ChatGPT proved an open Erdős conjecture in number theory using a method no human expert had previously considered, in what researchers are calling a ‘vibe-mathing’ advance.
Key Takeaways
An amateur used ChatGPT to produce a valid proof of an Erdős conjecture, a class of problem that has stumped professional mathematicians for decades.
The proof method was entirely novel: no human had previously attempted or even conceived of the approach the model used.
Experts were surprised and believe the technique may generalize to other open problems beyond this specific conjecture.
The term ‘vibe-mathing’ signals a recognized pattern: AI reaching correct results via unconventional reasoning paths that bypass established mathematical tradition.
Hacker News Comment Review
Commenters split on interpretation: some argue LLMs naturally escape expert blind spots because they are not locked into a single research tradition the way specialists are, making genuinely novel approaches more likely.
Survivorship bias concern surfaces: many people are currently running AI on hard unsolved math; this publicized success may be one hit among many silent failures rather than evidence of reliable capability.
No consensus on whether this is a repeatable research method or a striking outlier, but the ‘additive thinking’ framing – humans build on prior foundations and get stuck, LLMs do not – gets traction as a partial explanation.
Notable Comments
@adamgordonbell: Published the full prompt used – no web search allowed, explicit instruction for “non-trivial, novel and creative proofs” in number theory and primitive sets; model thought for 80 minutes 17 seconds.