YHK - yet another hacker news clone

I don’t think we know whether or not that’s true yet. Imagine a problem which requires a paradigm shift or new novel techniques to solve. There is no proof (yet) that an AI could create one.

ANY problem?

But in a human way? I don't think so. The 700+ solutions that were put out by openAI are in no way accepted as solved until humans say so. It's kind of like saying SC2 was solved when Alpha beat the best players. The professional community just went on playing much the same. Math should do the same. Just with better tools

But how do you know which problems are worth making progress on? Traditionally, you'd find those by working on solving previous problems.

> The point is that AI will be able to advance on any problem better than any human.

Define "better".

Did any ai made any new interesting question or conjecture?

> The point is that AI will be able to advance on any problem better than any human.

If that was true it would of course be significant.

If you had no morals, 2 trillion dollars to spend, ability to commit intellectual property theft without consequences, and most of the smartest people in the world actively working to advance your cause... ...you really think you couldn't compete with the clankers?

The thing about much human progress on various problems is that human mathematicians formulate a human comprehensible machinery for the purposes of solving a given problem and then that machinery naturally suggests (to humans) further questions which then give rise to more machinery - And, in a sense, the value is ultimately the machinery, which has tended in the past to be relevant to physics, computer science, logistics, sociology and philosophy.

When AI writes proof no human can understand, it doesn't advance mathematics this way. Maybe AIs can understand their own proofs - meaning not just verify them but extract a machinery/broader-perspective (but I wouldn't count on it). But even machinery an AI isn't necessarily useful for humanity/society.

But the question is whether the AI will itself be able to decide on which problem to advance, and do it in an ethical and aligned way with humanity. And that if it does, its significance will be understood by humans.

Otherwise we're just creating a black box, easily manipulated by their owners, who would be ruling over human lives. That's not what people want

I think I’ll take the professional mathematician perception of how AI affects his field over random HN commenter saying it’s “pants on head stupid”

People are allowed to process their anxieties. And processing takes time. That said publicly doing it on the great modern internet attention/noise factory complicates the story.

I don't think it was a particularly well-reasoned essay (I thought the classification of finite simple groups is almost evidence for the opposite of what he says), but at the same time I don't think you understood his point.

If we have a theorem proving machine, then we can use it to prove theorems. If we have a machine to solve the Langlands program in one day, then we'll think of more things to prove after that. There's a million unsolved questions in number theory unrelated to Langlands, and if we knew Langlands (and why it was true) we could make new conjectures that our theorem proving machine could solve, rather than having to speculate for 50 or 100 years like now.

The possibility he's not considering is that the machine might be better even at conjectures, and then there really is no role for humans once the machine already knows things our primitive meat brains are too small to understand. But what he's saying isn't "pants on head stupid".

Lure people? It isn't a cult.

This is really well put, I totally agree with you.

There’s an immediate resistance towards change rather than embracing it and finding opportunities to improve and work with it.

Yes, this. Unless there is a true singularity where no more questions are ever asked, there will be definition be infinitely many problems to solve, and most of them we have not even glimpsed yet.

Singularity? Probably not.

Tech bro dictatorship? Unfortunately a bit more likely.

None of the above? Then we have a small shot at a great future.

Having a machine that solves hard problems must be a good thing.

To a first approximation I agree that it’s similar to industrialization. However there’s a key factor which distinguishes this case, and which makes the analogy less than perfect: there isn’t a profit motive in mathematics, so there was no push for this development from inside the field. Instead, the industrialization was entirely exogenous, from companies which do in fact have that profit motive and view math as a means to achieve it.

There might be a “proof motive” in math which one could argue will drive the full automation of theorem proving. But we must recognize that profit is more universally valuable (i.e. it has value outside the industry in which it was created), whereas proofs are only valuable inside the math community (at least the pure math proofs the labs have been publishing thus far).

How you get somewhere is important and tools change how you get there.

You can drive 1000 miles and arrive at the destination on the highway quickly.

Or you can take the slow road and walk. You discover unrelated things, make new relationships, see the scenery, listen and smell what is around you and have time to contemplate things which may or not be related.

This particular tool economy robs us of all these things in the rush to the destination.

I'd sacrifice "progress" a little for some of the better bits of humanity.

Two possible walls for advancing math with AI: first, it could be that the kind of problems that AI solves are the ones that don't open new avenues to concepts and ideas, and second, problems complexity is usually not linear, and the new and interesting problems to solve could be at a level of complexity beyond what AI can currently solve. Perhaps mathematicians could work to find ways to help AI cope with those walls.

Requoting the original blog post:

> To me, someone who chooses a worthwhile problem, obtains a proof completely using AI, understands it thoroughly, and uses it to develop interesting further questions or directions has made a substantial mathematical contribution. I would give that person substantial credit even if they supplied no new ingredient in the original proof.

Given the approximate $10-22 million API costs of solving these major math problems currently, we will also have to acknowledge that getting credit for major mathematical contributions could in many cases be less meritocracy and more about funding.

Less capable (but good enough) mathematicians with more capital will have a huge advantage over great mathematicians who are broke.

I'm not a mathematician, but that situation rubs everyone (except those with the most capital) the wrong way.

Are humans going to be able to recognize the things AI discovers?

It took us a while to make the planets line up neatly in a heliocentric system. Just last month I read that a whale mother "might" grief while carrying her stillborn child.

The limiting factor is human imagination and comprehension. No offense, but see your comment.

I think AI has already invented new math, but the guys haven't looked for it because they didn't think it possible. And even under their noses, they wouldn't understand what they see.

> It's not what you look at that matters, it's what you see. —Thoreau

Can we stop with this ridiculous narrative? That didn't happen.