Who wants a calculator when AI begins doing unique arithmetic?
OpenAI says considered one of its general-purpose reasoning fashions disproved an 80-year-old geometry conjecture posed by Hungarian mathematician Paul Erdős. The end result, which the corporate stated was reviewed by exterior mathematicians, considerations the variety of pairs of factors that may be organized at equal distances from each other.
The AI large stated that the mannequin “has disproved this longstanding conjecture, offering an infinite household of examples that yield a polynomial enchancment,’’ and added that the proof has been checked by a bunch of exterior mathematicians.
That can be a significant declare by itself. It lands with additional weight as a result of OpenAI just lately confronted criticism for overstating GPT-5’s position in fixing different Erdős issues, making this announcement each a possible milestone and a check of the corporate’s credibility.
General-purpose reasoning mannequin used
Also noteworthy is how the end result was discovered. OpenAI famous that it got here from a brand new general-purpose reasoning mannequin, versus a system skilled particularly for arithmetic, tailor-made to look via proof methods, or focused on the unit distance downside specifically.
“As part of a broader effort to test whether advanced models can contribute to frontier research, we evaluated it on a collection of Erdős problems,’’ the company said. “In this case, it produced a proof resolving the open problem.”
Why this declare faces scrutiny
This isn’t the primary time OpenAI has made a brash declare.
Last October, the corporate confronted backlash after a few of its researchers touted math breakthroughs by GPT-5. Former OpenAI VP Kevin Weil posted a now-deleted publish on X that “GPT-5 found solutions to 10 (!) previously unsolved Erdős problems and made progress on 11 others.”
The challenge was that GPT-5 didn’t truly remedy these issues, however fairly, discovered options that already existed in literature.
Expert response to the proof
However, it seems the corporate has realized a lesson.
Accompanying the announcement have been companion remarks that OpenAI printed in help of the mathematicians’ disproof, together with these from Thomas Bloom, who oversees the Erdos Problems web site and who had characterised Weil’s publish as “a dramatic misrepresentation.”
Bloom wrote that when he assesses the significance and affect of an AI-generated proof, he asks himself if it has taught one thing new about the issue, and whether or not we perceive discrete geometry higher now.
“I think the answer is a moderated yes: This shows that there is a lot more that number theoretic constructions have to say about these sorts of questions than we suspected,’’ Bloom said. “Moreover, the number theory required can be very deep. No doubt many algebraic number theorists will be taking a close look at other open problems in discrete geometry in the coming months.”
Another professional who reviewed the outcomes, University of Toronto mathematician Arul Shankar, wrote, “In my opinion, this paper demonstrates that current AI models go beyond just helpers to human mathematicians — they are capable of having original ingenious ideas, and then carrying them out to fruition.”
His colleague, Professor Jacob Tsimerman, stated he was additionally impressed by the outcomes, noting that he had as soon as tried unsuccessfully to disprove the space downside.
A bigger takeaway
This result’s vital, OpenAI stated, as a result of not solely has an AI system autonomously resolved a longstanding open downside, but it surely additionally “offers an early glimpse of a new kind of collaboration between AI and human mathematicians.”
The greater takeaway is that “higher mathematical…
