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Anthropic

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

Leaderboard

RankModelOrganizationBenefitHarmNetEventsLast impact
8Claude

Claude · version unspecified

Anthropic+2.540.002.5458 Sep 2026
27Anthropic Internal Research Model — 2026-08

Claude · internal / unreleased

Anthropic+1.490.001.49110 Aug 2026
31Claude 3.7 Sonnet

Claude

Anthropic+1.370.001.37124 Feb 2025
42Claude Fable 5

Claude

Anthropic+0.620.000.62321 Jul 2026

Timeline

Events

Benefit8 Sep 2026

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.

MathematicsprovisionalTier 3 Major+1.13
Benefit23 Aug 2026

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.

MathematicsdisputedTier 3 Major+0.55
Benefit20 Aug 2026

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.

MathematicsprovisionalTier 3 Major+1.48
Benefit12 Aug 2026

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.

MathematicsdisputedTier 2 Notable+0.09
Benefit10 Aug 2026

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.

MathematicsprovisionalTier 3 Major+1.49
Benefit21 Jul 2026

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.

MathematicsprovisionalTier 2 Notable+0.20
Benefit20 Jul 2026

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.

MathematicsprovisionalTier 2 Notable+0.30
Benefit9 Jun 2026

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.

MathematicsprovisionalTier 2 Notable+0.26