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Levent Alpöge

Mathematician, member of technical staff, Anthropic · as of 2026-10-04 · source

Wikipedia

Number theorist at Anthropic behind a run of Claude-assisted results in 2026, including the claimed Jacobian-conjecture counterexample and elliptic-curve rank records.

News mentioning Levent Alpöge (8)

  1. OpenAI claims a Millennium Prize problem: 10,000 AI agents prove forced Navier–Stokes blow-up; priority dispute erupts ★★★★★

    On 8 Sep 2026 OpenAI released a 166-page paper and a Lean formalisation proving that the 3D incompressible Navier–Stokes equations with a smooth external force can develop a finite-time singularity from smooth initial data. This fits option (C) of Fefferman's official Clay problem statement. About…

  2. Caltech team (Anandkumar) reports a stable self-similar singularity candidate for the unforced 3D Euler equations on R³, found with PINNs and LLM help ★★★

    On 7 Sep 2026, the evening before OpenAI's Navier–Stokes announcement, Anima Anandkumar's Caltech group posted a self-similar singular profile for the unforced incompressible 3D Euler equations on all of R³. Physics-informed neural networks found it, and LLMs helped simplify the bounds and…

  3. Claude-assisted construction claims a complex structure on the 6-sphere, answering Hopf's 1947 problem (pending verification) ★★★★★

    On 23 Aug 2026 Anthropic's Levent Alpöge posted a 100+ page document, produced with an internal Claude model, claiming that the 6-sphere S⁶ admits an integrable complex structure. This would answer Hopf's 1947 question. A Lean formalisation was reported on 27 Aug. Experts describe an emerging…

  4. Claude-assisted search breaks the elliptic curve rank record: rank 30, then 31 ★★★

    An elliptic curve over Q with rank at least 30 was reported on 20 Aug 2026 and one with rank ≥31 on 23 Aug. These broke the Elkies–Klagsbrun rank-29 record from 2024. The rank-31 curve has 31 explicit independent rational points, so the bound is unconditional. The ICARM record page credits Claude…

  5. Claude-assisted constructions complete Hadamard matrices for every order below 2000, including 668 ★★★

    Claude-assisted searches constructed Hadamard matrices for the 12 remaining unknown orders below 2000 (668, 716, 892, 1132, 1244, 1388, 1436, 1676, 1772, 1916, 1948, 1964). Order 668 had been the smallest open case of the Hadamard conjecture for about 21 years.

  6. Claude proves more than two-thirds of Riemann zeta zeros are simple and on the critical line (up from 41.6%) ★★★★★

    Anthropic reported that an unreleased research version of Claude, running in Claude Code with ~60 subagents, raised the unconditional lower bound on the proportion of Riemann zeta zeros that are simple and on the critical line from ~41.6% to 67.2%. The previous 37 years had added only ~0.8…

  7. Hessian conjecture refuted in five variables, derived from Claude-found Jacobian counterexample ★★★

    Five days after Levent Alpöge's Claude Fable 5-assisted counterexample to the Jacobian conjecture, Guowu Meng and Liang Yang used "Schur descent" on it to build a five-variable counterexample to the related Hessian conjecture. The Hessian conjecture now holds for n≤3, fails for n≥5, and is open…

  8. Claude Fable 5 finds a counterexample to the Jacobian conjecture in dimension 3 ★★★★★

    Anthropic mathematician Levent Alpöge posted an explicit polynomial map F: C³→C³ with constant Jacobian determinant −2 that is not injective, found with Claude Fable 5. This refutes Keller's 1939 Jacobian conjecture in every dimension n≥3; the two-variable case remains open. Within days…

Posts (4)

Mentions are matched automatically by name, so a few may be about a namesake. Last checked 2026-10-04. All people · corrections: contact@postcutoff.com