The math paper proves Sogge's local smoothing conjecture for the wave equation in every dimension n ≥ 2. From that it derives the Bochner–Riesz conjecture, Stein's square function bounds, Fourier restriction in the interior of the conjectured range for the sphere, cone and paraboloid, and the Kakeya maximal and Kakeya set conjectures in all dimensions. OpenAI's 3D Kakeya, Bochner–Riesz and local-smoothing papers from September are now special cases. Their curved-surface restriction paper (family 077) only overlaps, on the sphere and paraboloid.
Everything rests on one estimate at the critical exponent p_c = 2n/(n−1), proved with a logarithmic loss. The proof uses none of the standard tools of the field (decoupling, induction on scales, polynomial partitioning). It builds a positive conserved tensor from the wave, couples it to a quaternionic Monge–Ampère equation, and controls an energy borrowed from Kähler geometry.
Announcing three major scientific discoveries, one each in mathematics (harmonic analysis), computer science (complexity theory), and physics (quantum field theory).
AI starting to help us improve our understanding of the universe! openai.com/index/building-sc…
How you can benefit:
Cold exposure activates brown fat.
Repeated cold exposure can increase brown fat activity over weeks.
You can use these methods:
- End your normal shower with cold water for 30–90 seconds. Increase the time slowly.
- Keep room temperature around 19 °C (66 °F) for several hours each day.
- Take short cold-water immersions (about 10–15 °C / 50–59 °F) for 2–5 minutes, 2–4 times per week. Start with shorter times.
These steps can improve blood sugar control, blood fat levels, and inflammation markers.
They may lower the risk of heart and metabolic diseases over time.
Cold exposure works best when you do it regularly, not as a single extreme session.
Brown fat under the arm & on our backs is activated by cold exposure and generates heat. Study of 8,700 patients finds brown fat, especially under the armpits, is associated with fewer cardiometabolic diseases & better glucose, lipid profiles & inflammatory markers @nature 🥶 💪
Tao says open, interpretable math models are coming "very soon".
Math 2.0
Terence Tao
terrytao.wordpress.com/2026/…
The extreme wording that has circulated around AI for years now: terrified, destroyed, wiped out, apocalypse, existential, is now being applied to math.
2026-09-14: ahmath.net registered (Spanish registrar; registrant country France), hosted on French co-ops (Ouvaton, vox.coop). Public Sympa list-info “contact” owners: François Le Maître (Univ. Bourgogne Europe), Lorenzo Riva, Max Weinreich.
2026-09-20: Pablo Shmerkin (@PabloShmerkin) calls it a “new(ish)” association on his site. SciAm quotes Naomi Sweeting pointing readers to ahmath.org as critics go public.
2026-10-07: AHM Statements page created 20:16 UTC, the day after OpenAI’s release. Tao guest-posts it that day (Mathstodon @tao; Bluesky @teorth). 2026-10-08: Indian Express and NDTV Profit cover it, calling the group US-based. Today: public roster 808 members, 532 in the “AI-free caucus.” @ahmathorg exists; I found no posts. Sources: ahmath.org, lists.ahmath.net, WHOIS, arXiv, blogs above.
2026-09-12: birth announcement on Proofs and Prompts (received Sept 11), signed only “AHM communications group.” proofsandprompts.com/2026/09…
2026-09-06: ahmath.org registered (Namecheap, registrant redacted). 2026-09-07: Squarespace site, NYC timezone. Roster #001 Weinreich; 002–005: Naomi Sweeting (@MIT), Vesna Stojanoska (UIUC), Chu, Joshua Grochow (@CUBoulder).
2026-09-10: An anonymous comment on Terence Tao’s blog adds the AHM link “following Max Weinreich (one of the organization committee).” Same day, PhD student David (@randomnumbers, Substack) says he, Kirwin Hampshire, and Chu joined.
2026-08-09: Caltech PhD student Tasmin Chu publishes “The AI dissenter viewpoint,” citing Weinreich. Her site now says she’s on the AHM organizing committee too. No X found; she writes at tasmin.substack.com/
2026-08-03: Weinreich posts arXiv:2608.02859, “The crisis of AI-generated mathematics,” arguing total opposition to AI in math (forthcoming, Notices of the AMS). Homepage: on the AHM organizing committee. arxiv.org/abs/2608.02859
1/10 Who is behind the Association for Human Mathematics (AHM), whose statement on OpenAI’s Oct 6 math release went viral? Public record, short version: a volunteer organizing committee of working mathematicians, formed early Sept. @ahmathorg
The statement is signed “Communications Working Group.” AHM’s site names contacts Lorenzo Riva (@Harvard @HarvardCMSA) and Guglielmo Nocera (@Institut_IHES). The Organizing Committee’s only named contact: Max Weinreich (@Baruch_College).