Maryam Mirzakhani, the first woman to receive the prestigious Fields Medal for mathematics, has died in the US.
The 40-year-old Iranian, a professor at Stanford University, had breast cancer which had spread to her bones.
Nicknamed the "Nobel Prize for Mathematics", the Fields Medal is only awarded every four years to between two and four mathematicians under 40.
It was given to Prof Mirzakhani in 2014 for her work on complex geometry and dynamical systems.
Iranian President Hassan Rouhani said Prof Mirzakhani’s death caused "great sorrow," state media reported.
Foreign Minister Mohammad Javad Zarif said her death was a cause for grief for all Iranians.
Prof Mirzakhani and her husband, Czech scientist Jan Vondrak, had one daughter.
Some social media users criticised Iranian officials for not using recent images of Prof Mirzakhani which showed her uncovered hair. Iranian women must cover their hair in line with a strict interpretation of Islamic law on modesty.
Stanford University President Marc Tessier-Lavigne described Prof Mirzakhani as "a brilliant mathematical theorist and also a humble person who accepted honours only with the hope that it might encourage others to follow her path".
"Maryam is gone far too soon but her impact will live on for the thousands of women she inspired to pursue math and science," he said.
"Her contributions as both a scholar and a role model are significant and enduring and she will be dearly missed here at Stanford and around the world."
Born in 1977, Prof Mirzakhani was brought up in post-revolutionary Iran and won two gold medals in the International Mathematical Olympiad as a teenager.
She earned a PhD at Harvard University in 2004, and later worked at Princeton before securing a professorship at Stanford in 2008.
Her receipt of the Fields Medal three years ago ended a long wait for women in the mathematics community for the prize, first established in 1936.
Prof Mirzakhani was also the first Iranian to receive it.