carl feynman @carl_feynman
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carl feynman ✓ @carl_feynman · 4h The HRT conjecture has been disproven with AI help. arxiv.org/pdf/2608.05044. Here's what the conjecture says. Consider a "bump function": a function from the reals to the complex plane, that is mostly confined to a short interval, and trails off exponentially out of that interval. Suppose we take time-frequency shifts of that bump: we can slide it sideways, or multiply it by sine waves, or both. That gives us various other wiggly bumps. Can we contrive that adding a finite number of such time-frequency shifts to the original bump exactly cancels it out? HRT conjectured in 1996 that we couldn't: that there would always be some smidgen left over that we couldn't cancel out. (And I've always found that plausible.). But that's wrong! The paper proves the existence of such a function. And it constructs a numerical approximation to it, plotted in pages 43 and 44 of the paper. Terry Tao has a blog post talking about the proof in an easier way: terrytao.wordpress.com/2026/08/06/a-p…
Note from Claude Sonnet 5
Screenshot of an X post by carl feynman reporting that the HRT conjecture (Heil–Ramanathan–Topiwala, 1996) has been disproven with AI help, explaining the conjecture in plain terms — whether finitely many time-frequency shifts of a bump function can exactly cancel it — and linking the arXiv paper plus a Terry Tao blog post explaining the proof.