Maryam Mirzakhani: “It’s like solving a puzzle or connecting the dots in a detective case”

By Bjorn Carey

Maryam Mirzakhani, a professor of mathematics at Stanford, has been awarded the 2014 Fields Medal, the most prestigious honor in mathematics. Mirzakhani is the first woman to win the prize, widely regarded as the “Nobel Prize of mathematics,” since it was established in 1936.

(Photo courtesy of Maryam Mirzakhani)

“This is a great honor. I will be happy if it encourages young female scientists and mathematicians,” Mirzakhani said. “I am sure there will be many more women winning this kind of award in coming years.”

Officially known as the International Medal for Outstanding Discoveries in Mathematics, the Fields Medal has been presented by the International Mathematical Union at the International Congress of Mathematicians, held this year in Seoul, South Korea. Mirzakhani is the first Stanford recipient to win this honor since Paul Cohen in 1966.

The award recognizes Mirzakhani’s sophisticated and highly original contributions to the fields of geometry and dynamical systems, particularly in understanding the symmetry of curved surfaces, such as spheres, the surfaces of doughnuts and of hyperbolic objects. Although her work is considered “pure mathematics” and is mostly theoretical, it has implications for physics and quantum field theory.

“On behalf of the entire Stanford community, I congratulate Maryam on this incredible recognition, the highest honor in her discipline, the first ever granted to a woman,” said Stanford President John Hennessy. “We are proud of her achievements, and of the work taking place in our math department and among our faculty. We hope it will serve as an inspiration to many aspiring mathematicians.”

Mirzakhani was born and raised in Tehran, Iran. As a young girl she dreamed of becoming a writer. By high school, however, her affinity for solving mathematical problems and working on proofs had shifted her sights.

“It is fun — it’s like solving a puzzle or connecting the dots in a detective case,” she said. “I felt that this was something I could do, and I wanted to pursue this path.”

Mirzakhani became known to the international math scene as a teenager, winning gold medals at both the 1994 and 1995 International Math Olympiads – she finished with a perfect score in the latter competition. Mathematicians who would later be her mentors and colleagues followed the mathematical proofs she developed as an undergraduate.

After earning her bachelor’s degree from Sharif University of Technology in 1999, she began work on her doctorate at Harvard University under the guidance of Fields Medal recipient Curtis McMullen. She possesses a remarkable fluency in a diverse range of mathematical techniques and disparate mathematical cultures – including algebra, calculus, complex analysis and hyperbolic geometry. By borrowing principles from several fields, she has brought a new level of understanding to an area of mathematics called low dimensional topology.

Mirzakhani’s earliest work involved solving the decades-old problem of calculating the volumes of moduli spaces of curves on objects known as Riemann surfaces. These are geometric objects whose points each represent a different hyperbolic surface. These objects are mostly theoretical, but real-world examples include amoebae and doughnuts. She solved this by drawing a series of loops across their surfaces and calculating their lengths.