Have you observed an ant sitting on a sugar donut? As it crawls over the surface, you may have noticed it tries to find the shortest path to get to another point on the donut’s surface.
On a curved surface, measuring this straight line between two points is not easy. But Dr Maryam Mirzakhani from Stanford University has been able to calculate this distance.
Her research in the field of geometry on hyperbolic surfaces, led her to win the Fields medal – often regarded as the Nobel prize of mathematics. Dr Mirzakhani is the first woman to win this prestigious medal in its 78 year history. She shares the prize with three other eminent young mathematicians Artur Avila, Manjul Bhargava and Martin Hairer.
The World Of Geodesics
In case you are wondering why we would be interested in the shortest distance on a donut, it is because the donut has a curved surface similar to our own Earth. Many of us travel from one part of the world to the other, and we would all like our trips to be as short at possible.
Did you know that most flights that travel long distances chart their path to go over the North Pole? A flight from Seattle to Istanbul would rather travel north along its longitude to the North Pole and then make its way southwards along the longitude that runs towards Turkey. There could be other efficient paths to get to our destination that may be unexplored. It is this study of lines along curved surfaces that is known as geodesics.
Geodesics are actually fascinating. A path along curved surfaces, if extended endlessly on both directions, will eventually form a circle. Like in spheres, geodesics can be drawn on complicated shapes like a donut or pretzel. In some of these complex shapes, the line may even cross itself! Dr Mirzakhani’s work studies a way to count the geodesic and actually tell if a line crossed over itself. Her work actually counts uncrossed geodesics separately.
The Fields Medal is an award given once every four years that recognizes outstanding mathematical achievement 'for existing work and for the promise of future achievement', by the International Congress of Mathematicians. Each time the Congress meet, up to 4 awards could be granted. Since the medal is given to young talent, Fields Medalists should not have celebrated their 40th birthday before January 1st of the Year of the Congress.
For Dr Mirzakhani, math had never been her childhood passion. She had dreamed of being a writer! However, growing up during difficult times in Tehran, Iran, she was encouraged to seek and overcome challenges. Math began to fascinate her during her higher grades.
Dr Mirzakhani's story is certainly remarkable, and it is an inspiration to girls and women that math need not belong to the domain of men alone!