Comment by Bourget
9 hours ago
If it's worth anything: I have a PhD in (theoretical) mathematics and I entirely stand by stabbles' comment.
There is a real, undeniable possibility of AI becoming better at mathematics in the same way that it became better at chess and Go, and in such a scenario, one may expect the community's response to be comparable.
It makes no sense to compare mathematics with chess. Chess is a sport. No one is interested in watching two machines compete. Chess doesn't have a practical impact. Etc. What you seem to suggest is that AI will be able to completely (or at least in a great part) replace mathematicians. It could be the case in the future, but no one knows right now, and more importantly: tech companies don't even think about it! they don't think on the externalities.
Does mathematics still have a practical impact without humans in the loop? I don't think there's one single answer to that question, but I think it's worth considering exactly what that impact may be.
Tech companies are as much the topic of this post as AI, I think that's the immediacy.
To a significant extent, the pursuit of mathematics research is a pursuit of human understanding of mathematics, without knowing where it might lead, or whether it might lead anywhere at all. I don't see how the motivation for that goes away on its own, but the institution supporting it is certainly threatened by the potential loss of grant money and graduate student applications.
> Does mathematics still have a practical impact without humans in the loop?
There's a single answer to that question: yes, math very much has an impact without humans in the loop.
Math has a lot of applications, and those applications don't care whether eg the new faster matrix multiplication algorithm was found and proven correct by a machine or a meatbag.
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Well, what you are saying that the situation is even better for math than for chess?
Chess is only valuable as an entertainment. So no one really gains anything from computers becoming really good at chess.
But with math, everyone in the world would gain from computers becoming really, really good at it.
But solving math problems is not the same as increasing understanding of math concepts.
> No one is interested in watching two machines compete
I’ve watched quite a lot of YouTube videos where two machines compete, so you may not be completely right here
The Square One commentary on the AlphaZero v Stockfish game from 2017 is pretty entertaining: https://www.youtube.com/watch?v=LnVDUQksIDk
In other videos he's called out the influence that this and similar games have had on human players in recent years, particularly around square denial and thorn pawn strategies.
https://tcec-chess.com/
Top chess engine championship is pretty fun to watch.
> What you seem to suggest is that AI will be able to completely (or at least in a great part) replace mathematicians.
There is no bound on the amibitions of AI. AI is set to replace anything done by people, and there won't be any room left for people. There isn't any task done by humans that AI won't be better at.
This is not a tenable outcome.
We should never have built machines with agency, rather than optimization processes that operate as subroutines of humans.
You say it like it's a bad thing.
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> We should never have built machines with agency...
We haven't quite crossed that bridge, but we do appear to be standing on it.
Stockfish isn't owned by a club of three trillionaires. It does not cost $15 million to achieve a result in Stockfish.
Stockfish does not steal research or scoop researchers.
The concentration of computing resources and capital should be examined by the math community.
The trailing edge of AI is catching up fast. There's plenty of open source (and even more open weight) AI models and they are getting better and better.
If that's your only objection: in a few years you can prove Rieman's hypothesis on your smartphone, no need for any trillionaires to give you permission. Does that make any change to your argument, or did it not actually matter?
This is the real problem. We're looking at a future where those who control AI have an insurmountable advantage in everything. They can control the amount of intelligence the masses have access to -- for their own safety, of course -- and they will never, ever be able to close the gap.
There's lots of competition in AI. Where do you see the 'insurmountable advantage in everything'?
Say they do. What then? Will people buy from them? What if we decide not to?
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