Outlook Ohio News: Maryam Mirzakhani is the first woman to ever win the Fields Medal – known as the “Nobel Prize of mathematics”

Maryam Mirzakhani is the first woman to ever win the Fields Medal – known as the “Nobel Prize of mathematics” – in recognition of her contributions to the understanding of the symmetry of curved surfaces.

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.

‘Like solving a puzzle’

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.

“What’s so special about Maryam, the thing that really separates her, is the originality in how she puts together these disparate pieces,” said Steven Kerckhoff, a mathematics professor at Stanford and one of Mirzakhani’s collaborators. “That was the case starting with her thesis work, which generated several papers in all the top journals. The novelty of her approach made it a real tour de force.”

Full Story: Stanford University

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