"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."
From 2004 to 2008, she was a Clay Mathematics Institute Research Fellow and an assistant professor at Princeton University. In 2008, she became a professor of mathematics at Stanford, where she lives with her husband and 3-year-old daughter.
Mirzakhani's recent research further investigates the symmetry of surface geometry, particularly within theories regarding Teichmüller dynamics. In general, her work can best be described as pure mathematics — research that investigates entirely abstract concepts of nature that might not have an immediately obvious application.
"Oftentimes, research into these areas does have unexpected applications, but that isn't what motivates mathematicians like Maryam to pursue it. Rather, the motivation is to understand, as deeply as possible, these basic mathematical structures," said Ralph Cohen, a professor of mathematics and the senior associate dean for the natural sciences in Stanford's School of Humanities and Sciences. "Maryam's work really is an outstanding example of curiosity-driven research."
The work, however, could have impacts concerning the theoretical physics of how the universe came to exist and, because it could inform quantum field theory, secondary applications to engineering and material science. Within mathematics, it has implications for the study of prime numbers and cryptography. Despite the breadth of applications of her work, Mirzakhani said she enjoys pure mathematics because of the elegance and longevity of the questions she studies.
"I don't have any particular recipe," Mirzakhani said of her approach to developing new proofs. "It is the reason why doing research is challenging as well as attractive. It is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out."
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