EDIT: FFS why does this subject always get people frothing at the mouth before they even read the main point stated, only to go on and accidentally agree with it eventually? Pls read first before getting mad at stuff that I explicitly argued against.
EDIT 2: OK apparently there's still miscommunication, and I think the 1st edit somehow made it worse. When I say "useful" I put it in scare quotes on purpose and as I clarify in the 1st, 4th and 5th paragraps, it is NOT about value but about practical/technological utility.
I originally posted this on R*ddit to an audience of math nerds (so be warned that it is written with reddit STEMlords in mind) because there was a relevant convo going on and it would be fun to also have it here.
Sure, there is a lot of modern math that is practically useful, but the majority of pure math really isn't "useful' in any way, shape or form for now, and probably won't be any time soon, possibly forever. Like, even areas which are apparently "useful", like computer science, is full of things that have absolutely 0 practical utility and are solely of academic interest. Whether P does or doesn't equal NP doesn't really matter to anyone doing practical work. People wouldn't get upset about their discipline getting slighted or whatever if this stupid idea that scientific research should have "practical application" (which generally means "someone can sell it for money") hadn't proliferated, starting from schools.
Even when someone finds an "application" through some kind of far fetched (or not so far fetched) reasoning, it's some application to, like, highly theoretical physics that may or may not actually have something to do with the real world, and even if it does, it is only relevant in extremely niche experimental circumstances to the extent that it can't ever conceivably lead to technological progress. And even IF it does, sometimes it's just progress relevant only to more research about more stuff without application.
So even then you have to resort to saying something like "the result is not useful but maybe one of the methods used to prove it can be used for something else", and then that something else turns out to also not be useful but again "maybe one of the methods used to find that something else is useful for another something else and that other something else is useful for another other something else and then that other other something else has a practical application that is only relevant to research, but then maybe that relates to some other other other...", etc and it gets kind of silly. That or someone says something abstract like "it's useless now but it may be useful some time!". Maybe. Or maybe not.
In the end of the day the same arguments could be used to justify anything being useful via some contrived butterfly effect style conjecture. This of course is usually done because otherwise people can't get grant money otherwise, governments demand that research will produce results they can use to blow up people or sell stuff. Also the result of a bad educational system that emphasizes this kind of "usefulness", which therefore renders it unable to convince students that something is worth learning unless it is "useful". Of course "why should I learn this if it's not useful to me" is a very valid concern of students, but the problem is somewhere else. First, schools DON'T really teach any of the stuff that is useful and interesting to most people. If they did, then math would get a lot less attacks on that front. Schools teach with 30% of the students in mind, the ones who will really apply the things they learned. The other 70% can just go to prison or whatever as far as the educational system is concerned. Second, schools are very boring and antagonistic towards kids and since kids are miserable learning stuff, they need extra justification to learn them. Third, the schools themselves teach kids to think like that so it's no surprise that they do. Fourth, school math mostly sucks and is super boring for most people.
So yes, most modern pure math is indeed "useless". That is not the issue. The issue is, why does this matter? Why is it bad? Should it be bad? I don't think so. It's a false idea that gets perpetuated at many levels starting from school. But then there is the issue of mathematics being very exclusionary and distant from most people, which makes it harder for them to care, which brings us to the issue of outreach but whatever, that's a different matter.
Everything as in what? It would depend on what the proof is and what the nature of the problem is. If said angel gave an algorithm AND that algorithm turned out to be a fast one yeah. But odds are against that.
Yes, that is my point.
Except tons of physics research that is extremely well funded doesn't have any such benefits, and it's funded because the people who fund it don't understand that.
Thing is, WHAT math and physics were useful for these things? Definitely not string theory.
All physics is useless theoretical physics before a practical use is found. Electricity and lasers were LHC-tier experiments until they became core components of modern society. The steam engine was a useless party trick according to ancient Greeks.
No, this is a big misunderstanding. Early scientists working on electricity were doing experiments in their homes. What you say about ancient Greeks proves this point. They were far from being LHC tier experiments. They were things that people could easily do. I brought up string theory. Now, it is not known whether or not string theory is right. The issue is that to even tell any kind of difference between it being true or false, you have to have access to something like the entire energy of the sun. Again, that's just for you to be able to see a measurable difference, let alone use it for something.
Einstein postulated lasers, theoretically, from Planck's work. It wasn't from home experiments, it was from mathematical models. You bring up string theory because it hasn't been proven useful yet, but you're ignoring examples like the theory of relativity being applied via math to correct micro-inaccuracies in GPS satellites.
Yes, mathematical models of early quantum mechanics. Actually it was a bit "worse" than that in that when he did, QM was more phenomenological than rigorously grounded.
I do not at all debate that you can make theoretical predictions that have practical applications. I know. Except most of these predictions have to do with phenomena that can conceivably be applied, unlike string theory. QM wasn't developed to explain phenomena we don't even know if they exist and would require an accelerator the size of the solar system to detect. It was developed to explain basic fundamental phenomena that you can test in the simplest physics lab, and in fact started out as a phenomenological theory. This is much different. Is it possible to find a few examples of something that no one could see how it could ever be applied which did find an application, however that is extremely rare. And then there is stuff that inherently can't have applications due to the nature of what they are predicting.