i>, 1823). Particularly in an age when women were not well-educated and when they were excluded from scientific academies, Germain\u2019s substantial achievements were indeed remarkable.<\/p>\nSophie Germain was only thirteen when the French Revolution broke out, forcing her to spend most of her time indoors. During that period, she turned to her father\u2019s library. Fascinated by books on mathematics, she taught herself against her parent\u2019s wishes (Pengelley relates that at one point they even took away her clothes and candles to prevent her from studying at night!). Germain\u2019s father was a silk merchant so it was not through his mentorship that she developed her abilities but rather through her own effort and perseverance. At one point, Germain took on the identity of a student at the \u00c9cole Polytechnique who had died (Antoine-August LeBlanc). When the professor discovered that it was really a woman who was submitting such fine work under LeBlanc\u2019s name, he was astonished. Germain eventually corresponded with Johann Carl Friedrich Gauss (1777-1855) in G\u00f6ttingen, one of the most celebrated mathematicians of the time. Pengelley recounts that upon receiving a letter from Germain, Gauss praised the way she contributed to the \u201ccharms of this sublime science,\u201d as giving him great joy.<\/p>\n
Pengelley gave a cogent and fairly detailed explanation of the theorem by Pierre de Fermat (c.1601-1665) that Germain was hoping to prove. Basically, the theorem states that no three positive integers a, b, and c can satisfy the equation an<\/sup>\u00a0+\u00a0bn<\/sup>\u00a0=\u00a0cn<\/sup> for any integer value of n greater than two. At the time that Germain was working on the problem, it was known that the theorem could be proven to hold for some numbers but much work remained before the theorem could be proven conclusively. Germain\u2019s letters and manuscripts demonstrate that she had a good handle on the problem and that she had made considerable progress toward a solution. Pengelley found that she had made a mistake in one of her proofs but peering closer found scribbled in the margins, \u201cvoyez errata\u201d\u2014Germain\u2019s own admission that she saw she had made an error!<\/p>\n Germain did win a prize from the French Academy of Sciences for her work on elasticity and she eventually was able to attend the Society\u2019s meetings, but she was never made a member nor was any of her work published. Her manuscripts were taken by Guillaume Libri, described by Pegelley as a \u201cmathematician, historian, bibliophile, thief, and friend of Sophie Germain.\u201d Because Libri ended up with her manuscripts, they were preserved and eventually made available for Pengelley\u2019s research. Finding a proof for Fermat\u2019s theorem has been a problem that has attracted the attention of mathematicians for a long time, however, in the twentieth century, it came to the fore because of its implications for cryptography. Andrew Wiley, a mathematician in England, finally solved the Fermat Theorem in 1995. It had been one of the most famous problems in mathematics and Sophie Germain\u2019s efforts made an important contribution to the discovery of a proof. Dr. Pengelley\u2019s work is of interest to historians in the way he has used primary sources to teach mathematical concepts but has also revived interest in an under-appreciated figure, Sophie Germain, whose achievements deserve to be more widely celebrated.<\/p>\n *Tamara Caulkins<\/a> is pursuing a Ph.D. in History of Science at Oregon State University.<\/p>\n","protected":false},"excerpt":{"rendered":" by Tamara Caulkins* On May 20, 2014, the OSU Department of Mathematics sponsored a history lecture by Dr. David Pengelley, of New Mexico State University. Dr. Pengelley presented an animated lecture on the French mathematician, Sophie Germain (1776-1831). Dr. Pengelley\u2019s interest in Germain was sparked by his use of primary historical sources in his… Continue reading