This article has been reviewed according to Science X's editorial process and policies. Editors have highlighted the following attributes while ensuring the content's credibility: AI models are good at finding answers to mathematical puzzles but are not as good at research judgment, according to theoretical computer scientists. The researchers, co-led by Princeton's Pravesh Kothari, documented their use of AI in a case study shared on arXiv, outlining the ways in which AI tools excelled and fell short in reaching an important solution to an open mathematical problem.
AI is excellent at finding answers, they argue, because the models are trained on published papers, textbooks and solved problems. But, as of August 2026, these models were not as good at the process of recognizing the value of a theoretical result over numerical evidence or determining the significance, generality or downstream use of a result, according to the authors. This is because training data rarely includes information on the long process of mathematical discovery, which includes failed approaches, unlikely results and changes in strategy.
Using AI tools, the researchers successfully narrowed the bounds of the Grothendieck constant, a mathematical concept first identified by Alexander Grothendieck in 1953. The paper that details the math research is not yet peer reviewed, but the results have implications for creating more efficient algorithms in graph theory and quantum information. The work is also published on the arXiv preprint server.
Kothari, an associate professor of computer science and a senior author on the paper, called the Grothendieck constant "a beautiful problem." "The interesting bit is that we can take very little credit for the research as human beings," said Kothari. AI models did most of the work, he said, with humans providing guidance only when the models got stuck. "If I had the same level of involvement on a paper last year, I would not be listed as an author," he added.
To do the work, 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. The humans posted instructions to a bulletin that the agents would read periodically. The models were set up to run through the problem in iterations while maintaining a permanent memory to improve upon previous work.
Around iteration 18, the researchers noticed that the models were stuck—they were essentially looping and unable to move ahead. The humans intervened and redirected the agents by reframing the question. After about 30 additional iterations, the model succeeded in narrowing the bounds of the constant.
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