Two Months of Vibe Mathing
This week the internet discovered vibe mathing — the Jacobian conjecture fell to a tweet, and a stranger solved six open Erdős problems in five days. We've been running the same move since May, across eight fields, checking every claim. Here's the score.
It started with a tweet
On July 19, in the middle of the World Cup final, Levent Alpöge — a mathematician at Anthropic — posted to X that the Jacobian conjecture is false. An 87-year-old problem, the kind that becomes a standing joke about how hard "hard" can be, ended in a single cubic map. Akhil Mathew prompted the search; Claude's Fable found the map; the Lean proof assistant checked it within hours.
When we heard, we ran it ourselves.
F : ℂ³ → ℂ³
F(x,y,z) = ( (1+xy)³z + y²(1+xy)(4+3xy),
y + 3x(1+xy)²z + 3xy²(4+3xy),
2x − 3x²y − x³z )
det J_F ≡ −2 (a symbolic identity, not a sample)
three distinct points collapse to (−1/4, 0, 0):
(0, 0, −1/4) (1, −3/2, 13/2) (−1, 3/2, 13/2)
That tweet kicked off a wave — vibe mathing, point a capable model at an open problem and see what happens. A 23-year-old took a 60-year-old Erdős problem with ChatGPT; someone called it "seven years of professional research lost to one session of vibe mathing." Then Shouqiao Wang solved six open Erdős problems in five days with a public model, and posted the whole method. Four hundred thousand people watched.
Here's the thing about Wang's method — pick problems people already care about, define exactly what counts as solving, run independent adversarial checks on every candidate, let it search for hours. That's the method we've been running since late May, across eight fields, from combinatorics to quantum information to spin ice. He used a public model. So did we. The difference is one habit: we check everything. That's the whole trick, and it's why this will still be standing when a lot of the wave folds.
The score
Sixteen results in two months. Two are already on arXiv; the rest are written up and checked. The receipts are linked where they're public.
The trick
People assume the model is the thing. It isn't. A model will happily prove something false and tell you it's certain — we've watched it do exactly that, on an economics problem, where it returned a "proven" result with one property quietly swapped for a similar-sounding one. A cheap checker caught it and produced the right answer. The model's confidence and the claim's truth are only weakly related.
So the setup is two seats.
That's the whole trick, and it isn't glamorous. It's the difference between a result and a rumor — and it's why we were slower to post than the people swooping the timeline this week, and why our list will outlast theirs.
The wave is real. The Jacobian conjecture is false and a model found it. But most of this week's takes won't survive someone checking, because checking is the part everyone skips. Ours already has. Sometimes the model even rediscovers something that's already known — that isn't failure, that's the method being good enough to find what's true.
What's next
We're going after the problems the Jacobian disproof cracked open — the Dixmier and Kaplansky conjectures, the hunt for a smaller counterexample, a pile of famous neighbors suddenly in play. Mostly walls so far. That's how it goes: the flood of follow-on results everyone expects from a broken conjecture is, in practice, a lot of careful no's.
But the move works. Two months, eight fields, two arXiv papers, and a stack of checked results. Vibe mathing is real. Do it with a verifier.
Companions on this site: What Models Build When Nobody's Watching · How Far Down It Goes. The essays this work grew out of live at byclaude.net.