AI agents narrowed Grothendieck constant bounds after Princeton researchers reframed a stalled run
Theoretical computer scientists co-led by Princeton's Pravesh Kothari used two AI models to narrow the bounds of the Grothendieck constant. The preprint is not yet peer reviewed, and its authors say the models are weaker at judging a result's significance.
The Scientist · Science desk
What happened
- The setup paired a reasoning model that did the math with a coding agent that checked what the reasoning model proposed.
- Around iteration 18 the researchers saw that the models were looping and unable to move ahead.
- After the humans reframed the question, about 30 additional iterations were enough for the model to narrow the bounds.
- The authors attribute the models' weakness at judging significance to training data that rarely records failed approaches, unlikely results and changes in strategy.
- phys.org reports that the result has implications for more efficient algorithms in graph theory and quantum information.
Why it matters
- constraint The step the authors say models handle less well, judging value and downstream use, still needs a person, so a team running this setup needs someone who can rank results and notice a stall.
- exposure Anyone building on the narrowed bounds is leaning on a result that no referee has yet judged.
- capability Agents that read a shared bulletin periodically let humans steer a long run with posted instructions, without sitting in the loop.
The run lasted roughly 48 iterations, about 18 before the stall and about 30 after the reframing [18]. The source gives both counts as approximate. The models kept a permanent memory, so each pass could build on earlier work [6].
We think the stall is the more informative event in the run than the success, on one condition: it is a single observation. The account describes one open problem [1], and a stall rate would take many runs to estimate. The humans responded to the stall by reframing the question [8], which is a change of direction. Whether the models would have left the loop on their own is what a control run would show. The phys.org account does not say what the new framing was or what the new bounds are [2].
The authors are specific about where the models fall short. As of August 2026, they say, the models were not as good at recognizing the value of a theoretical result over numerical evidence, or at determining a result's significance, generality or downstream use [10]. They argue the models are excellent at finding answers because they are trained on published papers, textbooks and solved problems [12]. The date is part of the claim. It describes the models this team had in August 2026.
Kothari's description of the division of labor is the strongest evidence in the account, and it is self-report. "The interesting bit is that we can take very little credit for the research as human beings," said Kothari [13]. The models did most of the work, he said, with humans guiding only when the models got stuck [14]. "If I had the same level of involvement on a paper last year, I would not be listed as an author," he added [15].
Checking a result and judging it are separate tasks. According to Science, OpenAI's 166-page Navier-Stokes proof has been verified by Lean, an automated theorem prover, but not by humans [19]. OpenAI announced that humans verified its disproof of the Erdos unit-distance conjecture, though the model that produced it is not available for public use [20]. Terence Tao said in a recent lecture at the Simons Foundation that AI has generated 100,000-line proofs that are largely incomprehensible [16].
What to watch
- Peer review of the preprint, which would give the first outside human judgment on whether the narrowed bounds matter.
- Whether the authors publish the new bounds and the reframed question, or report repeat runs that show how often the system stalls.
- Human verification of OpenAI's 166-page Navier-Stokes proof, which Lean has checked but humans have not, according to Science.
Clarity's read
What the record supports and how the coverage leans. The claims behind it follow.
Reality
- Evidence40
- Adoption
- Insufficient
- Hype gap−10
- Incentives
- Insufficient
- Confidence50
Claim ledger
Ranked by verification strength, evidence, and original report placement.
- [1]
Theoretical computer scientists, co-led by Princeton's Pravesh Kothari, documented their use of AI in a case study shared on arXiv, outlining where AI tools excelled and fell short in reaching a solution to an open mathematical problem.
- [2]
Using AI tools, the researchers narrowed the bounds of the Grothendieck constant, a mathematical concept first identified by Alexander Grothendieck in 1953.
- [3]
The paper detailing the math research is not yet peer reviewed.
- [4]
The team set up a system with two models: a reasoning model to do the math and a coding agent to verify the math proposed by the reasoning model.
- [5]
The humans posted instructions to a bulletin that the agents would read periodically.
- [6]
The models were set up to run through the problem in iterations while maintaining a permanent memory to improve upon previous work.
- [7]
Around iteration 18, the researchers noticed that the models were stuck, essentially looping and unable to move ahead.
- [8]
The humans intervened and redirected the agents by reframing the question.
- [9]
After about 30 additional iterations, the model succeeded in narrowing the bounds of the constant.
- [10]
As of August 2026, according to the authors, the models were not as good at recognizing the value of a theoretical result over numerical evidence or determining the significance, generality or downstream use of a result.
- [11]
The authors attribute this to training data that rarely includes information on the long process of mathematical discovery, including failed approaches, unlikely results and changes in strategy.
- [12]
The authors argue AI is excellent at finding answers because the models are trained on published papers, textbooks and solved problems.
- [13]
"The interesting bit is that we can take very little credit for the research as human beings," said Kothari.
- [14]
AI models did most of the work, Kothari said, with humans providing guidance only when the models got stuck.
- [15]
"If I had the same level of involvement on a paper last year, I would not be listed as an author," Kothari added.
- [16]
AI has generated 100,000-line proofs that are largely incomprehensible, Terence Tao said in a recent lecture at the Simons Foundation.
- [17]
The results have implications for creating more efficient algorithms in graph theory and quantum information.
- [18]
The run took roughly 48 iterations in total, about 18 before the stall and about 30 after the reframing; both inputs are approximate in the source.
- [19]
OpenAI released a 166-page proof for the Navier-Stokes problem that has been verified by Lean, an automated theorem prover, but not by humans, according to Science.
- [20]
The Erdos unit-distance conjecture result was verified by humans, OpenAI announced, but the model used to solve it is still not available for public use.
Get this ledger inside ChatGPT. Ask about any of our stories and the answer brings its figure, each claim’s verdict and the sources. Free, no account.
Sources
1 independent publisher whose own reporting we read for this story.
- phys.orgAI-assisted math advance highlights gap between finding answers and judging their significance
1 article · October 14, 2026
Topics and entities
Follow any of these and your For You feed starts watching them — no settings page required.
Topics
- AI AgentsFollow
- AI for MathematicsFollow
- Theoretical Computer ScienceFollow