It was first given out in 1936?and news has broken that, this year, Stanford profesor Maryam Mirzakhani has become the first woman to win the prize. Per this profile in Quanta Magazine, Mirzakhani was raised and received her undergraduate degree in Iran before attending graduate school at Harvard, where she finished her doctoral thesis in 2004. She's won the Fields for her work with the "dynamics and geometry of Riemann surfaces and their moduli spaces" which?and I apologize to mathematicians out there for whatever I do to butcher this description?roughly means that she considers abstract questions related to non-Euclidean entities such as, for example, the surface of a pretzel.
Here's something from the Quanta piece that may or may not make you feel better about your own brain:
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