The usual common belief that women are bad at mathematics meets its match in Hypatia and several other lesser known female mathematicians. One of these was recognized in her lifetime as the second Hypatia. She was Maria Gaetana Agnesi, eldest child of a mathematics professor at the University of Bologna, Pietro Agnesi. She was from early on recognized as a child genius, learning seven languages by the age of 11. She studied ballistics and geometry at the age of 14, eventually devoting herself full time to calculus and wrote the first book discussing both differential and integral equations. She was, unfortunately, prone to ill health and developed seizures which were ascribed to too much study.
Her most important publication was the two-volume Instituzioni analitiche ad uso della gioventù italiana, (Analytical Institutions for the Use of Italian Youth) (1748) which served as an important textbook on Euler's calculus. In the book she discusses a particular curve called by Grandi versoria or "versiera" in Italian, an apparent pun for "witch." For some reason the curve, which was analyzed by Agnesi, became "Agnesi's Witch." She was elected to the Bologna Academy of Sciences, based on this work.
Even in the male-dominated academic society of Italy in the Eighteenth Century, she was included in the highest intellectual circles of Bologna and was appointed a professor of mathematics, natural philosophy and physics at the University of Bologna by Pope Benedict XIV. She, unfortunately, never served, having taken up the religious life in support of the poor and elderly. She apparently worked on mathematics only to please her father and considered it just a hobby. One wonders what she would have accomplished if she had continued her studies after her father's death!
She died in the poor house she worked in and was buried in a mass grave.
Internet References:
Maria Gaetana Agnesi http://www.agnesscott.edu/...
Maria Gaetana Agnesi http://www.britannica.com/...
Maria Gaetana Agnesi http://www.math.wichita.edu/...
Maria Gaetana Agnesi http://en.wikipedia.org/...