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Until very recently society dictated that it wasn't very respectable for women to be mathematicians. In a patriarchal society where the world was dictated by the likes of men, women were oppressed if they had an opinion. Obviously, a woman establishing a theorem was unheard of. However there were a few women who dared to go against the flow and their achievements demonstrate that women have as much to contribute to Mathematics as any of their male counterparts.

It is hard to perceive who the first female mathematician was. Hypatia was certainly one of the earliest. She was born in 370 CE. She was the daughter of Theon, the last known member of the famed library of Alexandria. She followed his footsteps in the study of mathematics and astronomy. She collaborated with her father on commentaries of classical mathematical works, translating them and incorporating explanatory notes, as well as creating commentaries of her own and teaching a succession of students from her home. A philosopher, a follower of Neoplatonism, a belief system in which everything emanates from the One, Hypatia was highly popular among crowds who listened to her public lectures about Plato and Aristotle.
 
Born in an Era of revolt and revolution, Sophie Germain was born in the year 1776. Paris was exploding with revolution when young Sophie retreated to her father’s study and began reading. After learning about Archimedes’ death, she began a lifelong study of mathematics and geometry, even teaching herself Latin and Greek so that she could read classic works. Unable to study at the École Polytechnique because she was female, Germain obtained lecture notes and submitted papers to Joseph Lagrange, a faculty member, under a false name. When he learned she was a woman, he became a mentor and Germain soon began corresponding with other prominent mathematicians at the time. She became the first woman to win a prize from the French Academy of Sciences, for work on a theory of elasticity despite not having formal training and access to resources that male mathematicians had at that time. Her proof of Fermat’s Last Theorem, though unsuccessful, was used as a foundation for work on the subject well into the twentieth century.
 
Augusta Ada Byron, born on December 10, 1815, (later Countess of Lovelace) was brought up single handedly by her mother after her father , poet Lord Byron was forced to leave England due to a scandal shortly after her birth. Her overprotective mother, who wanted her to grow up to be unemotional and unlike her father, encouraged her study of science and mathematics. As an adult, Lovelace began to correspond with the inventor and mathematician Charles Babbage, who asked her to translate an Italian mathematician’s memoir analyzing his Analytical Engine (a machine that would perform simple mathematical calculations and be programmed with punchcards and is considered one of the first computers). Lovelace went beyond completing a simple translation, however, and wrote her own set of notes about the machine and even included a method for calculating a sequence of Bernoulli numbers; this is now acknowledged as the world’s first computer program.

Because Russian women could not attend university, Sofia Vasilyevna (1850-1891) contracted a marriage with a young paleontologist, Vladimir Kovalevsky, and they moved to Germany. There she could not attend university lectures due to societal norms, but she was tutored privately and eventually received a doctorate after writing treatises on partial differential equations, Abelian integrals and Saturn’s rings. Following her husband’s demise, Kovalevskaya served as lecturer in mathematics at the University of Stockholm and later became the first woman in that region of Europe to receive a full professorship. ‘She continued to make great strides in mathematics, winning the Prix Bordin from the French Academy of Sciences in 1888 for an essay on the rotation of a solid body as well as a prize from the Swedish Academy of Sciences the next year’.

In 1935, Albert Einstein wrote a letter to the New York Times, praising profusely the recently deceased Emmy Noether as “the most significant creative mathematical genius thus far produced since the higher education of women began.” Noether had overcome many hurdles before she could collaborate with the famed physicist. She was brought up in Germany and her mathematics education suffered a great deal because of rules against women matriculating at universities. ‘After she finally received her PhD, for a dissertation on a branch of abstract algebra, she was unable to obtain a university position for many years, eventually receiving the title of “unofficial associate professor” at the University of Göttingen, only to lose that in 1933 because she was Jewish.’ And so she moved to America and became a lecturer and researcher at Bryn Mawr College and the Institute for Advanced Study in Princeton, New Jersey. There she developed many of the mathematical foundations for Einstein’s general theory of relativity and made significant advances in the field of algebra.

Despite being bound by the backward, orthodox societal norms, these women showed remarkable progress in the field of Mathematics and Science. It is noteworthy how they achieved excellence in their respective fields despite lack of resources and a prevalent chauvinistic society.  It is undoubtedly true that we would have never achieved the milestones of success in the field of Mathematical Science if it hadn’t been for these and hundreds of other strong-headed women who decided to defy the society for good, and push the world of Science into a more progressive stage.