The Art of Maryam Mirzakhani’s Mathematics
When we think of math, most of us don’t immediately draw a connection to painting. But to mathematician Maryam Mirzakhani’s daughter, that’s just how her mother’s work looked – like “painting.” The first woman and the first Iranian to win the prestigious Fields Medal, Maryam had just turned 40 when she died earlier this year. Her contributions to the field of math “open[ed] new frontiers of research that are just starting to be explored,” according to her thesis advisor Curtis McMullen, and she set the course for women across the world to rise in the field of mathematics.
Growing up, Maryam did not want to be a mathematician. With an active imagination and a passion for storytelling, she had wanted to be a writer until she began to enjoy and excel at math in school with the help of an encouraging teacher. Once she embraced her aptitude for math, there was no stopping her. She and her friend Roya Beheshti, now a math professor at Washington University in St. Louis, made the Iranian math Olympiad team in 1994, where Maryam’s score earned her a gold medal. Maryam never lost her love of storytelling, however; she even compared her research in mathematics to the process of writing a novel:
“There are different characters, and you are getting to know them better,” she told Quanta Magazine in 2014. “Things evolve, and then you look back at a character, and it’s completely different from your first impression.”
In 1999, Maryam came to the U.S. to attend graduate school at Harvard, where she was drawn in by the study of hyperbolic geometry. Hyperbolic geometry, put simply by Scientific American, “describes surfaces that are curved like a Pringles potato chip or the curly ends of a leaf of kale. Unlike chips or vegetables, however, these surfaces close up like donuts, usually with multiple holes. If that is hard to visualize, there’s good reason: The surfaces Mirzakhani studied were not bound by the constraints of the real world.”
These surfaces are incredibly complex to study. At the time that Maryam started graduate school, mathematicians were unable to figure out exactly how many “simple” closed loops – loops that close neatly without intersecting themselves multiple times – of a certain length could exist on a hyperbolic surface. In her 2004 doctoral thesis, Maryam created a formula to determine how the number of simple loops increases as the size of the hyperbolic surface increases. In doing so, she also solved two additional major research questions on moduli spaces.
When she was awarded the Fields Medal in 2014 “for her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces,” Maryam became the first ever woman to receive the prize. The Fields Medal, first awarded in 1936, is considered one of the highest honors a mathematician can receive. Given to those aged 40 and under, the prize is intended not only to mark great achievement but also to encourage further triumphs for young mathematicians.
Although Maryam was only able to continue her research for a few years after being awarded the Fields Medal, her impact on the field and on other young mathematicians is undeniable. Her tenacity, in addition to answering major research questions, opened doors for other young women to triumph in the field of math! Her work serves as an inspiration for the next generation of kids to follow their passions and push through barriers toward success.
This article is part of a series on women in STEM – check our blog soon for the next one!