The professor at Stanford University in California was among four Fields Medal recipients at the International Congress of Mathematicians held in Seoul, and the first female among the 56 winners since the prize was established in 1936.
“This is a great honour. I will be happy if it encourages young female scientists and mathematicians,” Ms Mirzakhani was quoted as saying on Stanford’s website.
“I am sure there will be many more women winning this kind of award in coming years,” she said.
Ms Mirzakhani, 37, was born in Tehran and lived there until she began her doctorate work at Harvard University.
Mirzakhani got her bachelor in math from Iran’s prestigious Sharif University of Technology in 1999 and received her master and PhD degrees from Harvard University in the United States in 2004.
She said she had dreamed of becoming a writer when she was young, but she pursued her enthusiasm for solving mathematical problems.
Ms Mirzakhani was recognised for her work in understanding the symmetry of curved surfaces, according to the Stanford site.
She has also won the Blumenthal Award for the Advancement of Research in Pure Mathematics and the Satter Prize of the American Mathematical Society.
She became full professor of Mathematics at the age of 31 in 2008 at Stanford University where she is currently working.
Her research interests mainly include hyperbolic geometry, Teichmüller theory, ergodic theory, and symplectic geometry.
“It is fun – it’s like solving a puzzle or connecting the dots in a detective case. I felt that this was something I could do, and I wanted to pursue this path,” she said.
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.
In a statement, the ICM announced that fluent in a remarkably diverse range of mathematical techniques and disparate mathematical cultures, Mirzakhani embodies a rare combination of superb technical ability, bold ambition, far-reaching vision, and deep curiosity.
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.