There is no question that male mathematician's like Euler, Newton, and Euclid made remarkable impacts in the world of math, but there are many women of the past that did the same. When I think back to middle school and high school I don't remember learning about relevant women in the field of math, or in science for that matter. Here are a few women that made contributions to mathematics:
1. Amalie Noether: Noether was born in Germany into an already very mathematical family. She was highly influential in the world of mathematics. Amalie published papers that dealt with abstract algebra and ring theory. It was debated whether math should be more applied rather than conceptual, but Noether's work on abstract algebra led to principles unifying algebra, geometry, linear algebra, topology, and logic. Her most notable impact to mathematics is with her theorem, known simply as "Noether's Theorem." This boils down to differentiable symmetry of the action of a physical system, with respect to a Lagrangian function, has a corresponding conservation law.
2. Maria Agnesi: Agnesi, born in Milan in 1718, is most recognized for her work on differential and integral calculus as shown in her book, Analytical Institutions. It is said that she originally wrote Analytical Institutions for her brothers but it was eventually published in 1748 for the greater good. The first few sections of this textbook include the analysis of finite quantities, maxima, minima, tangents, and inflection points. Also included in this text is Agnesi's equation to the cubic curve, shown below, now known as the "Witch of Agnesi," which is y = a*sqrt(a*x-x*x)/x.
3. Sophie Germain: Germain is one of the first mathematicians, male or female, to come up with part of a solution to Fermat's Last Theorem in regards to a large class of exponents. A Sophie Germain prime is a prime number n where 2n+1 is also prime. Her prime numbers make appearances in number theory and even cryptology.
4. Florence Nightingale: Florence Nightingale focused more on statistical findings, as she would collect, tabulate, interpret, and present graphical displays of descriptive statistics. The well known and widely popular pie chart was preceded by Nightingale's "polar-area diagram," which shown below.
These women had some trouble being able to get their ideas out in to the public as skepticism ran high when seeing a female's name in a heading. Some of the women went as far as publishing their work under a male name to get recognition.
Equality between men and women can be a touchy subject so I will tread lightly, but it has come a long way. Generally, we tend to associate men to fields of study in the math and sciences which according to a study done by the National Science Foundation (http://www.nsf.gov/statistics/wmpd/2013/pdf/tab2-9_updated_2014_05.pdf) we aren't far off as there are almost 4 times the amount of males that enter the field of engineering than females. To further this though, some may believe that males are better suited for these fields of study rather than women. This stereotype or theory that people may have might be impacting the number of women entering math and science related fields. It is interesting to follow the history of women in mathematics and see how far our society has come because of them.
On a personal level, I came in to college declaring a major in engineering and my Engineering 101 class would provide some great evidence of the lopsided ratio of men to women in a science related field. There was only one other female in my discussion class of EGR 101 out of roughly 40 students! I spent about 1 1/2 years taking classes for this major and I will say that I did feel that many of the guys felt as if they were superior to the women in terms of there technical skills and ability to grasp the concepts. As I transitioned to a mathematics major I noticed many more females in my classes and that feeling of male dominance was non existent. I felt the field of Engineering was just not for me and perhaps I switched majors because of the constant pressure I felt to prove myself to the guys, but if this were the case it was a subconscious thought. Whatever the case may be, I am very happy I switched to mathematics!