Net Good IndexSubmit a correction

Benefit Ledger · provisional · Mathematics

Ryu and Jang, using GPT-5 Pro, prove point convergence of Nesterov accelerated gradient

In October 2025 UCLA mathematicians Ernest Ryu and Uijeong Jang resolved the long-open question of whether Nesterov’s 1983 accelerated gradient method converges in iterates, in a collaboration they describe as heavily assisted by GPT-5 Pro. The human authors wrote and checked the final proof.

Tier 3 MajorMethodology 0.1
Submit a correction

Current score

+1.01

10 base · Major (tier 3 of 5, 10 pts)
× 0.4500 attribution · Material acceleration
× 0.5000 evidence · External expert evaluation
× 0.6000 realization · Complete public manuscript
× 0.7500 durability · Useful for many years
Event-level product before credit split: 1.01

Resolving NAG point convergence is a major optimization theorem (tier 3). Humans led and wrote the proof (AI attribution 0.45). Evidence is an arXiv paper plus an OpenAI writeup (0.45). Realization is a public complete argument (0.60). Follow-up ingest: independent source raised evidence; added a follow-up source. Follow-up ingest: added a follow-up source.

What happened

Nesterov acceleration has been a workhorse of convex optimization since 1983, but point convergence of the iterates (as opposed to function-value rates) had remained open. Ryu and Jang announced continuous-time convergence on 21 October 2025 and discrete NAG on 24 October, then posted arXiv:2510.23513. They say GPT-5 Pro generated many arguments, most incorrect; Ryu filtered them and recognized a structural rearrangement that became the backbone of a human-written proof. OpenAI later covered the collaboration. This is material acceleration by a named GPT-5 Pro release, not autonomous authorship and not GPT-5.6 Sol. Update (2025-10-28): Review of the Anthropic Summer 2025 Pilot Sabotage Risk Report October 28, 2025 External review from METR of Anthropic's Summer 2025 Sabotage Risk Report Read more. Review of the Anthropic Summer 2025 Pilot Sabotage Risk Report October 28, 2025 External review from METR of Anthropic's Summer 2025 Sabotage Risk Report Read more Update (2025-10-23): Summary of our gpt-oss methodology review October 23, 2025 Details on external recommendations from METR for gpt-oss Preparedness experiments and follow-up from OpenAI. Read more. Summary of our gpt-oss methodology review October 23, 2025 Details on external recommendations from METR for gpt-oss Preparedness experiments and follow-up from OpenAI. Read more

Model attribution

+1.01

GPT

Generated candidate arguments and a structural idea that Ryu developed into the final NAG point-convergence proof.

The arXiv paper states the work was conducted with GPT-5 Pro; Ryu describes filtering mostly incorrect arguments and writing the proof himself.

Attribution 0.4500 · Credit share 100% · OpenAI

Claims

  • Ryu and Jang proved point convergence of Nesterov accelerated gradient, in a collaboration they describe as heavily assisted by GPT-5 Pro.

    outcome · supported

  • GPT-5 Pro autonomously authored the published proof without human filtering.

    attribution · disputed

Sources

primary sources

independent sources

other sources

Secondary domains: Computer Science

Revision history

  • 13 Sep 2026 · 0.00 → 0.91

    Imported events under methodology 0.1.

  • 17 Sep 2026 · 0.91 → 1.01

    Ingest update: independent source raised evidence; added a follow-up source.

  • 17 Sep 2026 · 1.01 → 1.01

    Ingest update: added a follow-up source.

Submit a correction