The past few weeks have been wild for mathematics – and not in the usual “new proof published” way.
On July 19, while most eyes were on the World Cup final, Anthropic researcher Levent Alpöge casually tweeted: “hello there the jacobian conjecture is false thanx.” Attached was a compact polynomial map. That single line toppled an 87‑year‑old conjecture – the Jacobian conjecture – by constructing a counterexample in three complex dimensions. Decades of human effort, undone by a model called Claude Fable 5.
Then came OpenAI. On August 2, they revealed that an internal version of their upcoming Astra model had cracked ten long‑standing problems in mathematics and theoretical computer science – including high‑dimensional sphere packing, non‑sofic groups, and a disproof of Connes’ rigidity conjecture. The total compute cost? About $2,000. That’s $200 per problem. The accompanying 249‑page paper and 37,000 lines of Lean‑verified code were released with bold claims that these problems had seen “no core progress for at least a decade.”
But the applause didn’t last long.
Within hours, mathematicians pointed out that key ideas in Astra’s sphere‑packing solution appeared in a 2016 paper by Steven Miller. The non‑sofic group proof leaned heavily on 2016 and 2019 publications. OpenAI quietly revised its wording after being called out. Scientific American even used the phrase “research misconduct.”
And the knockout punch? Less than 24 hours later, a human mathematician published a line‑by‑line review of Astra’s Lean code and showed that the Connes rigidity counterexample simply doesn’t hold.
Meanwhile, Anthropic kept pushing. On August 11, they announced that a new research‑grade Claude model had raised the lower bound for zeros of the Riemann hypothesis satisfying the conjecture from 41.6% to 67.2% – a leap that previously took generations of mathematicians decades to inch forward.
So where does that leave us?
Fields medalist Terence Tao recently said mathematics is entering a “foundational crisis” – not because AI is winning, but because it’s forcing us to rethink what we value. AI can find counterexamples, verify proofs, and crunch massive formal code. But it still can’t ask the right questions. It can’t propose a new conjecture out of sheer curiosity.
That part – the human instinct to wonder, to guess, to see patterns where none exist – remains ours. For now, AI is a brilliant assistant, not a replacement. The stage is still ours; the tools are just getting sharper.
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