An amateur solved a 60-year-old Erdős problem using a single GPT-5.4 Pro prompt; Terence Tao says it's a “nice achievement” with unclear long-term significance
A ChatGPT AI has proved a conjecture with a method no human had thought of. Experts believe it may have further uses
Scientific AmericanJoseph Howlett
Context & Ripple Effects
Related coverage traces a progression from GPT-3.5 performing better on older coding tasks than newer ones to GPT-5-class reasoning systems being positioned for harder problems and competitive-programming results. This case places mathematical research in that same capability arc.
Tao's earlier discussion of AI-generated Erdős solutions emphasized hybrid contributions and “cheap wins”; his qualified response here makes the distinction important: a verified result can be notable without yet establishing a durable new research method.
First-order effects
The amateur gains access to a level of mathematical problem exploration previously associated with specialist training, while the proof itself becomes subject to expert scrutiny for correctness and novelty.
ChatGPT's reasoning-oriented Pro offering receives a concrete research-use case, though Tao's caution limits any immediate claim that it has changed mathematics broadly.
Second-order effects
Mathematicians and AI researchers have greater incentive to test models on open problems, but verification, attribution, and explanation become more central bottlenecks when candidate proofs can be generated quickly.
Reasoning-model providers will be pushed to demonstrate not just benchmark performance but reproducible, human-checkable outputs on frontier tasks; paid access to extended reasoning may matter more in that competition.
Third-order effects
If such results recur and survive review, mathematical work could shift toward hybrid workflows in which humans formulate, validate, and extend machine-generated approaches rather than perform every search step themselves.
The lasting impact depends on whether AI outputs yield reusable methods, not isolated solved problems; that uncertainty is precisely why this remains an early signal rather than evidence of wholesale research automation.
The trend: This is one data point in the spread of reasoning models from benchmark and coding performance into expert workflows where verification and methodological novelty determine their real value.
I should say before I get mobbed on that I don't think Tao meant it that way or intended to demoralize. There are just too few voices of real encouragement in the world so it's worth trying to do a little better in the miniscule ways that I can
This is so funny because it directly contradicts Tao's “when a problem is posed everyone tries their repertoire of techniques on it, then if it doesn't crack we set it aside and wait till someone comes up with a new technique, at which point we try that trick on many old problems
@QiaochuYuan Clearly true with other kinds of knowledge (although not if one sees all reality as boiling down to math anyways of course)- the devas and the kinds of knowledge they possess, the humans having a different version of the Prajnaparamita Sutra, the angels having a diff…
@Ananyo Interesting statement from Tao because that's what a lot of ostensibly smart people would say when a genius solves a proble they could not. And given he is one of the smartest humans on the planet.....
@yoitsyoung I tried re-running his same exact prompt 10x. However, it seems to consistently keep giving up and providing partial results. I wonder if it's some sort of lottery where you have to keep resending until it finally gives in?
Pretty remarkable to think this problem went unsolved purely because of some strange, collective “block” that prevented humans from approaching it the right way Naturally the next question is: where else might these blocks be?
@Ananyo He attacked it with a statistical model of all of humanities knowledge. The answer was out there but in different locations. Doesn't mean ChatGPT was intelligent. The kid did this using a tool. ChatGPT would have never have done this on its own. That's what people don't
for the record i skimmed the discussion of this erdos problem and i don't think the situation is quite this dramatic, yet, but it's nice to have some fuel for the imagination huh
It's going to be extremely funny in ten years from now when someone using GPT 11.4 or whatever asks for some vibecoded app that vaguely involves the Traveling Salesman Problem and it just bangs out a constructive proof of P ≠ NP as an aside while bitching about React plugins
Sounded so crazy I had to check how he prompted ChatGPT. He only wrote 9 sentences. “Don't use the internet. </problem> </lemma 1> </lemma 2> </lemma 3> REMEMBER: this unconditional argument may require non-trivial, creative and novel elements.” Wow.
23 years old with no advanced mathematics training solves Erdős problem with ChatGPT Pro. “What's beginning to emerge is that the problem was maybe easier than expected, and it was like there was some kind of mental block.”-Terence Tao https://www.scientificamerican.com/ ...
spooky implication that there is potentially some whole universe of “shadow math” that you have to make inhuman mental movements to access so no human have done so yet, that is going to be increasingly revealed by frontier models [image]
@yoitsyoung Yeah, the models will give up quite fast if they “know” based on internet search that a problem is open for Y years. Just make them believe its a test of their ability and there is a result they don't yet know and they are much more capable.
@Ananyo Buried at the end: Tao saying the problem was ‘maybe easier than expected... like there was some kind of mental block.’ A 23-year-old without a Ph.D. did the trying-weird-things labor. ChatGPT Pro lowered the prior on which approach was worth checking.
taos referenced “mental block” is simple: garbage consensus conventions that arent strictly required by plain logic, but are fallaciously treated as such “because thats how we do things.” its “bugmens' math,” nothing mystical or special here
@Ananyo Can't agree with Tao on this. The implication is either: 1) The “outsiders' perspective” truly is valuable in higher maths 2) You can thank ChatGPT Pro, and the human doing the prompting was basically irrelevant. 3) some mixture of both
@yoitsyoung How much math solved by AI now is just using the right phrasing? Astounding it was as simple as “this unconditional argument may require non-trivial, creative and novel elements”
@yoitsyoung @sama Why not set aside a (relatively) small amount of compute and have GPT 5.5 autonomously and continuously working on thousands of open problems?
A 23-year-old with no advanced math training just vibe-mathed a 60-year-old Erdos conjecture with one ChatGPT 5.4 Pro prompt. The AI used a method no mathematician had tried. The proof has been confirmed by Terence Tao. Pretty cool news.