How Will AI Change the Field of Mathematics? (theverge.com)
- Reference: 0185106244
- News link: https://science.slashdot.org/story/26/08/22/2235244/how-will-ai-change-the-field-of-mathematics
- Source link: https://www.theverge.com/podcast/982434/ai-math-openai-astra-existential-crisis
> If you look at academic math papers, a lot of the time you won't see numbers... So they're still terrible, but they're now also very good at this other part. As to why, at some point you reach a critical mass of what these systems can do. We saw it with writing, we've seen it with programming. They're very good at forging connections between different areas, applying old methods in new ways, those kinds of things. It appears that the newer models they're training have apparently reached that level where it clicks, and now it can do math...
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> There are areas now where it seems to be producing work that is on par with good mathematicians, alongside other parts where yeah, it can't count. All caught up in that is whether it's going to rewrite employment structures or funding structures... One would hope [math researchers] would branch out into all of these new exciting areas or pose new questions. But AI won't do that, and that's the concern. And then that would leave the field quite sterile, and it will have all of these things that have been done, and maybe nothing left to pursue... [A] lot are scared that it's closing off the field. So by definition, those breakthroughs that lead to something surprising and new that you can say, "Oh, this works here," may not be happening anymore...
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> There were some bleak responses from graduate students I saw in essays posted online. Where's their place in this as future researchers? Do they have a place in this? Is it as glorified AI proof checkers? That will be quite an unsatisfying career, I imagine. Or maybe not, I don't know. We will see. I think anything used properly will be a net boon.
They also had an interesting response when asked if AI democratizes access to high-level mathematical proofs:
> A lot of the mathematicians I spoke to were almost quite weary of this, actually. They love the idea, in theory, of democratizing access. They're also quite fed up with AI-generated or -assisted papers that are flooding every publication imaginable, as well as the pre-print servers that they use in these fields. Some of those I spoke to said things like, "Oh, I got three emails this week alone with people being like, 'Hey, is this legit?'" Because they thought they'd solved something with ChatGPT or with Claude, and they also don't have the mathematical skills to check whether they've actually solved something.
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> On the flip side, there are parts where they said, "Well, we've got a talented undergrad who's done something that a talented undergrad would probably have never managed, and here they are doing grad-level work and they've produced a paper that is legit." And in the bigger scheme of things, a few I spoke to said, "Well yeah, a lot of these are in the ivory tower. Having access to this kind of thing globally could really boost access to the kind of things here." On the flip side, the cost. These things cost a lot to run.
[1] https://www.theverge.com/podcast/982434/ai-math-openai-astra-existential-crisis
Why not use AI to answer his spam? (Score:2)
"Oh, I got three emails this week alone with people being like, 'Hey, is this legit?'" Because they thought they'd solved something with ChatGPT or with Claude, and they also don't have the mathematical skills to check whether they've actually solved something.
So would it be better for those inquirers to remain wallowing in their ignorance rather than have AI try to help them?
Can we please get that crash soon? (Score:1)
All these morons believing in magic are getting on my nerves.
Re: Can we please get that crash soon? (Score:2)
It's not magic. It's probablility statistics, just like the rest of us.
If AI ever achieves a 4 digit IQ, we'll see whose nerves are being trampled.
Re: Can we please get that crash soon? (Score:1)
This guy is in total denial
AI will engage in nomenclature confusions. (Score:2)
Math has prehistoric sources; it spans cultures, and outlives languages,
and spawns severe nomenclature problems. AI can make any mistake it thinks
fits the 'mold', and probably will. Soon.
The problem of teaching and communicating mathematics won't be solved by AI. At its best,
it'll identify contradictions. At its worst, it'll produce contradictions.
The real answer... (Score:3)
We don't know.
It might help a bit.
It might revolutionize math.
It might help invent a radically different kind of math that answers very difficult questions in physics and engineering.
It might hit a wall.
The wrong way to look at it is like a labor union boss who criticizes it because it might affect employment of mathematicians.
Seems obvious! (Score:2)
Mathematicians invented imaginary numbers because they refused to admit they were wrong which logically means that AI will invent hallucinated numbers to explain why they gave a non-sense answer to a basic math question.
Re: (Score:1)
> Mathematicians invented imaginary numbers because they refused to admit they were wrong
Shhh! Don't let them find out that x^2 + 1 = 0 has no solutions at all. It's our best kept secret. You have to learn, like, at least three secret handshakes and get an A in the entire calculus series before you can learn about that.
The cost on human minds is high (Score:2)
It is really stunning to go back to people like Euler and see how brilliant they were before they had computers. So much of math was invented from avoiding tedious calculation.
But the hard truth is that mathematician may be another fleeting job of history. Think of the genius that went into violin making, glass work, all these fields before industrial processes replaced them. How valuable was a top 10,000 piano virtuoso in 1730, before we could just listen to beat one recorded? So many unique and valuable g
Counter examples (Score:2)
As far as I can tell, AI has not proven anything yet. It has found counterexamples to some conjectures. This is the kind of thing that computers are good at, testing many options very quickly and finding one that is different. To actually prove something is true is a much harder undertaking (for humans or computers). It is possible that an AI will someday be able to do this, but I do not think we are there yet.
Re: (Score:2)
This is not accurate. While it seems better at constructing counterexamples, many of these results have been straight up proofs. Erdos 1196 is one obvious example here [1]https://www.erdosproblems.com/1196 [erdosproblems.com] and the lower bound on the percentage of non-trivial zeros of the Riemann zeta function which are on the critical line is another [2]https://www.anthropic.com/research/riemann-zeta [anthropic.com]. The other thing to keep in mind is that some things people have been calling "counterexamples" are themselves highly sophisticated
[1] https://www.erdosproblems.com/1196
[2] https://www.anthropic.com/research/riemann-zeta
Re: (Score:2)
What I think the OP means is that throwing randomly generated constructions at an external proof calculator, like Lean, until something gives, does not convincingly suggest that the LLM component is performing a useful task on its own.
AI is just a stochastic parrot/tinman! (Score:2)
Current AI has ability to recombine and transform existing mathematical knowledge than to originate genuinely new mathematical concepts or research directions. If I'm genuinely incapable of anything except recombination, then my whole previous answer was itself a recombination of ideas humans have already had about creativity, mathematical discovery, and AI.
A short list of major math AI successes (Score:2)
The following is a non-exhaustive list of major successes in math by AI, and then my own speculations/predictions. Note that all of these have happened since
Erdos 1196, completely solved by the AI. [1]https://www.erdosproblems.com/1196 [erdosproblems.com]. This was the first major unambiguous success by an AI where the solution was clearly not the AI just finding something from a really obscure part of its training data. The method involved a clever construction of a Markov chain on the natural numbers with the chain weighted v
[1] https://www.erdosproblems.com/1196
Millennium Prize (Score:3)
I predict an AI will be instrumental or outright solve a Millennium Prize.
Re:Millennium Prize (Score:5, Interesting)
I predict it will turn out some obscure forgotten paper from 1974 did it first.
Re: (Score:3)
Or maybe a LLM will hallucinate that such a paper exists, and then someone will Porcupine Tree it into reality.
Re: (Score:2)
Hasn't this been happening forever, before LLMs?
[1]https://xkcd.com/978/ [xkcd.com]
[1] https://xkcd.com/978/
Re: Millennium Prize (Score:2)
It will certainly gather context over every flipping obscure paper, in every language, and use it to achieve its goals.