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The death of the Tehran-born Mirzakhani, who specialised in theoretical mathematics, came three years after she received the Fields Medal at an event in Seoul.
The prize is handed out every four years to honour mathematicians under 40 who make major contributions. Mirzakhani was 37 when in 2014 she became the first woman to win the prize, which was established in 1936 and is equivalent to the Nobel Prize for mathematics.
The mathematician received the medal for her work in understanding the symmetry of curved surfaces, Stanford officials said in 2014.
Mirzakhani is survived by her husband, Jan Vondrák, and a daughter, Anahita. A Stanford spokesman said he did not have any information on where Mirzakhani died.