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.
- reisse
The elephant in the room no one talks about yet, imo, is "should public funding of math studies be adjusted due to AI breakthroughs?"
The sports comparison is wrong here because general public never paid for the specific match results. The value was always in the show, the advertising and betting around it, the health and educational value of doing sports, etc. And the sport mostly lives on what it earns, not on public funding.
Math, on the other hand, was paid for because people and states believed progress in math might lead to meaningful improvements in other branches of science, and, in turn, in our lives. If this is better served by AI, should we keep paying for the same number of tenure positions? Should we increase their number to handle the speedup brought by AI? Or decrease because they're being replaced? Should we pay more to those using AI to do their research, or to those explaining and exploring the AI-generated results?
- justinparus
"It is not the destination, but the journey that matters"
For now, AI will be another tool in the toolbox of mathematicians. With humans driving the conversation to help understand the world better. If/when AGI is reached maybe we won’t be in the driver seat as much. I don’t think that matters. The goal of math is to achieve greater understanding of the world, regardless if humans are driving or if an AI is.
- stabbles
Wouldn't AI make the field of mathematics more ambitious? In software development it feels that way: there are often tasks I can take on that would have been too risky in 2025, because it was unclear if they were worth it. Now you generate a prototype and can make much better judgement calls what is possible and what is worth pursuing.
- 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.
- HedonicEscal8r
I appreciate the wordplay in the title.
- 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.