The International Mathematics Union awarded the prize Wednesday to Maryam Mirzakhani and three others.
The prize and $13,700 are awarded every four years to mathematicians 40 years old or younger. It was established in 1936.
Mirzakhani, 37, won for complex theoretical math on the symmetry of curved surfaces, including spheres and even doughnuts.
As a teenager, Mirzakhani won gold medals at international math contests. She earned her bachelor's degree in Iran and got her doctorate at Harvard University.
The other winners are Artur Avila, a Brazilian-born professor at the Institute of Mathematics of Jussieu in Paris, Manjul Bhargava of Princeton University and Martin Hairer of the University of Warwick in England.
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