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AI Disproves 80-Year-Old Erdős Conjecture
OpenAI announced on May 20 that one of its AI models disproved a conjecture posed by Hungarian mathematician Paul Erdős in 1946, solving what’s known as the planar unit distance problem.
Image: nature.com - AI cracks 80-year-old mathematics challenge
The problem asks: given a set of points on a plane, how many pairs can be exactly the same distance apart? Erdős showed that larger grids could contain same-distance pairs growing slightly faster than the number of points, and he conjectured no arrangement could do better. For nearly 80 years, mathematicians believed him.
OpenAI’s model proved otherwise. It used techniques from algebraic number theory to discover a new family of point arrangements that breaks the limit Erdős proposed, according to Nature. The system chose points with coordinates that were solutions to particular equations, finding constructions that outperform square grids.
Image: OpenAI - An OpenAI model has disproved a central conjecture in discrete geometry
“If Erdős were alive, I am sure that he would just be raving about this advance,” said Tom Trotter, a mathematician at Georgia Tech who co-authored papers with Erdős, per Nature.
Sebastien Bubeck, a mathematician at OpenAI, said he believes this is the first time AI has autonomously produced a significant result in any research field. The proof came from a single prompt, a machine-rewritten statement of Erdős’s question. “It’s kind of remarkable to see the model really reasoning through the problem like a human,” said OpenAI mathematician Mehtaab Swahney.
Daniel Litt, a mathematician at the University of Toronto who independently verified the proof, called it “the first result produced autonomously by an AI that I find interesting in itself.”
What the AI Did and Didn’t Do
The broader problem remains unsolved. As the Guardian reported, the AI showed Erdős’s proposed limit was too low but did not establish a new answer for how fast the pairs actually grow.
OpenAI has not released the full 125-page chain-of-thought reasoning, nor named the specific model. Bubeck described it as an experimental, general-purpose reasoning model rather than one trained specifically for mathematics.
Image: the Guardian - OpenAI makes breakthrough on 80-year-old maths problem
Independent Verification
The result has been validated by outside mathematicians. Thomas Bloom, who maintains the Erdős Problems website and had previously criticized OpenAI’s earlier Erdős claims, co-authored a companion paper. He wrote that the AI achieved its results by “persevering down paths that a human may have dismissed as not worth their time to explore,” the Guardian reported.
Bloom added a caveat: “While the original proof produced by AI was completely valid, it was significantly improved by the human researchers at OpenAI and the many other mathematicians involved in the present paper. The human still plays a vital role.”
Mathematician Tim Gowers, also writing in the companion paper, described the result as “a milestone in AI mathematics.”
OpenAI had been embarrassed last year when it claimed an earlier Erdős breakthrough that turned out to be based on existing literature the model had absorbed. This time, independent verification appears solid.
For the most complete account of the mathematics involved, Nature’s coverage by Davide Castelvecchi is the best single read.
Sources: Nature, The Guardian See also https://cdn.openai.com/pdf/74c24085-19b0-4534-9c90-465b8e29ad73/unit-distance-remarks.pdf
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A lot of shooting the messenger votes here. Downvoting reality isn’t a good look.
So, how come when you ask ChatGPT how many r’s are in the word ‘strawberry’ it says there are two? Or that ‘December’ is spelled with an x? The damn thing can’t even be used as a timer. But OpenAI can solve complicated mathematical problems?
Because of the tokenizer. It turns words into tokens, which do not contain any letters.
“While the original proof produced by AI was completely valid, it was significantly improved by the human researchers at OpenAI and the many other mathematicians involved in the present paper. The human still plays a vital role”.
I.e. calculators and slide rules were useful tools as well.
Tbh that’s cope you know this is nothing like a calculator or slide rule.
This is called jagged intelligence in the field and is a very interesting problem to research.
Because you’re using LLMs. AI is more than that. LLMs are generally the worst of it.
I guess this is one of the 1% of use cases where AI/LLMs actually make sense. Brute force, where humans have already given up.
Generally usefull in science, math, genetics and medicine when needed research in a hugh amount of data, there AI can solve in hours problems which in traditional research needs month or years. As said in other ocassion, the problem isn’t the AI/LLM as such, but the corps which use it, including it even in a toaster, as tool for data mining, manipulations and surveillance, apart of stupid users which use it to create memes and to substitute the own research, creativity and intelligence, instead of using it as what it is, as tool to help in large repetitive work or research, with specialized specific AI apps. AI is a problem as long we use it like a child with a new toy
It’s kind of remarkable to see the model really reasoning through the problem like a human
100% bullshit.
the AI achieved its results by “persevering down paths that a human may have dismissed as not worth their time to explore,
So it just auto-completed its way down what a human would have (mistakenly) considered a dead end. Fine, it brute forced it.
a caveat: “While the original proof produced by AI was completely valid, it was significantly improved by the human researchers at OpenAI and the many other mathematicians involved in the present paper. The human still plays a vital role.”
And it produced garbage anyway, which meant it just let the real mathematicians know the assumed dead end was actually useful.
That’s some serious cope.
Dogmatists are always such sore losers.
Douchebags that are sabotaging all kinds of scientists in the US say they’re doing science better than them with the opaque services they want people to blindly pay for. Look! Numbers!
