  In this explanatory work, we make an attempt to briefly discuss the work and
technical achievements of twenty female mathematicians. The work may be useful
as a historical resource, but there is very little biography or history, and
the primary focus is on the mathematics. In fact, the main use will probably be
for a student who is coming to a new area of mathematics for the first time and
needs an overview of some of the key results and references viewed through the
work of one of that area's main contributors. The work of the following
mathematicians is discussed: Sofia Kovalevskaya, Emmy Noether, Mary Cartwright,
Julia Robinson, Olga Ladyzhenska, Yvonne Choquet-Bruhat, Olga Oleinik,
Charlotte Fischer, Karen Uhlenbeck, Krystyna Kuperberg, Nicole
Tomczak-Jaegermann, Dusa McDuff, Karen Vogtmann, Carolyn Gordon, Frances
Kirwan, Leila Schneps, Claire Voisin, Olga Holtz, Maryam Mirzakhani and Maryna
Viazowska. There is a website based on this document
(https://tusindfryd.github.io/twenty-female-mathematicians/) created by
Dominika G\'oral. Changes, corrections, and additions can be suggested at the
website, but the website is currently not being actively maintained, so any
suggestions for corrections and changes will be made to the document instead.
The research areas of the mathematicians in question can be found at the
website.
