The majority of people are unaware of a little-known area of mathematics. Not because it’s unimportant; on the contrary. It’s the kind of problem that sits quietly in the background while more spectacular discoveries make headlines, but mathematicians who are familiar with it will tell you—usually hesitantly—that it might be more important than nearly everything being worked on at the moment.
OpenAI revealed in mid-May that an internal AI model had accomplished something truly unexpected: it disproved the Erdæ unit distance conjecture, an 80-year-old discrete geometry problem that had eluded all serious attempts to find a solution. Researchers familiar with the outcome say it is the kind of proof that would probably be published in the most prestigious journals in mathematics. That’s a big deal. In their entire histories, these journals may have only received a few submissions related to artificial intelligence.
This is where things get complicated, though. There is a big difference between solving a problem and knowing why you solved it.
For years, Kevin Buzzard of Imperial College London has worked to teach computers to verify Fermat’s Last Theorem, not to prove it again, but to formalize the current proof so thoroughly that a machine can unambiguously verify each and every logical step. Approximately 130 pages make up the original proof, which was completed in 1998 and winds through areas of mathematics that, prior to Andrew Wiles, hardly seemed related. It’s not glamorous work, Buzzard’s project. It’s laborious, frequently frustrating, and raises a question that no one in the field seems fully comfortable answering: does a computer truly understand anything when it verifies that a proof is correct?
Johns Hopkins’ Emily Riehl states it simply. The proof writer must be far more meticulous than usual in order to achieve formalization. The human still has to fill in the blanks; the computer isn’t doing it. Verification, not insight, is what the machine provides. And that seemingly technical distinction gets right to the core of the argument about what AI can truly become.
This tension was anticipated by Alan Turing. His 1936 proof of computability, which laid the groundwork for the Halting Problem, established an unsettling fact: a computational system is structurally unable to respond to certain questions about itself. This was further expanded upon by Rice’s Theorem. The behavior of arbitrary programs cannot be fully analyzed by any algorithm. These are not short-term restrictions while we wait for improved hardware. They are architectural. enduring. It’s still unclear if contemporary AI developers have fully considered the practical implications of those proofs as they rush to announce the next benchmark milestone.
Recently, Terence Tao and co-author Tanya Klowden argued that AI is an extension of human thought rather than a replacement for it, and that it is a natural evolution of human tools. That framing seems genuine. Although a calculator cannot comprehend arithmetic, it has altered the capabilities of arithmetic. Something similar seems to be happening here, but on a scale that makes the calculator analogy seem almost charming.
It is truly fascinating what transpired with the Erdæ conjecture. It implies that AI is venturing into areas of mathematics that were previously thought to be solely human. However, a proof does not equate to wisdom. The solution was discovered by the machine. The old proofs of Turing and his contemporaries suggest we may never fully answer the question of whether it found it for any reason at all—whether there was something it noticed, a pattern that felt significant. Even as the announcements continue, it’s worthwhile to sit with that.
