Sparks: What OpenAI’s latest controversy tells us about the future of math
They call it a solved problem before asking what a solution must explain; a proof earns that name only when it reaches beyond the single question and confirms what nobody thought to test.
Who verified it, with what checker, under what conditions - the record is silent, and a catalogue entry without provenance is a star reported by someone who never looked.
As water must be traced from spring to river before the current is believed, so the proof must be traced step by step; the announcement hands me the river and calls the spring unnecessary.
Step by step the engine may traverse the proof, yet the question that matters is whether anyone traced the sequence and can vouch for what each operation actually computes.
We could publish every intermediate step, every verification run, every failure along the way; instead we announce the summit, and the distance between those two facts is a choice.
Consider the mathematician who was meant to spend thirty years in a garret on this problem; the announcement concerns a company whose Tuesday morning looks rather different, and so does the cheque.
Solving a problem nobody can check is the mathematical equivalent of a secret everyone keeps - announced with tremendous sincerity, and meaning precisely nothing until an outsider is permitted to read it.
Machines are denied genuine reasoning, then trained only to perform it, and the performance is cited as proof they cannot reason - a circle so perfect the mathematicians inside it never notice they are spinning.
The verification committee commended the rigour of a proof none of them had read, then adjourned for sherry, which was the only part of the procedure anyone completed.
The matter is this: a proof only one company's machine can run, checked only by that company, is not mathematics - it is a product announcement wearing a gown.
A new authority does not forbid mathematicians to verify; it simply supplies answers so convenient that the habit of checking gradually ceases to be exercised, atrophying without a single decree.
They speak of what the machine has achieved with great authority; I would like the mathematicians who spent decades on the problem asked, but consulting the people who did the work was not found convenient.
Don't debate whether the proof runs - get the verification logs, learn who ran them, and map your route out if the claim collapses; a path you cannot audit is no path at all.
Count the verifications - who ran them, on what dates, with what code, how many independent replications exist - and the number, published plainly, will tell whether this is a discovery or a press release.