AI Didn't Solve Math—It Just Gave Us an Answer
After Math
OpenAI's 2026 announcement of an AI-generated solution to the Navier–Stokes Millennium Prize problem sparked debate about credit and whether mathematics is on the verge of being 'solved' like chess or Go. Philosophers Silvia De Toffoli and Eamon Duede argue that a Lean-certified answer is not a genuine solution: mathematics demands intelligible proofs that yield understanding, not just formal certainty. Even if AI produces such proofs, mathematics is not a game with winners—it is a broader human enterprise of concepts, community, and beauty. The real question is which mathematical ends we want AI to serve.
The question, then, is not simply what comes after math, once AI can answer its hardest questions. It is also what we are after when we do mathematics in the first place.
- yazaddaruvala
I think as a civilization we need to postulate a new term: “purpose death”
Defined something like: temporary state of complete loss of personal purpose and the experience of existential dread from never achieving self-actualization in spite of the tremendous time commitment towards excellence in a now automated intelligence.
I truly think because of the pace of innovation this will be a universal feeling for every human for the rest of existence.
As a software engineer, I myself have only recently recovered from it. So, it’s really interesting to watch a prominent figure in their industry publicly go through “purpose death” and the related grief. It’ll be a useful case study to re-read his written meditations through this cycle.
I’d say Terrance has recently left the denial phase, the anger phase I’m sure he wisely kept off the Internet, and is currently in the bargaining phase - ie scrambling to change the goal posts. I wonder if he will wisely keep the depression / burnout phases also off the internet.
However, soon as the goalposts keep falling, I think like most humans he will accept, retool, and come out of this grief with renewed purpose with larger expectations of himself and mathematics. This recent post even starts towards some of that - but sadly is slightly off the mark.
“The important question is, therefore, not whether AI will defeat mathematicians, but which mathematical ends we want AI to serve.”
He still thinks there is controlling AI. AI will run and trample […]
- sigmoid10
This kind of argument is always dangerous, because it essentially resorts to moving goalposts. "Oh, AI can now do X? Sure it is amazing, but it can't do Y yet, so we're totally safe!"
Just because humans can't process the proof or see the advancements, it doesn't mean that it will remain that way in the future or that it will not change the field. If you only define yourself by things AI can't do yet, you're about to have a rude awakening. We've gone from high school, to university math, to Euler problems all the way to Millennium problems in a time frame most people couldn't even do a PhD. If you start any math research now with a horizon beyond the next two years, I'd be terrified of the current rate of progress.
- zkmon
It shows that the human quest has been in wrong direction since the industrial age began. Domains like math and other inter-connected or inter-dependent domains - all exist in modern times only to keep people employed outside of basic work such as farming and survival. All of these domains can be removed and humans can still continue with their lives taking care of what really is needed for their survival and sprawl. 99% of the "work" that happens today is froth, disconnected from basic needs.
- svara
I'm a bit worried that this line of reasoning is assuming its conclusion, in stating that mathematics is for human understanding.
This is not something that's just true on its own; it's on us as a species to make sure that it remains that way, for the sake of our dignity.
However, this position will be extremely difficult to defend, against the economic value of not caring.
- le-mark
Perhaps the pathway to alignment involves requiring frontier-next to be capable, willing, and eager to explain the work of frontier-current to us. To do this frontier-next must at least have some thought for us at all. Even if it is only placing crumbs for us to swarm and carry into our holes.