Math Professor Lauren Williams Explores New Ground

Williams feels at home researching underexplored subjects.

Lauren Williams

Lauren Williams
Photograph by Jim Harrison

Jealous of elementary-school classmates who spoke foreign languages, Robinson professor of mathematics Lauren Williams found another way to communicate: code. Employing math tricks and patterns, she and her sister developed a system for conversing. Initially more interested in words than numbers, she’d attempted to write and illustrate her own fantasy novel. But after winning a fourth-grade math competition in her hometown of Palos Verdes, California, computation ascended. Summer programs for high-school students taught her that her interest wasn’t just a list of rules, but a creative field: “The idea that I could figure out something new that nobody knew before was very cool.” She entered the College interested in combinatorics, but no classes on the subject existed. Unfazed, Williams took algebra courses and worked on a combinatorics thesis with Richard Stanley at MIT. After graduating in 2000 and enrolling in a Ph.D. program there, she continued exploring new and under-studied fields: cluster algebras, tropical geometry. Her research continued as a professor at UC Berkeley, starting in 2009, where she made further breakthroughs with the positive Grassmanian, a shape whose points represent components of simpler geometric objects. This work has helped her model shallow-water waves and subatomic particle collisions—and become only the second woman to receive tenure in Harvard’s math department, in 2018. “As a researcher, what’s probably most rewarding to me is finding connections between fields that you don’t expect to be talking to each other.” Though most thinking takes place at her desk, some ideas emerge when playing with her children, six and nine. “Mama,” one said on her fifth birthday, “this is the greatest year of my life: I’m five, my name starts with an E, and I was born in May.” The patterns continue. 

Read more articles by Jacob Sweet
Related topics

You might also like

Landscape Architect Julie Bargmann Transforming Forgotten Urban Sites

Julie Bargmann and her D.I.R.T. Studio give new life to abandoned mines, car plants, and more.

Preserving the History of Jim Crow Era Safe Havens

Architectural historian Catherine Zipf is building a database of Green Book sites.  

Most popular

What Trump Means for John Roberts's Legacy

Executive power is on the docket at the Supreme Court.

Harvard’s Endowment, Donations Rise—but the University Runs a Deficit

The annual financial report signals severe challenges to come.

Harvard’s New Playbook for Teaching with AI

Faculty across Harvard are rethinking assignments to integrate AI. 

Explore More From Current Issue

Wolfram Schlenker wearing a suit sitting outdoors, smiling, with trees and a building in the background.

Harvard Economist Wolfram Schlenker Is Tackling Climate Change

How extreme heat affects our land—and our food supply 

Professor David Liu smiles while sitting at a desk with colorful lanterns and a figurine in the background.

This Harvard Scientist Is Changing the Future of Genetic Diseases

David Liu has pioneered breakthroughs in gene editing, creating new therapies that may lead to cures.

A person walks across a street lined with historic buildings and a clock tower in the background.

Harvard In the News

A legal victory against Trump, hazing in the Harvard-Radcliffe Orchestra, and kicking off a Crimson football season with style