>Can every interesting mathematical question be answered that way? Probably not, and even questions that can may have more interesting and satisfying solutions that invoke novel ideas and insights. Perhaps, in the near future, AI systems will be able to come up with such insights, but, at the very least, let’s recognize that we are not there yet.

This keeps being repeated by AI skeptics, yet AI keeps solving more and more complex tasks. We've reached the point that it's even started solving Millennium problems.

>Telling us that some AI agent is spinning out theorems that are highly interesting to it and other AI agents does nothing for us.

This is the future of pushing the frontier though. AIs need to be pushed to get better and better. AI understanding of math is millions times more important than human's.

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socializer 2 hours ago | parent | next [-]

> This keeps being repeated by AI skeptics,

And now you're hearing it from a guy who's one of the foremost, early proponents of AI in math.

> AI understanding of math is millions times more important than human's.

Important to whom?

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charcircuit 2 hours ago | parent [-]

Important to the field of mathematics.

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socializer 2 hours ago | parent [-]

"The field of mathematics" is something that humans engage in, chiefly to advance human understanding in about the most abstract way possible. It's not some self-sufficient, sentient being that exists for its own sake. Also, contrary to what's often repeated by AI maximalists, it's not a major source of innovation in other disciplines; most of the math the world actually runs on is hundreds of years old.

We do math mostly for fun.

	▲	charcircuit 20 minutes ago \| parent [-]
		>It's not some self-sufficient, sentient being that exists for its own sake If humans didn't exist do you think a^2 + b^2 = c^2 would cease to be a thing? Math is built on top of logic and it is something that exists independent from the physical realm.

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askjdfksdbfhk 2 hours ago | parent | prev | next [-]

>AI understanding of math is millions times more important than human's.

This is a persistent misconception that I see on HN (although not usually framed as abrasively as you have chosen to frame it).

Math is not an engineering discipline. Pure mathematics research is not done with an eye towards practical applications in other fields. You should think of it more like the humanities--it is done because it enriches the human experience (and it's not very expensive).

You could give us a black box oracle that could tell us, with 100% certainty, whether the 50 most famous and important open conjectures in math were true or false, and it would be more or less worthless. What does it actually get you? This isn't a rhetorical question.

AI in math is valuable only insofar as it ultimately helps drive human understanding.

There is another side of math that is more driven by practical applications: statistics and "applied math" and whatnot. This is what most people think of when they try to imagine math research, because it is much closer to the math that they have learned in their school education. A lot (but not all) of this math would get more value out of black box results, yes. But don't conflate this with the entire field of mathematics as a whole.

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calf an hour ago | parent [-]

But why? Responding to vulgar economism/instrumentalism with, "Well actually mathematics is this and that, human understanding/journey etc. etc." does not explain why mathematics ought to be those ways. Without elaboration such assertions amount to professional dogmatic narrative in the other direction. Professionals can be very good at that kind of rationalization too.

	▲	jltsiren 30 minutes ago \| parent \| next [-]
		Some things are valuable, because they keep people alive and healthy in the short term. Some are valueble, because some people find them inherently valuable. Pure mathematics is in that category. And then there is bureaucracy. Bureaucracy has no direct value, but it may have indirect value, if it helps us achieve things that are more directly useful. Pure mathematics has had a lot of indirect value until now. It turns out that training people to do mathematics for the sake of doing mathematics, at any level from schoolkid to mathematics professor, teaches skills that transfer to other domains. If human thinking becomes obsolete, that indirect value may be gone, but the direct value will remain. The results in pure mathematics are largely irrelevant, except as means of acquiring transferable skills. Sometimes they have practical implications, but such situations are exceptional. And there is not much correlation between the practical value of a result and its value as seen by mathematicians.
	▲	askjdfksdbfhk an hour ago \| parent \| prev [-]
		I think I already answered this in my comment. I claimed that I don't see much value in a magical black box theorem-proving oracle whose proofs could not, and would not, be understood by humans. If you disagree (as the GP does, apparently), I ask you--what value do you see in it?

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jibalt 2 hours ago | parent | prev | next [-]

> This keeps being repeated by AI skeptics, yet AI keeps solving more and more complex tasks. We've reached the point that it's even started solving Millennium problems.

Yes, so? Still not "novel ideas and insights", which is what you responded to ... and the statement wasn't made by an AI skeptic.

> This is the future of pushing the frontier though. AIs need to be pushed to get better and better.

It would be far more honest to say "I want AIs to get better and better". But there are costs. What are you willing to accept?

> AI understanding of math is millions times more important than human's.

Ah, it seems that "replace humans with AIs" is not too much for you.

To whom is that more important? Not mathematicians.

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xanderlewis 2 hours ago | parent | prev | next [-]

> We've reached the point that it's even started solving Millennium problems.

Since you’re so certain, how long do you think it’ll be before all of the millennium problems are solved by AI (by leveraging the current literature)?

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goatlover 2 hours ago | parent | prev | next [-]

Math as a field is unbounded. There's always more to discover, new systems to invent, new problems to find. It's not just some predefined set of unsolved problems.

Math is also a matter of what is both interesting and useful to humans.

For some reason there is this virulent strain of anti-human AI rhetoric that machines will replace us. But what is the purpose of math as a field of study if we're not in the loop?

	▲	xanderlewis 2 hours ago \| parent \| next [-]
		It’s like people think problems are given to us by God. We make our problems up! > For some reason there is this virulent strain of anti-human AI rhetoric It’s just… nasty, isn’t it? Facts aside, one does have to wonder what motivates not the beliefs themselves, but the, well, frankly aggressive, way in which they’re expressed. Bitterness and envy felt towards those who have actually done the hard work and achieved things?
	▲	quaverquaver an hour ago \| parent \| prev [-]
		...but math does have applications! maybe there is some math that people can't understand, but which has engineering applications, and which machines might apply to solve problems?

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thereitgoes456 3 hours ago | parent | prev [-]

Tasks are not simply integer “difficulties” where, if your “intelligence” exceeds the “difficulty” then you will solve it.

The question is to what extent AI will affect creation of new branches and elegant ideas in mathematics. This question applies to every area. Has it created an interesting new way of thought in any area other than those where massive tree search can be mistaken for such?

I don’t think it’s impossible but the evidence doesn’t point clearly to it.