Science News posts a two-part series on Sophie Germain [Wiki] -- a mathematician born in France in 1776. The article describes Germain as "the first woman known to have discovered significant mathematical theorems." (Hypatia from the 4th Century is worth noting, though she is not known for any particular theorems)
Germain assumed the identity of a male student and took classes from Lagrange. She read class notes and sent in assignments under the name of the male drop-out. Lagrange found out her secret:
According to a commentator at the time, Lagrange "went to her to express his astonishment in the most flattering of terms," and the commentator goes on to say that "the appearance of this young 'geomètre' made quite a stir." Nevertheless, the barriers against Germain's inclusion in the mathematical community didn't come tumbling down.Later, she corresponded with Gauss under the male pseudonym, "Antoine-August LeBlanc." Gauss too discovered her real identity:
In 1806, Napoleon's armies were marching into Prussia, and Germain became concerned that Gauss might be in danger. She asked a friend who was a commander in the French artillery to find Gauss and ensure his safety. Her friend followed her request—but revealed her identity in the process.
Gauss initially responded with delight, writing to Germain: "The taste for the abstract sciences in general and, above all, for the mysteries of numbers, is very rare.… But when a woman, because of her sex, our customs and prejudices, encounters infinitely more obstacles than men in familiarizing herself with their knotty problems, yet overcomes these fetters and penetrates that which is most hidden, she doubtless has the most noble courage, extraordinary talent, and superior genius."
Gauss broke off correspondence with her shortly thereafter -- saying he was turning to astronomy and would have no more time for math.
Germain worked in isolation, taking on one of the most difficult problems in math, Fermat's Last Theorem. (It was not until 1995 that the theory was proven by Andrew Wiles, and that was in a roundabout fashion.) She defined what would be called Sophie Germain primes and worked on the math of elastic surfaces.
Gauss convinced the University of Göttingen to give her an honorary degree. Unfortunately she died in 1831 before receiving it.