[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.

[glenstein]

Exactly, you're almost getting it. Hence the value of "pure" research in both science and math.

[cubefox]

You are not yet getting it I'm afraid. The point of the linked post was that, even assuming an equal degree of expected uselessness, scientific explanations have intrinsic epistemic value, while proving pure math theorems hasn't.

[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?

[glenstein]

That's an odd choice, because prime numbers routinely show up in important applications in cryptography. To actually solve RH would likely involve developing new mathematical tools which would then be brought to bear on deployment of more sophisticated cryptography. And solving it would be valuable in its own right, a kind of mathematical equivalent to discovering a fundamental law in physics which permanently changes what is known to be true about the structure of numbers.

Ironically this example turns out to be a great object lesson in not underestimating the utility of research based on an eyeball test. But it shouldn't even have to have any intuitively plausible payoff whatsoever in order to justify it. The whole point is that even if a given research paradigm completely failed the eyeball test, our attitude should still be that it very well could have practical utility, and there are so many historical examples to this effect (the other commenter already gave several examples, and the right thing to do would have been acknowledge them), and besides I would argue they still have the same intrinsic value that any and all knowledge has.

[cubefox]

> To actually solve RH would likely involve developing new mathematical tools which would then be brought to bear on deployment of more sophisticated cryptography.

I doubt that this is true.

[amazingman]

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