[cubefox]

This illustrates how unimportant this problem is. A prior solution did exist, but apparently nobody knew because people didn't really care about it. If progress can be had by simply searching for old solutions in the literature, then that's good evidence the supposed progress is imaginary. And this is not the first time this has happened with an Erdős problem.

A lot of pure mathematics seems to consist in solving neat logic puzzles without any intrinsic importance. Recreational puzzles for very intelligent people. Or LLMs.

[glemion43]

It shows that a 'llm' can now work on issues like this today and tomorrow it can do even more.

Don't be so ignorant. A few years ago NO ONE could have come up with something so generic as an LLM which will help you to solve this kind of problems and also create text adventures and java code.

[danielbln]

The goal posts are strapped to skateboards these days, and the WD40 is applied to the wheels generously.

[sampullman]

Regular WD40 should not be used as bearing lubricant!

[danielbln]

Exactly!

[glemion43]

I don't get your pessimism...

Nothing of it was even imaginable and yes the progress is crazy fast.

How can you be so dismissive?

[danielbln]

You misread my comment.

[glemion43]

You mean like a small rocket build? Okay :)

[BoredPositron]

You can just wait and verify instead of the publishing, redacting cycles of the last year. It's embarrassing.

[jojobas]

It's hard to predict which maths result from 100 years ago surfaces in say quantum mechanics or cryptography.

[layer8]

The likelihood for that is vanishingly low, though, for any given math result.

[antonvs]

> "intrinsic importance"

"Intrinsic" in contexts like this is a word for people who are projecting what they consider important onto the world. You can't define it in any meaningful way that's not entirely subjective.

[cubefox]

Mathematical theorems at least have objectively lower information content, because they merely rule out the impossible, while scientific knowledge also rules out the possible but non-actual.

[antonvs]

You have it backwards. Mathematical theorems have objectively higher information content, because they rule out the impossible and model possibilities in all possible worlds that satisfy their preconditions. Scientific knowledge can never do more than inductive projections from observations in the single world we have physical access to.

The only thing that saves science from being nothing more than “huh, will you look at that,” is when it can make use of a mathematical model to provide insight into relationships between phenomena.

[MattGaiser]

There is still enormous value in cleaning up the long tail of somewhat important stuff. One of the great benefits of Claude Code to me is that smaller issues no longer rot in backlogs, but can be at least attempted immediately.

[cubefox]

The difference is that Claude Code actually solves practical problems, but pure (as opposed to applied) mathematics doesn't. Moreover, a lot of pure mathematics seems to be not just useless, but also without intrinsic epistemic value, unlike science. See https://news.ycombinator.com/item?id=46510353

[drob518]

I’m an engineer, not a mathematician, so I definitely appreciate applied math more than I do abstract math. That said, that’s my personal preference and one of the reasons that I became an engineer and not a mathematician. Working on nothing but theory would bore me to tears. But I appreciate that other people really love that and can approach pure math and see the beauty. And thank God that those people exist because they sometimes find amazing things that we engineers can use during the next turn of the technological crank. Instead of seeing pure math as useless, perhaps shift to seeing it as something wonderful for which we have not YET found a practical use.

[Ar-Curunir]

Even if pure math is useless, that’s still okay. We do plenty of things that are useless. Not everything has to have a use.

[drob518]

I’m not sure I agree. Pure math is not useless because a lot of math is very useful. But we don’t know ahead of time what is going to be useless vs. useful. We need to do all of it and then sort it out later.

If we knew that it was all going to be useless, however, then it’s a hobby for someone, not something we should be paying people to do. Sure, if you enjoy doing something useless, knock yourself out… but on your own dime.

[jstanley]

Applications for pure mathematics can't necessarily be known until the underlying mathematics is solved.

Just because we can't imagine applications today doesn't mean there won't be applications in the future which depend on discoveries that are made today.

[cubefox]

Well, read the linked comment. The possible future applications of useless science can't be known either. I still argue that it has intrinsic value apart from that, unlike pure mathematics.

[Thorrez]

There are many cases where pure mathematics became useful later.

https://www.reddit.com/r/math/comments/dfw3by/is_there_any_e...

[cubefox]

So what? There are probably also many cases where seemingly useless science became useful later.

[teiferer]

It's hard to know beforehand. Like with most foundational research.

My favorite example is number theory. Before cyptography came along it was pure math, an esoteric branch for just number nerds. defund Turns out, super applicable later on.

[baq]

You’re confusing immediately useful with eventually useful. Pure maths has found very practical applications over the millennia - unless you don’t consider it pure anymore, at which point you’re just moving goalposts.

[cubefox]

No, I'm not confusing that. Read the linked comment if you're interested.

[TheOtherHobbes]

You are confusing that. The biggest advancements in science are the result of the application of leading-edge pure math concepts to physical problems. Netwonian physics, relativistic physics, quantum field theory, Boolean computing, Turing notions of devices for computability, elliptic-curve cryptography, and electromagnetic theory all derived from the practical application of what was originally abstract math play.

Among others.

Of course you never know which math concept will turn out to be physically useful, but clearly enough do that it's worth buying conceptual lottery tickets with the rest.

[glenstein]

Just to throw in another one, string theory was practically nothing but a basic research/pure research program unearthing new mathematical objects which drove physics research and vice versa. And unfortunately for the haters, string theory has borne real fruit with holography, producing tools for important predictions in plasma physics and black hole physics among other things. I feel like culture hasn't caught up to the fact that holography is now the gold rush frontier that has everyone excited that it might be our next big conceptual revolution in physics.

[cubefox]

There is a difference between inventing/axiomatizing new mathematical theories and proving conjectures. Take the Riemann hypothesis (the big daddy among the pure math conjectures), and assume we (or an LLM) prove it tomorrow. How high do you estimate the expected practical usefulness of that proof?

[amazingman]

It's unclear to me what point you are making.