In class we discussed the famous mathematician, Sophie Germain. Upon discussing her I had thoughts that I’m sure many women in math have also had, “why have I never heard of a female mathematician until now?” This caused me to look into female mathematicians throughout history and what their accomplishments were.

The first known woman involved in mathematics is Hypatia. She was from Alexandria, Egypt, and was born sometime between 351-355 AD and died in 415. Her father, Theon, played a major role in her becoming the mathematician that she was. Theon was a professor at the University of Alexandria and was determined to have a “perfect child”[1]. This led to him teaching Hypatia to be very well rounded in all subjects, including math. Hypatia went on to teach at the University of Alexandria and became very popular. Her lectures often were on Diophantus’ “Arithmetica” and the techniques he used. One of the more interesting things about Hypatia was that she was not afraid to go to a group of men, and that she was highly admired by those men [2].

Elena Cornaro Piscopia was not only a mathematician, but was highly skilled in music, philosophy, and language. She was from Venice, Italy, and lived from 1646-1684. She was the first woman to ever receive a doctorate degree, in philosophy, not math, and was only thirty-two years old [3]. Another female mathematician who lived near the same time period of Piscopia was Émilie du Châtelet. She was a French mathematician and physicist who lived from 1706-1749. Her most famous work was the translation of Newton’s *Principia Mathematica [4].*

Sophie Germain is probably one of the most well-known female mathematicians. She was born in Paris, France 1776. She started her journey into mathematics around the age of 13 when she came across mathematical texts in her father’s library. She began to study them relentlessly, even though her parents did not support her. She began to have an interest in number theory after the release of Legendre’s *Essai sur la théorie des nombres. *From this point on she began to make huge progress in the field of number theory. As we all know she helped make advancements in the proof of Fermat’s Last Theorem, but she also went on to win an Academy Prize for her work in elasticity. While all this went on, I still find it interesting how she had support from many famous male mathematicians, such as Legendre, Gauss, and Poisson, yet when it came to publishing their own work or helping her further her own they were not as supportive. Germain was never mentioned in Poisson’s work, yet she helped him often and he had access to all of her work. Legendre began to help Germain in her work that won her the Academy Prize, but as time went on he refused to help her anymore. Women were not accepted as scholars during this time, so much so that Germain couldn’t even attend the Academy Prize sessions because she was a woman and not the wife of a male mathematician. It is truly amazing that through all the suppression she experienced that she was able to overcome it all to become one of the most well known female mathematicians ever [5].

Another female mathematician from a more current time period was Emmy Noether. She was born in Germany in 1882 and died in America in 1935. Noether was an algebraist and is known for her work in topology. She worked on Algebraic Invariant Theory and allowed the study of the relationships among the invariants to be possible. Invariant Theory deals with action of groups on algebraic varieties from the point of view of their effect on functions [7]. She made huge progress on ascending and descending chain conditions. A partially ordered set satisfies the ascending chain condition if every strictly ascending sequence of elements eventually terminates and it satisfies the descending chain condition if every strictly decreasing sequence of elements eventually terminates [9]. Most objects in abstract algebra that satisfy these conditions are called Noetherian after her. Some of these “Noetherians” include Noetherian induction, Noetherian modules, and Noetherian rings. Noether also did work in physics and published Noether’s First Theorem, which states that every differentiable symmetry of the action of a physical system has a corresponding conservative law, which she also proved [8]. She not only solved the problem for general relativity, but also determined the conserved quantities for *every* system of physical laws that possesses some continuous symmetry [6]. Noether’s advancements in math have lead others to call her the most important woman in the history of mathematics [6].

Lastly I will discuss a more current female mathematician, Maryam Mirzakhani. She was born in 1977 in Tehran, Iran. She has received many awards in her lifetime; she competed in two different International Mathematical Olympiads and received gold medals at both. She is also the first Iranian student to receive a perfect score at one of these Olympiads. In 2014 she was awarded the Fields Medal, an award that is given out every four years, to up to maybe four mathematicians under the age of forty. The award is often compared to the Nobel Prize of mathematics. She is the first female and Iranian to ever win the award [10]. Jordan Ellenberg explained her research when she won her award:

… [Her] work expertly blends dynamics with geometry. Among other things, she studies billiards. But now, in a move very characteristic of modern mathematics, it gets kind of meta: She considers not just one billiard table, but the universe of all

possiblebilliard tables. And the kind of dynamics she studies doesn’t directly concern the motion of the billiards on the table, but instead a transformation of the billiard table itself, which is changing its shape in a rule-governed way; if you like, the table itself moves like a strange planet around the universe of all possible tables … This isn’t the kind of thing you do to win at pool, but it’s the kind of thing you do to win a Fields Medal. And it’s what you need to do in order to expose the dynamics at the heart of geometry; for there’s no question that they’re there [10].

Mirzakhani is a modern day mathematician we can all look up to; she has accomplished things that no mathematician has, not just female mathematicians.

Overall throughout looking at the history of some famous women in math I have realized how amazing these women truly were. They were able to overcome many obstacles and repression to further advance a subject that they love, and I love: math.

[1] http://www.math.wichita.edu/history/Women/hypatia.html

[2] http://en.wikipedia.org/wiki/Hypatia

[3] http://www.agnesscott.edu/lriddle/women/piscopia.htm

[4] http://womenshistory.about.com/od/sciencemath1/ss/Women-in-Mathematics-History_4.htm#step-heading

[5] http://en.wikipedia.org/wiki/Sophie_Germain

[6] http://en.wikipedia.org/wiki/Emmy_Noether

[7] http://en.wikipedia.org/wiki/Invariant_theory

[8] http://en.wikipedia.org/wiki/Noether%27s_theorem