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Mirzakhani, 37, was born in Tehran and lived there until she began her doctorate work at Harvard University. She said she had dreamed of becoming a writer when she was young, but she pursued her enthusiasm for solving mathematical problems.
Mirzakhani was recognised for her work in understanding the symmetry of curved surfaces, according to the Stanford site.
The prizes are awarded every four years. Wednesday’s prizes were presented by South Korean President Park Geun-hye, the first woman to hold that post.
The other three Fields Medal winners on Wednesday were Artur Avila of the National Centre for Scientific Research in France and Brazil’s National Institute for Pure and Applied Mathematics; Manjul Bhargava of Princeton University and Martin Hairer of the University of Warwick in the United Kingdom.