Today Breakthrough Prize Foundation Announces Maryam Mirzakhani New Frontiers Prize for Women Mathematicians, to be awarded to outstanding early career outstanding women scientists in the field of mathematics. The award in the sum of $50,000 award will be presented to women mathematicians who have completed their PhDs within the past two years. In announcing this award, which comes at the heels of the Breakthrough Foundation’s Award Ceremony yesterday, which was started by group of tech executives that includes Mark Zuckerberg, and Anne Wojcicki, among others. Richard Taylor, the chair of Selection Committee for Mathematics, said that “recognizing some of the many aspiring women in mathematics is a fitting tribute to the beautiful intellect of Dr. Mirzakhani.” In such a way, it hopes to eternalize the memory of a famed female mathematician.
Maryam Mirzakhani was the first woman to receive the Field’s Medal in Mathematics, which is the most prestigious honor in the field of mathematics. She was born in Teheran, Iran and has showed outstanding mathematical promise early on, winning mathematics olympiads in Iran and also a gold medal at the International Math Olympiad in Hong Kong. After completing studies in Iran, she come to Harvard to do her PhD in mathematics, and where she took her notes in Persian. At Harvard, she was noted to be very curious and inquisitive, as well as persistent. Later on, she went to be a professor at Princeton University and then at Stanford University.
Maryam Mirzakhani’s work in mathematics lies in a highly complex and abstract area known as Riemann geometry and space moduli, which belongs to a branch of pure mathematics. Many of us who took calculus may remember Riemann sums, which is a way to calculate an area under the curve of a function using rectangles. Now imagine that instead of describing the area under the curve, you are trying to understand the principles of what maybe a weirdly shaped geometrical object in some space. Roughly speaking this would be a way to conceptualize abstract spaces. Riemann was the first mathematician, who 100 years ago, realized the importance of studying abstract spaces. This field of mathematics belongs to pure mathematics – it is a branch of mathematics that concerns itself the fundamental principles and the mathematical expression of those principles as expressed in the derivation of proofs. These proofs then contain the most powerful expression the laws of our world, which later can be used and applied to a wide variety of disciplines in applied mathematics and physics and eventually make our way into the world in the form of technological innovation.
Would a candle illuminate the full space of the dark room it is in or would some areas or points in the room remain dark? This a type of mathematical problem that has puzzled mathematicians since the 1950s and an easy example that each of us can visualize that would help us understand the field of mathematics that Dr. Mirzakhani worked in. Although it may surprise you, this has been a very challenging problem to solve known as the “illumination problem” due to the fact that abstract geometries in space are illusive to understand mathematically and visualize. This is the field that Maryam Mirzakhani worked in mathematically. In in her most famous work in 2013, together with Alex Eskin, she provided the solution to this problem, explaining that that light will travel around and illuminate all room shapes, except ones that polygonal rooms with angles which are fractions of whole numbers, and there only a finite number of points would remain unlit.
The above simple illustration conceptualizes a very abstract field of mathematics, which no doubt requires a special gift and talent, and imagination, which Maryam Mirzakhani’s possessed. In fact, her PhD advisor, Curtis McMullen, also a Field Medalist, said:
“She had a sort of daring imagination. She would formulate in her mind an imaginary picture of what must be going on, then come to my office and describe it. At the end, she would turn to me and say, “Is it right?” I was always very flattered that she thought I would know.”
Imagination, curiosity and creativity are integral in science, as I have written before. In fact, Maryam Mirzakhani’s daughter described her mother’s work as a ‘painting’ because she would doodle around and write mathematical formulas around it. May more women be inspired by Myriam Mirzakhani’s example, to be pioneers and painters in the fields of science and mathematics!