In the early 19th century, Sophie Germain (1776-1831) came up with some ideas to try to prove Fermat’s theorem under the hypothesis that \(n\) and \(2n+1\) were both primes. Today these numbers are known as Germain primes – primes that play a role in the RSA public key system, which is fundamental to the security of commercial exchanges on the internet. Germain’s ideas were not sufficient to prove the theorem for these cases, but they imposed strong restrictions on the existence of solutions.
The description of Archimedes’ death during the siege of Syracuse seems to be what sparked Germain’s passion for mathematics. She was self-taught, because as a woman she was barred from university – she would have liked to be educated at the École Polytechnique. Germain corresponded scientifically with illustrious mathematicians of the time – although given her female status, she used the pseudonym “M. Le Blanc” with some of them – including Lagrange, Legendre and Gauss, all of whom praised her mathematical qualities. In 1807, French troops occupied Brunswick, where Gauss lived. Germain knew the French general in command of the troops – he was a friend of his family – and, remembering the fate of Archimedes, asked him to show clemency to Gauss – whose Disquisitiones Arithmeticae she had already read. Gauss became aware of this intermediation, just as it was a woman who corresponded with him under the name of M. Le Blanc, which led him to express an opinion that was no doubt surprising given the misogynistic atmosphere of the time: “A person of her sex, because of our customs and prejudices, finds it infinitely more difficult than a man to get familiarised with these thorny investigations. If, in spite of this, she overcomes these obstacles and succeeds in penetrating into the deepest parts of these investigations, what she is showing is noble courage, extraordinary talent and superior genius”.
At this time when war is once again raging in Europe and Putin’s barbarity is raging in Ukraine, it is appropriate to recall Sophie Germain’s intercession for Gauss in one of the Napoleonic wars, and to wish the entire Ukrainian population, and in particular those who work in mathematics there, the luck they need to avoid the bombs and missiles that pour down on them every day.
References
Antonio J. Durán, Crónicas matemáticas, Crítica, Barcelona, 2018.
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