Entity trail

Levent Alpoge

Source-backed findings, relationship evidence, citations, and briefing history from the public MindPattern archive.

Briefing refs

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Corpus findings

2026-09-09 / rss-researcherNYU's Tristan Buckmaster says OpenAI called him three days before announcing, used his line of attack, and asked him to drop his Anthropic co-authorBuckmaster published a signed statement alleging OpenAI researchers requested urgent calls from 3 September and told him on 6 September they would announce Navier-Stokes using the same line of attack he and Levent Alpoge had been developing, after admitting they only started the week prior on a rumor. He says he asked whether the model trained on or accessed their Codex sessions, where they had put every draft, and got no answer on training, and that Sebastien Bubeck asked 'Why would you ruin your career?' and proposed removing Alpoge's name over his Anthropic affiliation. Bubeck denies it: 'We did not use their prompts or proofs to prompt our models or direct our agents.'
2026-09-09 / sources-researcherTristan Buckmaster's own statement: the Euler write-up 'can only be described as AI slop', and the credit belongs to Córdoba and Martínez-ZoroaBuckmaster (NYU) posted a signed statement alongside three results he released with Levent Alpöge (Anthropic) on 2026-09-07: finite-time blowup with smooth forcing for incompressible porous media, Boussinesq, and 3D incompressible Euler, plus an unreleased hypo-dissipative Navier–Stokes result whose Lean verification had not finished. He states the program was neither theirs nor proposed by an LLM, credits Diego Córdoba and Luis Martínez-Zoroa, and says Martínez-Zoroa deserves a Fields Medal. Concrete timeline: slow progress for most of a year, blowup results on August 15, Lean verification on August 22, and he calls the first LLM-generated proof Alpöge sent him 'the most horrendous I have ever read'. He used Claude and Codex (mainly GPT-5.6 Sol), with Astra only for write-ups and auditing, and apologises for presentation quality under outside pressure.
2026-09-09 / thought-leaders-researcherSimon Willison on the Navier-Stokes race: the uncomfortable question is what "improving model performance" means for your Codex sessionsWillison reads OpenAI's admission that it "cannot rule out that de-identified data derived from their usage of our products helped improve our models" as the real story, since Buckmaster and Alpöge had been drafting the project inside Codex sessions. He compares the dynamic to races on security vulnerabilities and raises a new hazard for anyone doing original work with agents: your unfinished problem may be seeding a competitor's solution. He notes OpenAI declined to answer Buckmaster's direct training-data question.
2026-09-09 / thought-leaders-researcherSébastien Bubeck calls the authorship allegations "false and inflammatory" and publishes his texts to AlpögeOpenAI's Bubeck responded on X that "A series of false and inflammatory allegations against me are currently circulating on social channels" and that he entered the discussion following academic norms. He posted a text-message exchange with Levent Alpöge proposing a coordinated release and saying credit should go to Alpöge and Buckmaster, and framed the disputed request as being about who could author OpenAI's own writeup rather than Buckmaster's paper. This is the only first-person rebuttal from the OpenAI side and it contradicts Buckmaster's account on the specific point of stripping authorship.
2026-09-08 / reddit-researcherMathematician says OpenAI told him an internal model had proved finite-time blow-up for forced Navier-Stokes, days after learning of his unpublished workTristan Buckmaster and Levent Alpöge published three results on finite-time blow-up under smooth forcing for 3D incompressible Euler, Boussinesq and incompressible porous media, and Terence Tao wrote that nothing in principle prevents the methods extending to Navier-Stokes. Buckmaster then alleged that on September 6 Sébastien Bubeck told him an internal OpenAI model had produced a roughly 100-page blow-up proof for forced Navier-Stokes along the same Córdoba–Martínez-Zoroa route, that OpenAI would not say when its first prompt was sent, and that he was twice pushed to drop Alpöge (an Anthropic employee) from the paper. Buckmaster also says he asked whether the model had access to the Codex sessions holding all their drafts and got no direct answer.
2026-08-28 / reddit-researcherA Claimed 100-Page Hopf Problem Proof Got Formalized Into 250,000 Lines of Lean Within DaysLevent Alpöge posted a claimed resolution of the 78-year-old Hopf problem, that the six-sphere admits a complex manifold structure compatible with its standard topology, written with Claude. Boris Alexeev's public HopfProblem repository holds the Lean formalization, with the statement adapted from the Formal Conjectures project. The r/singularity thread (229 upvotes) frames the days-long turnaround from claimed proof to machine-checked formalization as the actual story rather than the proof itself.
2026-08-28 / reddit-researcherFrontierMath Marked the Elliptic Curve Rank Problem Solved, With Claude Credited Alongside Two MathematiciansEpoch AI's FrontierMath open-problems board now lists the elliptic curve rank problem as solved: a curve over Q of rank at least 30 was posted August 20 credited to Claude with Levent Alpöge and Ava Howell, followed by a rank-31 curve on August 23 from the same team. That beats the Elkies and Klagsbrun record of 29 from 2024, itself the first improvement in eighteen years. Assuming BSD and GRH the curves have rank exactly 30 and 31.
2026-08-20 / sources-researcherFireship's 'The Summer Math Fell to the Machines': Claude Burned 31M Output Tokens Across 60 Subagents and 2,400 Shell Commands to Move a Riemann Bound From 41.6% to 67.2%Fireship's August 19 Code Report walks the three weeks in which AI closed more open math problems than the prior decade, including Levent Alpoge's counterexample disproving the Jacobian conjecture with help from Fable, Dimitri Rybin pointing GPT-5.6 at the 30-year-old dense Garg-Gommans conjecture and getting a seven-node nine-edge counterexample, and OpenAI's ten Lean-certified results shipped to GitHub. The detail builders should care about is the Anthropic run: Jarred Sumner, the Bun creator with no math background, asked Claude to take a stab at the Riemann hypothesis, got 650 dead-end ideas, told it to keep going, and an unreleased model then spent a day and a half coordinating roughly 60 subagents inside Claude Code, running 2,400 shell commands and burning 31 million output tokens. Anthropic's own writeup confirms the result: the proportion of provably confirmed zeta zeros moved from 41.6% to 67.2%, validated by two internal and two external number theorists and formalized in Lean, with Anthropic stating it does not expect the method to lead to a proof.

Graph relationships

WORKS AT
Anthropic
Levent Alpöge works at Anthropic and collaborated on finite-time blowup proofs.
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WORKS AT
Anthropic
Levent Alpöge is an Anthropic employee.
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Claude
Claude credited on FrontierMath for solving elliptic curve rank 30+ problem
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USES
Claude
Levent Alpöge wrote claimed Hopf problem proof with Claude
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Fable
Levent Alpoge received help from Fable to disprove the Jacobian conjecture.
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WORKS AT
Anthropic
Levent Alpoge is Buckmaster's Anthropic-affiliated coauthor
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Codex
Alpöge drafted the Navier-Stokes project inside Codex sessions.
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WORKS AT
OpenAI
Levent Alpöge is at OpenAI.
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Source trail

Tristan Buckmaster (NYU)simonwillison.net OfficeChai r/singularity (240 upvotes, 184 comments)GitHub (plby/HopfProblem), via r/singularity Epoch AI, via r/singularity Fireship (corroborated by anthropic.com/research/riemann-zeta)

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