At Microsoft Frontier in Paris with @satyanadella, Eiffel Tower in the backdrop. My takeaway so far: the model is the easy part. Context, harness, access and trust are where the real work is. #AI

The Church around the corner.

Just another Friday on Île de la Cité.

Update Sept 11, 2026: Today, CMI shares in the excitement of the global mathematical community as we contemplate the announcement that the Navier-Stokes problem has apparently been settled. claymath.org/news/navier-sto…

20/ Worse: a list designed to resist machines is a benchmark wearing a prize costume. It gets optimized against on day one. So maybe the successor isn't a list of conjectures at all. Maybe it's a criterion: What distinguishes a 166-page Lean certificate from math understanding?

17/ BQP ≠ BPP What it is: Prove that quantum computers are genuinely more powerful than classical ones. Why it matters: We've built an industry on assuming it. It has never been proven.

15/ The Status of the Continuum Hypothesis What it is: Is there a size of infinity sitting between the counting numbers and the real numbers? Why it matters: Gödel and Cohen proved our axioms can't answer it. Woodin asks whether there's a right answer anyway.

13/ Do One-Way Functions Exist? What it is: Functions that are easy to compute and infeasible to reverse. Locks without keys. Why it matters: All modern cryptography assumes they exist. It's strictly stronger than P ≠ NP — proving P ≠ NP would not save RSA.

11/ Constructive QFT for the Standard Model What it is: Build the mathematics of the actual theory of particle physics, rigorously, in four dimensions. Why it matters: Yang-Mills was the warm-up. The full theory — matter, renormalization — is what physics actually runs on.

9/ A Rigorous Theory of Turbulence What it is: Derive the observed statistical laws of turbulent flow — Kolmogorov's scaling — from the Navier-Stokes equations themselves Why it matters: Turbulence is the last unsolved pbl of classical physics. We model it. We don't understand it