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| ▲ | drob518 7 hours ago | parent | next [-] | | 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 2 hours ago | parent [-] | | 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. |
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| ▲ | jstanley 14 hours ago | parent | prev | next [-] | | 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 9 hours ago | parent [-] | | 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 8 hours ago | parent [-] | | There are many cases where pure mathematics became useful later. https://www.reddit.com/r/math/comments/dfw3by/is_there_any_e... | | |
| ▲ | cubefox 8 hours ago | parent [-] | | So what? There are probably also many cases where seemingly useless science became useful later. | | |
| ▲ | glenstein 7 hours ago | parent [-] | | Exactly, you're almost getting it. Hence the value of "pure" research in both science and math. | | |
| ▲ | cubefox 6 hours ago | parent [-] | | 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. | | |
| ▲ | glenstein 6 hours ago | parent [-] | | I 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. | | |
| ▲ | cubefox 5 hours ago | parent [-] | | "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" No, "so what" doesn't indicate disagreement, just that something isn't relevant. Anyway, assume hot dogs taste not good at all, except in rare circumstances. It would then be wrong to say "hot dogs taste good", but it would be right to say "hot dogs don't taste good". Now substitute pure math for hot dogs. Pure math can be generally useless even if it isn't always useless. Men are taller than women. That's the difference between applied and pure math. The difference between math and science is something else: Even useless science has value, while most useless math (which consists of pure math) doesn't. (I would say the axiomatization of new theories, like probability theory, can also have inherent value, independent of any uselessness, insofar as it is conceptual progress, but that's different from proving pure math conjectures.) | | |
| ▲ | cwnyth 4 hours ago | parent [-] | | It really speaks to the weakness of your original claim that you're applying this level of sophistry to your backpedaling. | | |
| ▲ | cubefox 2 hours ago | parent [-] | | There are 1135 Erdős problems. The solution to how many of them do you expect to be practically useless? 99%? More? 100%? Calling something useful merely because it might be in rare exceptions is the real sophistry. |
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| ▲ | teiferer 14 hours ago | parent | prev | next [-] | | 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 13 hours ago | parent | prev | next [-] | | 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 13 hours ago | parent [-] | | No, I'm not confusing that. Read the linked comment if you're interested. | | |
| ▲ | TheOtherHobbes 12 hours ago | parent [-] | | 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 6 hours ago | parent | next [-] | | 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 7 hours ago | parent | prev [-] | | 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 6 hours ago | parent [-] | | 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 5 hours ago | parent [-] | | > 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. | | |
| ▲ | glenstein 4 hours ago | parent [-] | | It already has! The progress that's been made thus far, involved the development of new ways to probabilistically estimate density of primes, which in turn have already been used in cryptography for secure key based on deeper understanding of how to quickly and efficiently find large prime numbers. |
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| ▲ | amazingman 14 hours ago | parent | prev [-] | | It's unclear to me what point you are making. |
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