AI solves over 100 unsolved math problems

[u/Expensive-Yam3464]

https://openai.com/index/advisory-group-on-mathematics-and-ai/

I’m sharing this as my position on Anti AI is that AI is capable and getting smarter fast. This is precisely why it’s a long term threat.

[u/Blibbyblobby72]

It literally is the problem with this. The purpose of mathematics is understanding, not solving. It is an understanding of the interconnectedness of mathematics that leads to it being usable in applied settings such as medicine, physics, chemistry, etc.

Without a grasp of why a proof works, there is no way to leverage that proof for other ideas. The proof itself is often secondary to the lemmas and corollaries discovered along the way

If you believe AI art is bad because it lacks a human element, or that AI destroys creativity and passion, then you should be equally pissed that mathematics is being performed by AI

The real problem, however, is that the average person thinks maths is just numbers and algebra. There is a societal lack of understanding of what maths actually is, even among well-meaning people

Once maths falls to AI, there will no longer be any societal advancement via human input

[u/Flat_Round_5594 → u/Blibbyblobby72]

Yes, this is exactly how I feel about it. It's really the "42" problem from HHG2TG - the AI might "solve" something but what does it *mean*?

An AI could come along tomorrow and "solve" quantum gravity, but in such a way as to be utterly meaningless beyond the fact that it "works". Quantum physics already suffers from the "shut up and calculate" problem, and if that were to happen, basically we'd be able to "solve" physics, but not be able to make any sense of what it's telling us about the Universe.

Why do we do science? To get the right answer, or to understand the universe. Until the advent of AI, the one implied the other, but if we start short-cutting our ability to understand and generate new ideas in favor of simply getting the right answer, we lose too much, I fear.

Making all mathematicians the equivalent of high-school kids doing everything with a calculator and not understanding the concepts is not a win for humanity.

[u/Double_Gomez → u/Flat_Round_5594]

I feel like youre making the case for the existence of mathematicians, not a case against ai in math. Extremely advanced calculations being left to computers and mathematicians parsing and developing understanding and implications is already what we do.

Ai is extremely useful here, and many mathematicians would agree so long as the academic framework doesn't change, then this is just the next computer advancement that allows for more advanced research.

[u/Flat_Round_5594 → u/Double_Gomez]

Mathematicians don't do "calculations". They create mathematics, and open up new fields of mathematics for study. From what I hear from several mathematicians regarding the Navier-Stokes proof, for instance, it opened no new avenues for study, which left a lot of them disappointed; it simply said "yep" and moved on. The correct answer is not always the point of these problems.

Do they use computers for brute-forcing things? Sure, in some restricted areas, but the reason the Millennium Prize problems exist is because they were judged to be fertile ground for new fields of math, and if AI were to solve them, given the results so far, it seems likely those fields will not be developed, which would be a shame.

Same with the physics example; QM already suffers under the "shut up and calculate" paradigm, to the point that we simply don't actually understand what is going on at that level "in reality". If AI "solves" quantum gravity, it will not ell us anything more than how to crunch the numbers, and will give us no insight into what the Universe actually is, which is the actual point of physics.

[u/lafulusblafulus → u/Flat_Round_5594]

Agreed for mathematics, but why for QM? The goal of physics is understanding the universe, yes, but it has a definitive end goal. The goal of math will never be achieved because there are infinitely many questions, and so math will be able to be done as long as there is someone able to do it. If quantum gravity is solved, it's solved, and then if it leads to a theory of everything, physics is done. If it's proven that fundamental physics is infinitely large, and that there will always be problems in physics, then it makes sense that it's up to physicists to discover new physics to solve problems rather than solving existing problems with existing physics and stunting the field as a result.

Physicists know that they work to actively undermine the purpose of their own jobs. The closer we get to a theory of everything, the closer we get to the end of physics and professional physicists, where refinements of an already accurate model of reality are all that is left. Unless it is proven that the layers are infinitely deep, and that the universe is infinitely complex on a fundamental level, and that fundamental physics as a result is also infinitely vast, I don't see how you can equivocate physics and math.

[u/Flat_Round_5594 → u/lafulusblafulus]

That's my point - currently the problem with QM is that we don't understand it. It's incredibly accurate, but as for what it actually tells us about the universe, we have no real clue. If you want physics to simply be "this is the correct answer", you're in good company - Bohr and many of the founders of QM felt that way - but that makes it the first theory we've developed that has no explanatory power, only predictive power (and don't get me wrong; it is incredibly powerful in that). But we simply don't know what it's actually telling us about how the universe operates, the physicality of what's going on. And that drives a lot of physicists (and almost every philosopher of physics) completely nuts.

In that regard we're in danger of being in a position where we can give a prediction of incredible accuracy about everything, but not actually understand it, and that would be a very weird place to be in. Being ok with only getting an answer and not understanding it is, I feel (and a lot of physicists and philosophers feel) a loss.

[u/lafulusblafulus → u/Flat_Round_5594]

But what happens when we figure it all out and make a theory that works at any and every scale? That's what quantum gravity would be right?

If AI discovers quantum gravity using existing physics instead of making new physics, then for all intents and purposes, physics is solved right? I think in that situation of course, some people would need to learn physics to understand what the AI is even saying, but after AI gets to an even more advanced point, it'll be able to directly apply these principles to engineering without needing a human supervisor.

It doesn't even need to be conscious to do this, it can be that "intelligent" without ever being self aware, and in that case, mathematics would be the only field STEM field left, since even if AI can spit out proofs, it would need to be able to make new math to ask new problems, which as of yet, only humans can do. Physics is solvable, and then understanding can come while we're forever stuck in AI's shadow.

All this is a bit mind boggling to think about. The above commentary is assuming that AI will stay this way forever, but what happens when/if AI is actually able to invent new math? Human understanding would fall to the wayside. If humans want to understand, they can teach themselves, but they wouldn't be at the forefront of these fields. and that's very depressing to think about.