Dumbo Could Already Fly - by Erik Hoel
The Intrinsic Perspective
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Dumbo Could Already Fly<br>100% pure human copium about OpenAI solving Erdős problems
Erik Hoel<br>May 23, 2026
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And lo, the machine thought, and thought, and thought, and one day it answered.<br>We finally have the first truly impactful intellectual contribution where explicit credit must be given to AI. It’s a historic moment. OpenAI released a disproof of a geometry conjecture first proposed by Paul Erdős 80 years ago, discovered by an unnamed internal model. According to Scientific American:<br>“No previous AI-generated proof has come close” to meeting those high standards, wrote Timothy Gowers, a mathematician at the University of Cambridge, in commentary solicited by OpenAI.<br>“This is the unique interesting result produced autonomously by AI so far,” says Daniel Litt, a mathematician at the University of Toronto, who was consulted by OpenAI to verify the proof but is not involved with the company.
The AI’s insight behind the finding is elegant (although the proof needed re-writing by humans to be clear and up-to-standard). There are many far greater problems in math, but it is still very much the definition of “new scientific or mathematical knowledge” which, for many—including myself—has been the highest bar when it comes to AI.<br>Now, “new information” is notoriously hard to define, since of course by any strict definition AI has contributed new information before (just think of all the protein structures that have come out of AlphaFold). But this discovery does seem different in kind, in that it is:<br>(a) Something verifiably true.<br>(b) Non-trivial or even important (at least, relatively so in its subfield of math).<br>(c) Something humans had spent previous time on and failed to crack.<br>(d) The AI was (reportedly) not purpose-built to solve this particular problem, but did so (reportedly) autonomously as a next-gen LLM similar to the current version of ChatGPT.<br>Intriguingly, the internal model succeeded by going the opposite of the expected direction. It disproved the optimality of what Paul Erdős thought to be essentially the best construction for this problem (some have suggested that the social pressure of Erdős’ authority pointed humans in the wrong direction). To put it as simply as possible, Erdős was asking: If you place a set of nodes down on a plane, how can you organize this set of nodes such that as many pairs of nodes as possible are an exact fixed distance apart?<br>Here is what the original thought-to-be-optimal construction looked like:
And here is the improvement, passing from human to post-human, in an image that will probably go down in history books:
This is a visual representation created by @mathandcobb (apparently there’s quibbling over this, but Nature is using it and I haven’t seen a better one yet).<br>In response to this development, many are crowing that human mathematics is over. Here’s a comment comparing this moment to when the game of Go fell to deep learning, which in turn heralded the modern AI age:
Pedro Domingos@pmddomingos
Mathematicians are having a Lee Sedol moment.<br>5:26 AM · May 22, 2026 · 19.5K Views
25 Replies · 30 Reposts · 284 Likes
People are getting extremely confident about this.
Jason Abaluck@Jabaluck
Math won't be exhausted, but we'll get to a point where the contribution of human mathematicians is less than what the average person today contributes to Terry Tao's thinking about number theory. The levels of abstraction will exceed what any human brain can grasp.<br>5:45 PM · May 22, 2026 · 2.41K Views
13 Replies · 3 Reposts · 42 Likes
EXCEPT… A CURRENT MODEL CAN ALREADY DISCOVER THIS?!?
Let’s review the implicit pitch of this announcement: That the newer internal model at OpenAI is a step up in capabilities, and therefore is becoming powerful enough to begin to automate mathematics itself.<br>But to actually show that scientifically, you need controls. Specifically, you need to show that previous models could not do this. Otherwise this could just be a function of search (and there was indeed probably a lot of search across all open Erdős problems until they got a hit). Or, there might be something uniquely easy about this problem. Or, the result could be via minor improvements in elicitation (“elicitation” means the work of getting the models to accomplish things via prompts or harnesses or even just asking in the first place). These don’t take away that AI solved something, but they would take away the implied conclusion: That the models are getting smarter and smarter at some fixed rate, and are soon to surpass humans.<br>Meanwhile, a very good mathematician was able to get the currently available-to-all ChatGPT 5.5 Pro to reproduce the output! Below is this being described by one of the mathematicians quoted in OpenAI’s initial release, Timothy Gowers, who in turn is quoting the mathematician Xiao Ma, who showed ChatGPT 5.5 could do it (Ma previously made progress on...