SAN FRANCISCO, July 15 -- Stanford University mathematics professor Maryam Mirzakhani, the first and to-date only female winner of the Fields Medal since its inception in 1936, died Saturday at age 40.

In a news release, Stanford said Mirzakhani died after a long battle with cancer.

The quadrennial Fields Medal, which Mirzakhani won in 2014, is the most prestigious award in mathematics, often equated in stature with the Nobel Prize.

Born in Tehran, Iran, and self-professed as a "slow" mathematician, Mirzakhani specialized in theoretical mathematics that read like a foreign language by those outside of mathematics: moduli spaces, Teichmüller theory, hyperbolic geometry, Ergodic theory and symplectic geometry.

She attended an all-girls high school in Tehran, led by a principal unbowed by the fact that no girl had ever competed for Iran's International Mathematical Olympiad team. Mirzakhani first gained international recognition during the 1994 and 1995 competitions. In 1994, she earned a gold medal. In 1995, she notched a perfect score and two gold medals.

College at Sharif University in Tehran followed by and then graduated from school at Harvard University, where she was guided by Curtis McMullen, a fellow Fields Medal winner.

According to Benson Farb, a mathematician at the University of Chicago, Mirzakhani solved two longstanding problems in 2004. Either solution would have been newsworthy in its own right, but Mirzakhani then connected the two into a thesis described as "truly spectacular." It yielded papers in each of the top three mathematics journals.

She joined Stanford in 2008, where she served as a professor of mathematics until her death.

She denied herself the easy path, choosing instead to tackle thornier issues. Her preferred method of working on a problem was to doodle on large sheets of white paper, scribbling formulas on the periphery of her drawings. Her young daughter described her mother at work as "painting."

In recent years, Mirzakhani collaborated with Alex Eskin at the University of Chicago to take on one of the most-vexing problems in the field: the trajectory of a billiards ball around a polygonal table. The challenge began as a thought exercise among physicists a century ago and had yet to be solved. The resulting paper, now more than 200 pages in length, was published in 2013. It has been hailed as "the beginning of a new era" in mathematics and "a titanic work."

"Maryam is gone far too soon, but her impact will live on for the thousands of women she inspired to pursue math and science," Stanford President Marc Tessier-Lavigne was quoted as saying in the news release.

"Maryam was a brilliant mathematical theorist, and also a humble person who accepted honors only with the hope that it might encourage others to follow her path," he said.