Mathematicians Struggle to Make Sense of OpenAI's Latest Release

MATHematically, the field has been left reeling after OpenAI released nearly 400 AI-generated results across more than 700 manuscripts. The sheer scale of the deluge is overwhelming, with mathematicians struggling to digest everything in a short amount of time.

The release covers a diverse array of mathematical disciplines, including combinatorics, geometry, number theory, theoretical computer science, algebra, topology, probability and statistical mechanics, and mathematical physics. OpenAI’s models have been pumping out mathematics at an incredible speed, far outstripping the capacity of its human staff to properly scrutinize findings.

Many mathematicians are concerned about the quality of the results, with some describing them as ‘slop’ - low-quality, frequently erroneous AI-generated material that is increasingly common online. The term was coined by researchers who have seen a huge uptick in such material produced with tools like ChatGPT and Claude in recent years.

Álvaro Lozano-Robledo, a professor of mathematics at the University of Connecticut, said simply working through the roughly 40-page table of contents and abstracts took him the better part of an hour. ‘Just going over the entire list of abstracts is overwhelming,’ he noted.

The sheer volume of work makes even a preliminary assessment as to exactly what OpenAI has released difficult. Researchers are struggling to separate solutions from slop, with many fearing that some results may be incorrect or incomplete.

OpenAI’s models have been formalized in Lean, a programming language and proof assistant that allows results to be verified computationally. However, the degree to which each result had been verified varies wildly, with OpenAI acknowledging that the results are ‘at different stages of verification’ on GitHub.

The company said only 300 top-line results out of 719 manuscripts have been formalized, around 42 percent. It also noted that it will update the repository with more formalizations as they obtain them. However, several mathematicians complained about the lack of formalization, particularly given the sheer number of results.

Kevin Buzzard, a mathematics professor at Imperial College London, said he had identified numerous theorems in his area of work - algebraic number theory - but only around six immediately ‘stood out.’ Few, if any, of those appeared to be formally verified in Lean. He expressed concerns about having to read possibly-not-correct slop or wait for others to do the same.

Buzzard’s concerns were echoed by numerous other researchers who are worried about AI-generated material that is increasingly common online. They have seen a huge uptick in such material produced with tools like ChatGPT and Claude, which often demonstrates little understanding of the subject matter.

Some researchers told The Verge they had noticed papers that appeared to cover ground already trod by other mathematicians, though were wary of saying so publicly before reviewing the material. Others pointed to the unusual brevity of the work, with results compressed into a few dozen pages or less.

Nalini Joshi, a mathematics professor at the University of Sydney in Australia, said her quick search through the release revealed little that overlapped with her own work. However, she noted that some papers had short bibliographies and was ‘wary’ about attribution in the papers may be lacking the complete story.

Despite the slop and uncertainty, there is an overarching consensus among mathematicians that the release contains some genuinely impressive work. While stressing the difficulties assessing the volume of material - and the need to properly verify results - researchers said the work appeared to be of a very high caliber, despite shortcomings in its presentation.

Some researchers described papers as being ‘difficult’ or ‘practically impossible’ to follow. Brendan Hassett, a mathematics professor at Brown, told The Verge that he wouldn’t spend any more time trying to understand some of the results if they had been written by a person.

Stanford mathematician Jared Duker Lichtman said there were ‘tens’ of results he would put in this category, including progress toward the Riemann hypothesis and solutions to major problems like the four-dimensional Kakeya conjecture. These are significant achievements that could have warranted publication in top-tier journals and secured an academic career for their authors.

Mathematicians across the field are grappling with a landscape that has abruptly changed around them. Many had just watched years of work evaporate overnight, or knew colleagues who had. The disruption is concentrated heavily in some areas of the field, particularly probability, combinatorics, and theoretical computer science.

Some researchers expressed surprise at how little their own work appeared to have been touched by OpenAI’s release. Roney-Dougal said her corner of the field - largely centered on group theory - seemed to have escaped relatively unscathed. However, she joked that it is fortunate she works in a ‘very unfashionable area’.

OpenAI knew its release would be disruptive and had made some effort to soften the blow by engaging with the mathematical community through the Advisory Group on Mathematics and Artificial Intelligence (AGMAI). The company followed some of AGMAI’s advice, including disclosing significantly more information about its model and providing funding for workshops and conferences.

The release has sparked a range of reactions among mathematicians. Some are excited at the prospect of new discoveries, while others are worried about the impact on their own work and careers. As one researcher noted, ‘it’s not just about the math itself - it’s also about how we do research’.