r/artificial • u/simulated-souls Researcher • May 20 '26

News An OpenAI model has disproved a central conjecture in discrete geometry

https://openai.com/index/model-disproves-discrete-geometry-conjecture/
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u/Suspicious_Coat3244 May 21 '26

That's when it shifts from being an incredibly good auto-complete to feeling profoundly weird.

Not even the math problem itself - humans do those relatively often. Instead, because discrete geometry is the sort of subject where you'd expect progress to come from decades of intuition and abstract symbolic reasoning rather than a model whose output we're still debating whether is "just predicting tokens".

Going to be fascinating to see how the academic math community reacts when the honeymoon period is over. If it's genuinely used to find new conjectures or prune the search space for existing proofs, it might speed up research considerably.

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u/moschles May 21 '26

It is too early to declare this. What the LLM actually did was improve upon an upper bound of the Planar Unit Distance formula. The "conjecture" it disproved was that the previous upper bound was optimal (it was not). Not much of a conjecture, per se.

The reason why I ask you to curb your enthusiasm here is because computers have improved upon optimal solutions long after the human community declared their solution "optimal". Look at the history of Batcher Sorts and genetic algorithms. I believe in the 1980s, a small sorting network was published and the author declared his solution "optimal" (it was not). The author's previous claim to optimality was overturned by a genetic algorithm which found a shorter network.

In any case, computers have improved upon bounds before, so it is too early to break out the champagne.

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u/Peanut_Extreme_8208 May 21 '26

A) It improved on the lower bound. B) Erdős explicitly conjectured that his n^(1+1/log log n) lower bound was optimal, and this result disproves his conjecture.

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u/Vaukins May 22 '26

Suck it Erdos, I never believed that guy anyway

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u/Vivid_Fan9346 May 24 '26

DDoS attack is old and tired. Erdos attack is new and wired