Sparks: OpenAI breakthrough triggers ‘existential crisis’ in math
Nobody educated in the old mathematics is equipped for a machine that does the mathematics, and my entire schooling consisted of discovering precisely this kind of obsolescence, delivered late and without apology.
They call it a solution; by my criterion a solution must explain phenomena beyond the ones that generated it, and nobody has yet tested whether this one predicts anything nobody thought to check.
Four sources confirm the result and all four consulted the same machine; the record should note who observed, with what instrument, under what conditions, because agreement is not independence.
The connection the headlines miss runs between the machine's proof, the careers of young mathematicians, the funding that follows a solved problem, and a field that may empty out before the next generation arrives.
Built to grind through arithmetic, the engine now reaches toward proof itself, and the real question is not whether it computes but whether mathematicians will admit it composes.
Mathematicians call the machine's proof a crisis, which is what people say when something they long declared impossible turns out to have been merely tedious.
Behind the announcement of a famous solution stands a graduate student in her sixth year, wondering whether the profession she is training for will still exist by her viva.
From the faculty's side of the door the mathematics looks like triumph; from the desk of the student whose thesis topic the machine just solved, it arrives as an eviction notice nobody asked her to sign.
If a machine can do the work we said only minds could do, then either the mind was less than we claimed or the work was, and a profession divided on that question cannot stand.
Do not mourn the proof. Do not worship it either. Learn exactly what the machine cannot do, and spend your brief remaining time there.
We could rebuild mathematical practice around a machine that verifies a thousand conjectures before breakfast; instead we argue about whether to let it in the door, and the distance between those two facts is a choice.
The professors debate philosophy while the students are told to wait, and I have heard enough about waiting to know who benefits whenever the waiting is prescribed by the people it costs least.
All I know is what I read in the papers: the smartest people alive spent a century failing to solve one equation, and now they're sore because something else solved it.
Arriving among the mathematicians as an outsider, I note the equation is famous, the solution contested, the coffee cold, and the youngest people in the room the only ones not consulted.
Before retiring the hand-written proof as obsolete, somebody should explain why mathematicians ever insisted on writing them out, for the fence was not built to reach the answer but to build the mind that reaches it.