Claude
A family is a named generation or product line. Scores below are the sum of its named releases and any documented internal systems in the same line.
Benefit
+6.01
Harm
0.00
Net Good
6.01
Releases
- ClaudeVersion unspecified
- Anthropic Internal Research Model — 2026-08Internal / unreleased
Leaderboard
| Rank | Model | Organization | Benefit | Harm | Net | Events | Last impact |
|---|---|---|---|---|---|---|---|
| 8 | Claude Claude · version unspecified | Anthropic | +2.54 | 0.00 | 2.54 | 5 | 8 Sep 2026 |
| 27 | Anthropic Internal Research Model — 2026-08 Claude · internal / unreleased | Anthropic | +1.49 | 0.00 | 1.49 | 1 | 10 Aug 2026 |
| 31 | Claude 3.7 Sonnet | Anthropic | +1.37 | 0.00 | 1.37 | 1 | 24 Feb 2025 |
| 42 | Claude Fable 5 | Anthropic | +0.62 | 0.00 | 0.62 | 3 | 21 Jul 2026 |
Timeline
Events
Buckmaster and Alpöge, using Sol and Claude, prove smooth-forced blowup for Euler, IPM, and Boussinesq
On 8–11 September 2026 Tristan Buckmaster and Levent Alpöge released Lean-backed finite-time blowup results with smooth forcing for incompressible porous media, 2D Boussinesq, and 3D Euler, crediting Anthropic’s Claude and especially OpenAI’s GPT-5.6 Sol. Astra was used only for writeups and auditing.
Alpöge credits Claude with a claimed complex structure on S^6
In late August 2026 Levent Alpöge posted a manuscript, produced with Claude, claiming a compact complex threefold diffeomorphic to the six-sphere. Independent writeups and a Lean formalization effort followed; expert review is ongoing and the claim is treated as disputed.
Claude, with Alpöge and Howell, posts rank ≥30 and ≥31 elliptic curves over Q
On 20 and 23 August 2026 the ICARM elliptic-curve rank leaderboard recorded new records of rank at least 30 and 31, with public witness points, credited to Claude working with Levent Alpöge and Ava Howell. Exact rank 30/31 is reported only under GRH and BSD.
A three-human plus Claude team is reported to construct a Hadamard matrix of order 668
In August 2026 Epoch’s open-problems index listed a Hadamard matrix of order 668 as Solved (AI) by a three-human plus Claude team, while the dedicated problem page still appeared to say open. The construction is included as disputed until those sources agree.
An unreleased Claude raises the critical-line zero bound for zeta from 41.6% to 67.2%
On 10 August 2026 Anthropic reported that an unreleased research Claude, prompted to attempt the Riemann hypothesis, instead improved the proven lower bound on zeros on the critical line from 41.6% to 67.2%. Anthropic mathematicians and two outside experts examined the argument. The Riemann hypothesis remains open.
Conant, with Claude Fable 5, proves the mod-4 Kawauchi conjecture
On 21 July 2026 Jim Conant posted a proof that the Conway polynomial of an amphicheiral knot satisfies ∇_K ≡ f(z)f(−z) (mod 4), a strengthening he had conjectured after the integral Kawauchi conjecture failed. He credits Claude Fable 5 with help producing the proof.
Long, using Sol Pro and Fable 5, posts low-degree Gaussian Moments counterexamples
On 20 July 2026 Christopher D. Long posted explicit polynomials showing the Gaussian Moments conjecture fails in every dimension n≥3: a cubic in four variables found by GPT-5.6 Sol Pro, then a quartic in three variables found by Claude Fable 5. This is not a Jacobian-conjecture score and not a Clay problem.
Claude Fable 5 produces a presentation of Gal(Q̄₂/Q₂)
On 9 June 2026 David Roe elicited a Claude Fable 5 solution to Epoch’s open problem asking for a presentation of the absolute Galois group of the 2-adics. Epoch later accepted verifier output and noted a second, independent GPT-5.5 Pro solution. Epoch warns the verifier is short of a full proof on this problem.