One of the earliest attestable female mathematicians is Hypatia, said to be the daughter of Theon, who was considered one of the most educated men in fourth-century Alexandria, Egypt. Hypatia is known for her in-depth work on sections of cones, ultimately leading to our understanding of ellipses, hyperboles, and parabolas.
The name Hypatia isn't a household word, but one female mathematician's name is: Florence Nightingale. Florence Nightingale is of course more well-known for her untiring work toward revolutionizing nursing and hospital sanitation, but in the process of providing evidence to support her arguments, she used and developed new techniques of statistical analysis and new ways to graphically represent that information.
Nightingale opened up the field of statistics by showing that social phenomena could be measured and analyzed mathematically. She is credited with creating the polar area diagram, also known as the Nightingale Rose diagram, to illustrate the nature and effects of medical care during the Crimean War.
In more recent times, Amalie "Emmy" Noether was one of the first women to receive a doctoral degree in mathematics in Germany, in 1907. In 1933, she escaped from Nazi Germany and immigrated to the United States, taking a teaching position at Bryn Mawr College. Noether's work in abstract algebra and theoretical physics gained her recognition among the greatest mathematical minds of the time. In fact, shortly after her early death in 1935, a letter to the editor of The New York Times stated that "Noether was the most significant creative mathematical genius thus far produced since the higher education of women began."
This is high praise indeed from the man who penned the statement — her fellow mathematician, abstract physicist, and friend Albert Einstein.