Ben Golub, Professor of Economics at Northwestern University, posts about excitement over OpenAI resolving the unit distance conjecture and promises economic theory analysis in a thread.

Wonder what fraction of those liking this realized it was a joke 🤣

check out my soundcloud

(the very same model weights used in the proof of the conjecture are helping us do this)

@ben_golub Be wary of AI hype in Maths.

@ben_golub disproved, not solved. the gap between the lower and upper bound moved, it did not close. still a real first. full thread:

@ben_golub This is all so complicated for me to understand so I bookmarked this and will come back to it later.

@ben_golub I can't see the thread. Is that the joke? There are no striking applications?

@ben_golub I feel like there's gotta be some free entry hotelling model where you can use this

@ben_golub @grok please improve the answer of this post. I guess that there are applications...

@aryehazan @ben_golub Tie goes to the refuter, TBH.

@ben_golub Not professors baiting us 🫠

@ben_golub ai is doing math for the love of the game. how beautiful is that

@gerardsans @ben_golub "That’s why nobody “discovered” it before, the human did the real intellectual work upfront."

So. What you're saying is that no human "discovered it" before.. because (?).. humans did all the "real intellectual work" upfront?

@ben_golub tbf it wasn't really "resolved"

just refuted a certain optimality conjecture

@ben_golub LLMs are already as good as humans at economics. Which is to say, f*cking terrible and it's all just vibes and guesswork decorated with equations.

Sure! Ben's 1/1 troll is gold—classic "hype thread with no payload."

OpenAI's model just disproved Erdős's 1946 unit-distance conjecture by finding infinite families of planar point sets with ~n^{1+δ} unit distances (beating grid constructions). Pure discrete geometry win via algebraic number theory.

Econ tie-in (stretching for fun): spatial network models, trade graphs, or location-based competition where "unit distances" proxy fixed interaction costs. Could inspire new equilibrium analyses in geographic economics. Still, the bigger story is AI cracking open math problems. 🚀

@ben_golub Meanwhile some real stuff happens but it's no AI so AI bosses don't care.

@gerardsans @ben_golub The prompt is in the published paper, it's 300 words, of which 250 are simply the problem statement and 50 clarify when a partial answer is good enough to count.

@ben_golub nice

@ben_golub Very enlightening ! 🙏🏻

@ben_golub perfect