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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.

24 Oct 2025Tier 3 MajorMethodology 0.1

Current score

+0.91

10 base · Major (tier 3 of 5, 10 pts)
× 0.4500 attribution · Material acceleration
× 0.4500 evidence · External expert evaluation
× 0.6000 realization · Experimentally validated
× 0.7500 durability
Event-level product before credit split: 0.91

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).

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.

Model attribution

+0.91

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

other sources

Secondary domains: Computer Science

Revision history

  • 13 Sep 2026 · 0.00 → 0.91

    Imported events under methodology 0.1.