Lauren Williams receives MacArthur ‘genius grant’

Lauren Williams is a theoretical mathematician who recently felt stagnant in her research, a persistent annoyance for an academic grappling with challenging conceptual dilemmas.

Then, while Williams was engrossed in her home office, she received an astonishing notification: The MacArthur Foundation called to notify her that she had achieved a prestigious “genius grant” — a “no-strings-attached” fellowship that allocates $800,000 over five years to recipients.

“I was utterly astonished,” reflected Williams, Dwight Parker Robinson Professor of Mathematics. “I was essentially verifying for myself that I was awake and this was genuine.”

Williams was amongst the 22 fellows announced on Wednesday. The MacArthur Foundation commended Williams for “clarifying unforeseen links” between her domain of algebraic combinatorics and other fields in mathematics and physics.

The foundation remarked: “With a research approach driven by curiosity and a readiness to collaborate across disciplines, Williams is enhancing foundational mathematical theory and forging valuable connections between mathematics and various scientific realms.”

Williams focuses on algebra and combinatorics and their applications to challenges in mathematics and physics. In simple terms, combinatorics explores discrete, finite items that can be enumerated as opposed to those that are continuous — think of the seamless surface of the ocean in contrast to the waves.

A significant portion of her research deals with the “positive Grassmannian,” a geometric form whose points correspond to more straightforward geometric entities.

Other researchers have found that her theoretical contributions relate to a variety of phenomena including shallow water waves, tsunamis, fundamental particle collisions, protein synthesis, and the movement of traffic on one-way streets.

Williams remains both intrigued and bemused regarding why the positive Grassmannian continues to appear in such varied domains. “It’s one of the greatest enigmas I’ve encountered,” she stated.

Williams finds motivation in a quote from the British mathematician G.H. Hardy: “The mathematician’s patterns, like the painter’s or the poet’s, must possess beauty; the ideas, like the colors or the words, must harmonize together. Beauty is the primary criterion: There is no lasting place in the world for unattractive mathematics.”

“If you pose a question and the answer is not beautiful, then you asked the wrong question.”

At an artistic level, Williams observes numerous parallels between her work in pure mathematics and the arts: all solve problems within the constraints of their medium; all incorporate patterns, beauty, and harmony.

“If you pose a question and the answer is not beautiful, then you asked the wrong question,” she remarked.

Raised in the suburbs of Los Angeles, Williams grew up as an avid reader, aspiring writer, and violinist. In fourth grade, she recognized her aptitude for math after winning her school district competition, and she consistently nurtured her interest through summer programs and math contests.

As an undergraduate at Harvard, she majored in mathematics when there were no women on the department faculty.

After securing her Ph.D. at MIT, she returned to Harvard on a Benjamin Peirce postdoctoral fellowship and spent nine years on the faculty at the University of California at Berkeley before rejoining Harvard in 2018 as only the second female tenured professor in the Math Department’s history.

With the MacArthur grant shining a spotlight on her niche in academia, Williams aspires to motivate other young women aiming for careers in mathematics.

“When I was a student, I was quite anxious about whether I could secure an academic position and whether a career in academia would align with having children,” said Williams, now a mother of two. “To students contemplating a career in math academia but harboring similar concerns, I wholeheartedly encourage them to pursue it.”

Her career has been a balancing act — sometimes very literally. As a young professor, Williams had an infant who was an unpredictable sleeper, and night after night, she and her husband alternated rocking the child to sleep by bouncing on a yoga ball.

“If you’re holding a baby in a dim room, gently swaying, there is nothing you can do but think,” observed Williams. “One night, I began contemplating a question and that actually led to my next paper.”

Today, Williams is one of three women in the Harvard math faculty. This small group is achieving a remarkable track record with MacArthur Fellowships: Melanie Matchett Wood was recognized as a MacArthur Fellow in 2022.

(Also included in this year’s MacArthur cohort was Hahrie Han ’97, a political science professor at Johns Hopkins University, acknowledged for her research on how individuals engage in civil and political matters.)

For Williams, this accolade arrives at a particularly opportune moment. She had three federal research grants terminated in May — one of which was for a conference scheduled for the subsequent month, compelling her and her colleagues to hastily reorganize the event.

“This award truly couldn’t arrive at a more suitable moment, personally,” she stated.

On a broader scale, the acknowledgment signifies more than just an individual scholar. Like her cherished positive Grassmannian, her success mirrors that of many others.

“I’m astonished and honored, but also profoundly grateful to the numerous, if not hundreds, of extraordinary teachers, mentors, collaborators, friends, and family members who have supported me,” affirmed Williams. “The most overwhelming reaction for me is genuine gratitude.”