AI Just Proved a 50-Year-Old Math Conjecture—What Happens to Mathematicians?
Is mathematics about to enter the conservatory?
A new paper by Wang & Wu claims to prove the Spherical Hadwiger Conjecture, open since 1974, with AI assistance. The authors used OpenAI Codex to develop proof details and edit the manuscript. This milestone, coming alongside Claude's formalization of Fermat's Last Theorem, raises urgent questions about the future of pure mathematics. As AI takes over the labor of proving theorems, the author asks whether mathematics will become like classical music—preserved in a conservatory, but no longer a thriving creative field.
When intelligence is limited only by silicon and electricity, will we be willing to continue to support a culture that has mathematicians?
- dofm
> Our society does not support classical musicians in the same way that we support ‘popular’ musicians.
It really really does. Popular/rock/folk/classical musicians all earn much the same way now: a blend of teaching, occasional performance fees, functions performances like weddings and galas, music-related side-gigs (composition, arrangement and recording for commercial music), and non-music-related side gigs — teaching non-musical things, gardening, painting and decorating, bar work, office temp work, even full time jobs (doctors and lawyers, accountants). I know a couple of classical musicians whose actual money-making music is playing other instruments in funk/rock functions bands.
Even the "best" or most famous musicians, popular or classical, have side gigs. Approximately nobody makes their money only from performing or from recordings; that ended twenty-five or thirty years ago.
Elite soloists, maybe — but that is actually a pretty expensive life to live. I would be surprised if many of them risked a life where they had no other job.
The idea that a "conservatory" system exists that meaningfully supports classical musicians is nonsense almost anywhere in the world, I would think. Even the first-chair musicians and conductors have side gigs.
(ETA: I can't believe this is a workable model for mathematicians, either. Maybe for a couple of dozen the world over. But there is no performance, no regionality, little in the way of public dissemination, little in the way of refl […]
- madrox
We are largely having a reckoning with whether a discipline is the process or the outcome.
Music didn't enter the conservatory so much as the relative interest in various styles have changed over time. I get that the author was implying that by talking about pop music, but what was music doing before Mozart came around?
Every field is having this existential crisis right now, from art to math. Especially in art, the anti-AI hate mostly reduces to arguing that art is the process not the outcome.
The need for research-level math isn't changing (if anything, it may accelerate), but how we do it is. The languages, systems, and process I used to write code has changed a lot since I wrote my first line of BASIC in 1994. Mathematicians, I expect, have not encountered nearly the same amount of disruption in academia. I feel for them.
- whateverboat
> Could this model work for mathematicians? It’s easy to imagine: in Euclid’s time, mathematics largely existed as an intellectual pursuit worthy of a few inclined people.
NO! Pythagoras discovered his theorems because they wanted to divide up the revenue. While there have been sections of mathematics discovered by leisure, majority of mathematics has been discovered due to an engineering need.
- rtpg
> Classical music has been institutionalized, sent to the conservatory as a relic. A small segment of society has decided the ability to perform it is worth preserving, and devotes a sliver of capital to that end: training young people, and paying a few of the best players in the biggest cities to do it professionally.
I had a whole discussion with a German friend whose husband works in opera (this was after Chalomet's "opera as a dead art" comments) and their view was mostly that this view of the world does not hold for at least chunks of Europe. To their mind, there is still both active input into this space, support in this space, and there's societal support to some degree or another.
I don't know the realities on the ground, but that annecdote did make me wonder if I simply assumed that the world of classical music wasn't as dire if you leave the States, at least in terms of job stability.
The comparison to popular music is kinda funy too... plenty of pop musicians that don't live off of their music, right? Maybe we're not generating "Taylor Swifts of Oboe"s but I feel like the measure is more about the median (or even the 90th/95th percentile?) when it comes to art, rather than the top of the top.
- nxpnsv
Our AI system don't just do things. They do it because someone asks. A lot of the boom in AI maths results are solving human formulated problems mostly for PR benefit. Once the novelty passes, would Anthropic or OpenAI keep spending? And without mathematicians to ask the right questions and able to appreciate the results, why would AI driven research continue?
- rayiner
> Consider classical music. Our society does not support classical musicians in the same way that we support ‘popular’ musicians
“Society” is a leaky abstraction here. If you reify society as a thing that is capable of “supporting” or “not supporting” something you mean essentially the government. In that case, “society” probably provides more support to classical music than pop music, through grant programs, public funding of symphonies, etc.
- djmips
They didn't mention coders but my idea is to have Silicon habitats of programmers recreating nineties professional programming on Pentium PCs in dimly lit cubicles. Tourists shuffle by watching live coding like watching a blacksmith at a Colonial Williamsburg.
- chr15m
> I haven’t fully verified the proof; I worked through it with Claude Fable and it passes the sniff test, but fully digesting it will take a bit more energy than I have right now.
This is overlooked but really important. Nobody wants to watch robots play chess against each other - we watch human chess even though bots are better. Nobody needs math that has not been verified by humans. Human understanding and communication is the important part of mathematics.