Category: Mathematical Life
-
Every Theorem Begins with People
I was recently installed as the Robert G. and Maxine W. Scheibe Professor of Mathematics at Washington University in St. Louis. I’m honored by this recognition and grateful to the Scheibe family for their generosity, and to the University and my colleagues in the Department of Mathematics for their support. In my remarks, I told…
-
Go Get an Outside Offer
A senior colleague told me, more than once and always kindly, that if I wanted a raise I should go get an outside offer. He was not being cynical. He was doing me a favor; passing along, unprompted, the kind of thing nobody writes down and everybody is supposed to somehow already know. It was…
-
The Room Is Busier Than You Are
There is a particular piece of mental arithmetic I have done many hundreds of times, in many seminar rooms, and I have never once done it correctly. It goes: I am lost. Nobody else has asked anything. If I ask, thirty people will notice that I am lost, and some of them will remember. The…
-
The Gap That Closes and the Gaps That Don’t
Somewhere in my first year of graduate school, I decided I was behind, and I decided the fix was to work until I wasn’t. I don’t remember making this decision so much as arriving at it, the way you arrive at a habit; a seminar where two sentences in a row didn’t make sense, a…
-
Sounding Sure Is Not the Same Skill as Being Right
I’ve sat on grant panels where I watched two proposals land on the table back to back. One argued, with total fluency, for a result that was, if I’m honest, more hope than mathematics. The other was written by someone who understood the risks in their own approach better than anyone else in the room,…
-
Forty-One Hours: What Two Riesz Transform Papers Tell Us About AI and the Pace of Mathematics
On August 18, 2026, Yuyuan Ouyang, Daniel Spector, and Cody Stockdale posted a paper to arXiv settling a problem Elias Stein posed at the 1986 International Congress of Mathematicians: the best constant in the weak-type (1,1) bound for the vector Riesz transform on R^n is at most 2, independent of dimension. Forty years of open…
-
The Four Laws: From Thermodynamics to Mathematical Research
There’s something deeply satisfying about the number four in physics. The four laws of thermodynamics represent some of the most fundamental principles governing our universe. But what’s truly remarkable is how these laws appear, sometimes literally, sometimes metaphorically, in completely different domains. Let’s explore three “four laws” frameworks: classical thermodynamics, black hole thermodynamics, and a…
-
The Cost of Sitting on a Result
A while back I was finishing a paper with a few coauthors, extending an earlier result of ours to a more general setting. The key step, the thing that made the whole proof work, was, once you saw it, almost embarrassingly simple to state. It reframed a technical problem as something much more standard, and…
-
What Does the AI Proof of Crouzeix’s Conjecture Mean for Research Mathematics?
The recent solution of Crouzeix’s conjecture is remarkable mathematics. But the story of how the proof was found may be even more consequential for mathematicians. As described by Alex Townsend and Anne Greenbaum in SIAM News, Shanmu Jin, a neurosurgery resident and postdoctoral researcher with relatively little formal mathematical training, used GPT-5.6 Sol in ChatGPT…
-
The Habit Nobody Wants
What a self-taught miller can tell us about what actually separates successful researchers from everyone else. Nottingham, sometime around 1823. A miller named George Green climbs the stairs of his father’s windmill after a full day’s work, hauling sacks, tending the grindstones, breathing flour dust, and sits down under a candle with a borrowed mathematics…