The Jacobian counterexample has a human byline

A problem that stood since 1939 just took a serious hit. Around July 19–20, 2026, Harvard fellow Levent Alpöge announced a counterexample to the Jacobian conjecture: a three-variable polynomial map with constant Jacobian determinant that sends three different inputs to one output. The formula is reportedly about 216 characters long. It passed Wolfram Alpha and independent arithmetic checks, and Fields medalist Timothy Gowers called it significant — while noting that a counterexample search does not carry the theoretical depth of a structural proof.

Two caveats before anyone frames this as settled. Journal peer review is pending, and historical "counterexamples" to this conjecture have died on characteristic-p technicalities before; the coverage says checks are ongoing. I also have not seen Alpöge's original post directly — the facts here come via ground.news and secondary explainers.

Now look at how Alpöge himself credited the work: Akhil Mathew for the question, Claude Fable 5 for assistance. A mathematician chose the problem, directed the search, and signed the result. A model helped run it.

Four days to erase the mathematician

By July 23, Aakash Gupta's newsletter had compressed the story to Fable knocking the conjecture over with a single prompt, garnished with a claim that even Terence Tao had to ask ChatGPT about it. Alpöge's name appears nowhere in the item. And the Tao anecdote appears in none of the coverage I checked — the sources cite Gowers, not Tao. Treat it as unsourced until someone produces a link.

The consensus read is that this compression is harmless hype, the usual newsletter shrinkage. I don't think it's harmless, because the two framings are evidence for two different worlds. "AI disproved a major theorem" is evidence for autonomous capability — and this event is not that. "A mathematician using AI disproved it" is evidence for instrument-grade AI in expert hands — and this event is exactly that. Importing the wrong framing into your org means budgeting for autonomy you don't have and discounting the experts you still need.

Attribution is a sign-off decision

Here is the part that matters outside mathematics. My rule, and I now apply it to every AI-assisted deliverable: the byline belongs to whoever can defend the result under cross-examination, and the model gets a tools credit — same as the compiler, the profiler, and Mathematica always did. Alpöge instinctively followed that rule. The newsletter broke it within four days, and it broke it in the direction that erases the human.

This is not etiquette. At work, when a client's analyst ships an AI-assisted risk analysis, the same question decides who signs off, who gets audited when a number is wrong, and who gets paid. I watched a client team earlier this year try to log a model as the "author" of a generated compliance summary — their own audit trail then had no accountable person attached to a regulated document. We reworked the workflow so every artifact carries a human owner and a machine-assistance record, in that order. The fix took a day; noticing the gap took an incident.

"The model found it" is never a neutral summary. It is an attribution choice with liability consequences, and every enterprise rolling out agents is making that choice right now, mostly by default, mostly in whatever direction the demo deck pushes.

Steal this before your next AI-assisted deliverable ships: put two lines in the artifact's metadata — accountable owner (a person, who defends it) and assistance record (which model, which role: search, draft, check). If nobody will claim the first line, the deliverable isn't done. Run that rule across last month's AI-assisted output and see how many orphans you find.

The counterexample is likely a genuine milestone. The way it got re-bylined in four days is the more useful lesson, because your organisation's version of that rewrite is already happening in status reports.

Credit the instrument, sign as the human — a deliverable nobody will defend under cross-examination has no author, only a vendor.