Each year, the MacArthur Foundation announces its MacArthur Fellows or “Geniuses,” a class of researchers, scientists, artists, entrepreneurs and more who are changing the world through their endless creativity and groundbreaking contributions. And each year, Under the Radar with Callie Crossley highlights New England recipients of the award through its ongoing series “The Genius Next Door.” This is the first installment highlighting the Class of 2025.
Receiving the prestigious MacArthur Fellowship may be the most important prize of a professional’s career.
And for mathematician Lauren K. Williams, the start of that upward climb toward the MacArthur started after her very first math prize, back in the fourth grade.
“I’d studied a bit for this contest, and then it went much better than I was planning,” said Williams, the second female mathematics professor ever tenured at Harvard. “After that, several teachers took me under their wing, and really encouraged me and gave me more math to do.”
Decades later, Williams still has more math to do, and her pioneering work in theoretical mathematics has catapulted her to the forefront of her field.
Williams’ main focus of study is in the field of algebraic combinatorics, which connects counting problems with algebraic structures. She also studies a shape called the positive Grassmannian.
“[A] counting problem that you can do when somebody hands you something like a cube is to count the number of faces according to their dimension,” says Williams, explaining that we can all count the six sides or faces of a cube — two dimensions; 12 lines or edges of a cube — one dimension; and eight points or vertices of a cube — zero dimensions.
“So the positive Grasmannian is also a geometric object — a bit like a cube — but it can have much higher dimensions,” Williams said. “You can still do the same counting problem, so in my Ph.D, I came up with a formula to count how [the positive Grassmannian] breaks up into pieces of different dimensions.”
Unbeknownst to Williams, other scientists began using her formula for deconstructing the positive Grassmannian to decode seemingly-unrelated phenomena, such as traffic flow, translation protein synthesis and the patterns of how waves come together.
“That was actually really a big surprise to me — the connection between the positive Grasmannian and these other areas,” Williams said.
Along with her groundbreaking work, Williams also continues to push for more visibility and opportunities for girls and women in male-dominated mathematics and STEM fields. She says stereotypes and societal expectations are at the heart of what often hampers interest in math for girls in school. And it doesn’t stop after graduation, as illustrated by a recent experience she had with a large-language model.
“A few weeks ago … I asked ChatGPT, ‘What should a professor wear?’ And ChatGPT gave me two answers: a male outfit and a female outfit. And then I asked, ‘What should a math professor wear?’ And it only gave me the male outfit,” Williams said.
Still, Williams encourages all math-loving students to pursue degrees and enter academia, if that’s the path they envision for themselves. And now, with this MacArthur Foundation recognition, it’s her turn to serve as a role model for a whole new generation of fourth grade “math-prize recipients.”
“It’s a little intimidating to be put on that pedestal,” says Williams. “I hope I don’t fall off. I have a daughter who loves math. I’ve worked with many girls who love math, and so I just hope that many more of them come into this field.”
Guest
- Lauren K. Williams, theoretical mathematician at Harvard, member of the 2025 MacArthur “Genius” Fellows.
