How to Do Math Like a Medal-Winning Genius

Maryam Mirzakhani Courtesy of Maryam Mirzakhani

Maryam Mirzakhani, who was born and raised in Iran and is now a professor at Stanford University, has just become the first woman to win the highest honor in mathematics: the Fields Medal (pdf).

The work she does as a full-grown mathematician is so advanced that even the dumbed-down description of it is bewildering. To quote an article in the Guardian:

“Her thesis showed how to compute the Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces. Her research interests include Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry.”

Luckily, though, she did share an early childhood memory of a mathematical technique her older brother showed her that’s intelligible by ordinary people. “My first memory of mathematics is probably the time that he told me about the problem of adding numbers from 1 to 100,” she said in an interview with the Clay Mathematics Institute. “I think he had read in a popular science journal how Gauss solved this problem. The solution was quite fascinating for me. That was the first time I enjoyed a beautiful solution, though I couldn’t find it myself.”

The brute force way to add the numbers from 1 to 100 is to set up a long column like this:


and then add the 1′s column, the 10′s column, etc. The easy way is to pair the numbers like this:



There are 50 of these pairs, so the total is 50 x 101, or 5050. (For variations on this little trick, check out this website.) It’s a far cry from Teichmüller theory or symplectic geometry, but it does give a taste of the simple beauty that mathematicians strive for.