Some of the great women mathematicians include Hypatia, Agnesi, and Noether; each contributing their own piece into the world of mathematics.
Hypatia, more often remembered for her violent death, was one of the last great thinkers of ancient Alexandria and one of the first women to study and teach mathematics, astronomy and philosophy (source). Hypatia's father, Theon, one of the most educated men in Alexandria (source), taught mathematics and astronomy to Hypatia. She even worked with her father on some of his commentaries. Some think that Book III of Theon's version of Ptolemy's Almagest was actually the work of Hypatia (source). It is also thought that Hypatia helped her father in producing a new version of Euclid's Elements (source).
When searching for information on Maria Gaetana Agnesi, the first few things that appear are related to the "Witch of Agnesi" which is a curve that she studied in 1748 in her book Instituzioni analitiche ad uso della gioventù italiana, which is also the first surviving mathematical work written by a woman (source). In 1738 she published a collection of complex essays on natural science and philosophy called Propositiones Philosophicae, based on the discussions of the intellectuals who gathered at her father's home. In many of these essays, she expressed her conviction that women should be educated (source). Agnesi began working on her most important work at the age of twenty where she started dealing with differential and integral calculus in Analytical Instituations. The publication of her work in 1748 caused a sensation in the academic world, becoming a model of clarity that was widely translated and used as a textbook (source).
The search for Emmy Amalie Noether brought up many statements such as "Most Significant Mathematician You've Never Heard Of" and "Creative Mathematical Genius" both of which sparked my interested, so I dug deeper. Noether invented a theorem that united with magisterial concision two conceptual pillars of physics: symmetry in nature and the universal laws of conservation (source). So what is this theorem? "If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time" (source). In the 1920s, Noether did foundational work on abstract algebra, work in group theory, ring theory, group representations, and number theory (source).
Not only can women do mathematics but they can do it well. Small contributions that helped develop further understandings later on. There's obvious proof that women can indeed do math, so why is this topic even an issue?
Gender stereotype. That's why. As a society, for some reason, we are bred to believe that one gender does certain things better than others. This, however, is not correct. There are several women in math who accomplish great things. Three of them are listed above. And while these three may have made their contributions years in the past, there are several women today that are accomplishing great things. There are several women in the math department at Grand Valley. If women couldn't do math, wouldn't the department be solely men? They're obviously doing something right.
Women themselves need to believe that they are capable of doing math, as well. If you're smart, embrace it, don't shy away just because it's not "accepted" in society. Gender stereotypes will (hopefully) change and you're going to regret staying in your comfort bubble when you could be out doing something great. Maybe use a pseudo name like Ms. Sophie Germain did to get started. She created this and she was a woman. Who's to say you couldn't do the same?