In a recent Science News article, reporter Kathryn Hulick explains that an AI model built by OpenAI has disproved a famous, 80-year-old conjecture by mathematician Paul Erdős, a result that is correct but has triggered a debate over how mathematics should be done in the age of AI.
The conjecture, known as the unit distance problem, asked how many pairs of points on a flat surface can be placed exactly the same distance apart. Erdős proposed an answer in 1946, and no one had proven or disproven it until OpenAI’s model took it on.
Below are key highlights from the article:
- What happened. Hulick reports that OpenAI researchers gave the model the conjecture and walked away. When they returned, the model had produced a mathematical proof, posted on OpenAI’s website on May 20, disproving what mathematicians had long believed was true. Melanie Matchett Wood of Harvard University, who reviewed the result, calls it “a beautiful piece of mathematics that has been discovered.”
- How the model got there. According to Hulick, the AI was a general-purpose reasoning model that used no math-specific tools. It found its counterexample by combining ideas from algebra and number theory, fields not normally applied to this kind of geometry question, building a complex high-dimensional grid and projecting it onto a flat plane. Wood says the cross-field approach is itself notable and may inspire mathematicians to try similar combinations elsewhere.
- Perseverance, not insight. Hulick notes that OpenAI’s own researchers, including Sébastien Bubeck, describe the proof as relying on persistence rather than a creative spark. Wood and mathematician Thomas Bloom of the University of Manchester both say a true proof of the conjecture, rather than a disproof by counterexample, would have required real creative insight, and that current public AI models might have reached the same result. Bubeck himself concedes the work “isn’t exactly the spark of genius that we see sometimes in mathematics.”
- A call for guardrails. Hulick reports that on June 2, a group of experts published the Leiden Declaration, calling for tight guardrails around AI’s role in mathematical research. As of June 5, it had gathered 1,590 signatures.
- Can anyone check the work? Bloom tells Hulick that while this particular proof was straightforward for a human expert to verify, he has seen people post hundreds of pages of AI-generated math online that no one, including the poster, can actually read or check. OpenAI has also disclosed that its model solved the conjecture correctly in only half of repeated trials, and the company has not released data on its failures or how long the model spent on the problem.
- Who gets the credit. Wood raises a separate concern to Hulick: AI models draw on essentially everything ever published, yet provide no way to trace which ideas inspired which step of a solution, conflicting with mathematics’ long-standing practice of crediting prior work.
- Who gets access. Bloom also points out that if the most capable AI tools remain expensive and private, mathematics could become less open, and some people may start to question the point of learning the subject at all.
Despite the concerns, Hulick reports that researchers like Wood remain cautiously optimistic, expecting AI to become an indispensable part of mathematical work going forward.
Acknowledgement: This summary was generated using AI writing tools as part of my experimental learning process. For more information, check out the original article listed below.