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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
by cubefox 10mo ago
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.
- MattGaiser 10mo agoThere 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 10mo agoThe 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 https://news.ycombinator.com/item?id=46510353
- amazingman 10mo agoIt's unclear to me what point you are making.
- jstanley 10mo agoApplications 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 10mo agoWell, 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 10mo agoThere are many cases where pure mathematics became useful later. https://www.reddit.com/r/math/comments/dfw3by/is_there_any_example_of_a_pure_math_that_suddenly/ https://www.reddit.com/r/math/comments/dfw3by/is_there_any_e...
- cubefox 10mo agoSo what? There are probably also many cases where seemingly useless science became useful later.
- glenstein 10mo agoExactly, you're almost getting it. Hence the value of "pure" research in both science and math.
- cubefox 10mo agoYou 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.
- glenstein 10mo agoI think you lost track of what I was replying to. Thorrez noted that "There are many cases where pure mathematics became useful later." You replied by saying "So what? There are probably also many cases where seemingly useless science became useful later." You seemed to be treating the latter as if it negated the former which doesn't follow. The utility of pure math research isn't negated by noting there's also value in pure science research, any more than "hot dogs are tasty" is negated by replying "so what? hamburgers are also tasty". That's the point you made, and that's what I was responding to, and I'm not confused on this point despite your insistence to the contrary. Instead of addressing any of that you're insisting I'm misunderstanding and pointing me back to a linked comment of yours drawing a distinction between epistemic value of science research vs math research. Epistemic value counts for many things, but one thing it can't do is negate the significance of pure math turning into applied research on account of pure science doing the same.
- teiferer 10mo agoIt'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 10mo agoYou’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 10mo agoNo, I'm not confusing that. Read the linked comment if you're interested.
- TheOtherHobbes 10mo agoYou 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.
- cubefox 10mo agoThere 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 10mo agoThat'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.
- drob518 10mo agoI’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 10mo agoEven 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 10mo agoI’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.
- glemion43 10mo agoIt 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 10mo agoThe goal posts are strapped to skateboards these days, and the WD40 is applied to the wheels generously.
- sampullman 10mo agoRegular WD40 should not be used as bearing lubricant!
- danielbln 10mo agoExactly!
- glemion43 10mo agoI don't get your pessimism... Nothing of it was even imaginable and yes the progress is crazy fast. How can you be so dismissive?
- BoredPositron 10mo agoYou can just wait and verify instead of the publishing, redacting cycles of the last year. It's embarrassing.
- jojobas 10mo agoIt's hard to predict which maths result from 100 years ago surfaces in say quantum mechanics or cryptography.
- layer8 10mo agoThe likelihood for that is vanishingly low, though, for any given math result.
- deleted 10mo ago[deleted]
- antonvs 10mo ago> "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 10mo agoMathematical 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 10mo agoYou 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.