# Maryam Mirzakhani Explains The Work That Made Her The First Woman To Win A Prize In Mathematics

Stanford professor Maryam Mirzakhani became the first woman to earn the Fields Medal, the mathematics equivalent of the Nobel Prize. The Inquisitr reported on Maryam’s achievement yesterday, explaining that she won the prize for her work on “the dynamics and geometry of Riemann surfaces and their moduli spaces.”

In more basic terms described by Slate, Maryam’s work “roughly means that she considers abstract questions related to non-Euclidean entities such as, for example, the surface of a pretzel.”

If you’re still confused about what earned Mirzakhani the Fields Medal or what her brilliance in mathematics means in general terms, maybe you should give Maryam a chance to explain it herself. Vox reported on Maryam’s attempt to give a brief but detailed explanation of her studies on Riemann surfaces. Vox describes Maryam’s work even more simply as “understanding structures you can put on a surface.” You can watch the video above to see how Maryam became the first female to earn the award.

One of the examples Maryam Mirzakhani gives in the video is the mathematics of a billiard table. Maryam poses the question: If you hit a pool ball on a billiard table and it moves forever, what sort of patterns would it trace geometrically on the table? Would it eventually cover the entire surface? Mirzakhani also explains how her work pertains with the deformation of certain structures, like curved or inverted surfaces. What sort of geometric angles would come out of those deformed structures? What sort of surfaces would you get?

To go more in depth, Maryam talks about how geometry says a lot about very generic surfaces, for example a flat two dimensional square or rectangle. But the mathematics gets a lot more advanced when you start looking at the angles and geometry of very specific structures –particularly ones with curvature and unusual formations. This is the crux of the work that earned Maryam Mirzakhani her prize.

When The Guardianinterviewed Maryam about her work, this was her concise description:

“Most problems I work on are related to geometric structures on surfaces and their deformations. In particular, I am interested in understanding hyperbolic surfaces. Sometimes properties of a fixed hyperbolic surface can be better understood by studying the moduli space that parameterises all hyperbolic structures on a given topological surface.”

Maryam Mirzakhami was raised in Tehran, Iran. Maryam received her PhD from Harvard in 2004. When asked to comment about being the first woman to receive the Fields Medal, Maryam said:

“This is a great honor. I will be happy if it encourages young female scientists and mathematicians. I am sure there will be many more women winning this kind of award in coming years.”