ISLAMABAD July 31 (TNS): Nearly three years after she became the first woman to win math’s equivalent of a Nobel Prize, Maryam Mirzakhani died of breast cancer at age 40. She had been a professor at Stanford University since 2008.
Mirzakhani, a Stanford University professor, died in hospital in California after cancer in her breast spread to her bone marrow. The university president, Marc Tessier-Lavigne, said Mirzakhani’s influence would live on in the “thousands of women she inspired” to pursue maths and science.
Mirzakhani is survived by her husband, Jan Vondrák, and a daughter, Anahita — who once referred to her mother’s work as “painting” because of the doodles and drawings that marked her process of working on proofs and problems, according to an obituary released by Stanford.
“A light was turned off soon — far too soon. Breaks my heart,” former NASA scientist Firouz Naderi said in a tweet. He later added, “A genius? Yes, but also a daughter, a mother and a wife.”
Early in her life, Mirzakhani had wanted to be a writer. But her passion and gift for mathematics eventually won out.
“It is fun — it’s like solving a puzzle or connecting the dots in a detective case,” Mirzakhani said on winning the prestigious Fields Medal in 2014. “I felt that this was something I could do, and I wanted to pursue this path.”
Mirzakhani was born in Tehran, Iran, and she lived in that country before coming to the U.S. to attend graduate school at Harvard University. By then, she was already a star, having won gold medals in the International Mathematical Olympiad in the mid-1990s, after becoming the first girl ever named to Iran’s team.
“There were more accolades. Mirzakhani was the first Iranian woman elected to the National Academy of Sciences last year, in recognition of her ‘distinguished achievement in original research.’ She was in good company: Albert Einstein, Thomas Edison and Alexander Graham Bell were past honorees.”
Describing Mirzakhani’s work, Stanford says:
“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.
“In short, Mirzakhani was fascinated by the geometric and dynamic complexities of curved surfaces — spheres, doughnut shapes and even amoebas. Despite the highly theoretical nature of her work, it has implications in physics, quantum mechanics and other disciplines outside of math. She was ambitious, resolute and fearless in the face of problems others would not, or could not, tackle.”
Mirzakhani, as said earlier, considered being a writer before turning to mathematics. It is unlikely she believed she’d made a choice in favor of an inferior, or less artistic, discipline. And she expressed her immersion in mathematics in language every writer will recognize – “like being lost in a jungle and trying to use all the knowledge you can gather to come up with some new tricks and with luck you might find a way out”.
The luck, of course, is no such thing. It’s the mystery Keats called “negative capability”, the trust that the work will do itself if only we dare to plunge without irritability or insistence into the dark, not sure we will find a way out at all. The best writing happens in this way, unintended, unknowing, grateful and surprised. Such abnegation of will is what we mean by creativity. So the mathematician and the artist are companioned in the same dark, and do obeisance to the same gods. The pity of Mirzakhani’s death will be felt by poets as well as mathematicians.
In Iran, her home country, tributes were led by the Iranian president, Hassan Rouhani: “The grievous passing of Maryam Mirzakhani, the eminent Iranian and world-renowned mathematician, is very much heartrending,” he wrote.
Mirzakhani made several contributions to the theory of moduli spaces of Riemann surfaces. In her early work, Mirzakhani discovered a formula expressing the volume of the moduli space of surfaces of type (g,n) with given boundary lengths as a polynomial in those lengths. This led her to obtain a new proof for the formula discovered by Edward Witten and Maxim Kontsevich on the intersection numbers of tautological classes on moduli space, as well as an asymptotic formula for the growth of the number of simple closed geodesics on a compact hyperbolic surface, generalizing the theorem of the three geodesics for spherical surfaces. Her subsequent work focused on Teichmüller dynamics of moduli space. In particular, she was able to prove the long-standing conjecture that William Thurston’s earthquake flow on Teichmuller space is ergodic.
Most recently as of 2014, with Alex Eskin and with input from Amir Mohammadi, Mirzakhani proved that complex geodesics and their closures in moduli space are surprisingly regular, rather than irregular or fractal. The closures of complex geodesics are algebraic objects defined in terms of polynomials and therefore they have certain rigidity properties, which is analogous to a celebrated result that Marina Ratner arrived at during the 1990s. The International Mathematical Union said in its press release that “It is astounding to find that the rigidity in homogeneous spaces has an echo in the inhomogeneous world of moduli space.”
Mirzakhani was awarded the Fields Medal in 2014 for “her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces”.[27] The award was made in Seoul at the International Congress of Mathematicians on 13 August.[28] At the time of the award, Jordan Ellenberg explained her research to a popular audience:
[Her] work expertly blends dynamics with geometry. Among other things, she studies billiards. But now, in a move very characteristic of modern mathematics, it gets kind of meta: She considers not just one billiard table, but the universe of all possible billiard tables. And the kind of dynamics she studies doesn’t directly concern the motion of the billiards on the table, but instead a transformation of the billiard table itself, which is changing its shape in a rule-governed way; if you like, the table itself moves like a strange planet around the universe of all possible tables … This isn’t the kind of thing you do to win at pool, but it’s the kind of thing you do to win a Fields Medal. And it’s what you need to do in order to expose the dynamics at the heart of geometry; for there’s no question that they’re there.[29]
