What's this about?
Separately from Claude's Riemann work, the Heil–Ramanathan–Topiwala (HRT) conjecture was disproven with AI assistance — a counterexample was found — and Terence Tao, one of the world's leading mathematicians, wrote up a "partial digestion" of how the counterexample works.
What exactly is a "counterexample"?
A conjecture is a mathematical claim believed true but unproven. You can prove it true, or you can *disprove* it by finding a single counterexample — one concrete case where the claim fails. HRT concerned whether certain sets of shifted-and-modulated functions are always linearly independent; the AI-assisted work produced a case where they aren't.
Why is this notable?
It's the *second* AI-assisted math result in a single week (alongside Claude's Riemann bound), and Tao engaging with it lends heavyweight credibility. Together they mark AI shifting from doing homework problems to contributing to open research-level mathematics.