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# Solving for fun (and sometimes prizes)

One early Saturday morning in December, senior Danielle Wang took a seat alongside 164 others taking the 2018 William Lowell Putnam Mathematical Competition in Walker Memorial.

For six hours she and 4,622 other undergraduates from 568 institutions in the United States and Canada struggled over enigmatic problems involving group theory, set theory, graph theory, lattice theory, and number theory. For some taking the test, the questions are baffling. But each winter since starting at MIT, Wang has taken the exam for fun.

“There are some interesting problems on the test every year,” she says. “Every year I hope I’ll do better than the previous year. You get some money if you do well, and I’d say you don’t lose anything if you don’t.”

She earned Putnam’s honorable mention last year. In her first Putnam exam, she took home the 2015 Elizabeth Lowell Putnam Prize, which is awarded each year to the top-ranking female competitor.

This year, she looked around Walker and could see many familiar faces from her Math Olympiad days. She began Math Olympiads in middle school. Raised by computer scientists in San Jose, California, Wang grew up watching her brother compete in math competitions. One day, she simply decided that she would, too.

“I think it was like, ‘Math is the hardest thing, so I have to do the hardest thing,’” she recalls. “I have become less sure that that’s the best reason, but it’s a decent reason, I think.”

She joined a weekly math circle and the American Regions Math League team. In seventh grade, she earned honorable mention as a Math Prize for Girls contestant; the next year she took first place, and remained in the top or second-place spot throughout high school. Wang collected top prizes in the USA Mathematical Talent Search, Bay Area Mathematical Olympiad, USA Mathematical Olympiad, the Math Prize Invitational Olympiad, the European Girls’ Mathematical Olympiad, and China’s Girls Math Olympiad.

It was her experience with the Math Olympiad Summer Program (MOP) that cemented her decision to pursue a mathematics career, and eventually to apply to MIT.

“MOP has had a huge effect on my life,” she says. “I think you learn skills from math contests that are useful for other things, including ‘real math.’ Now, that’s not something I even cared about back then, but I realize now that it was a great (and one-of-a-kind) opportunity for learning these skills. MOP was a major part of math competitions, and if it wasn’t for it I wouldn’t have found the opportunity or motivation to do math as much, or at all.”

At MIT, she transitioned into a mentor role for participants in MOP as well as the A-Star Summer Math Camp. She was a runner-up for the 2019 Alice T. Schafer Mathematics Prize from the Association for Women in Mathematics. Last summer, she participated in a prestigious math research program at the University of Minnesota at Duluth, which helped her to publish two papers: as sole author on “The Eulerian distribution on involutions is indeed γ-positive” in the Journal of Combinatorial Theory Series A; and, with MIT doctoral student Aaron Berger, “Modified Erdös–Ginzburg–Ziv Constants for Z/nZ and (Z/nZ)2” in Discrete Mathematics.

A couple of months after she took the Putnam, the results were published. The highest exam score was 114 out of a possible 120 points, with a median score of a mere two points. That means many talented Putnam contestants earned a big zero. Out of 4,622 test-takers, Wang came in 13th place.

As the highest-scoring female, she also earned her second Elizabeth Putnam prize, which comes with a $1,000 award. This prize was introduced in 1992 as a way to encourage more female contestants. Two other MIT Elizabeth Putnam Prize winners are Ruth A. Britto-Pacumio in 1994 and Yinghui Wang in 2010.

“Math competitions, such as the Putnam, have always been a male-dominated scene — which makes Danielle’s impressive performance even more so,” says three-time MIT Putnam Fellow Yufei Zhao, who is an assistant professor of mathematics.

Zhao teaches 18.A34 (Mathematical Problem Solving), the Putnam Seminar that discusses methods for solving Putnam problems from previous years. It is also a class that attracts few female participants. “I did not know it existed,” Wang says. “Then I found out that all of my freshman math contest friends were in it, and I was like, ‘Hey, no one told me!’”

Zhao hopes that more female students will take the Putnam exam. “I hope that Danielle’s success in math competitions and research can be an encouragement to other female students,” he says.

Sometimes Wang feels the burden of being such a role model. “People might ask you questions like you represent all the other girls who do math, and I have felt, at some points, pressure to do well to prove something about my whole gender.”

However, other sources of encouragement include a growing number of STEM programs and female-centric math competitions, such as the Math Prize for Girls that is held annually at MIT.

Wang, who recently was accepted into MIT’s math PhD program, says that she has always felt supported as a female mathematician at MIT and elsewhere. “In my experience, the math community is totally OK with people being female.”

Registration for the 2019 Putnam Competition will open on Sept. 1. The contest is open to undergraduate students who must participate through their enrolled college or university.