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.
Whether P does or doesn’t equal NP doesn’t really matter to anyone doing practical work.
P=NP is monumentally important to practical work. If it’s true, all problems are easy to solve.
Leaving aside from that terrible abysmal awful example to address your general point: there’s a difference between basic research and engineering. We need to find out basic facts about what sort of world we’re in in order to do engineering later. We obviously can’t know the “practical application” of things that we don’t know yet; we need to find them out first. Did Rutherford think about the “practical application” of his model of the atom? Or did the street eventually find its own use for it?
P=NP is monumentally important to practical work. If it’s true, all problems are easy to solve.
that doesn’t necessarily follow right? like what if all NP problems are solvable in n^googolplex steps or somethinh
Even n^googolplex is still sub-exponential time, and in practice ridiculously shitty poly time algorithms can often be reduced in magnitude, whereas if you have an exponential time algorithm you need to find something completely different.
P=NP is monumentally important to practical work. If it’s true, all problems are easy to solve.
It is not, at least not necessarily. Whether or not such a solution conceivably exists doesn’t really matter at all to a programmer. Let’s say it turns out that P=NP. Cool, then said fast solution exists. Does that mean the programmer can find?Not necessarily. But they can try. Let’s say P does not equal NP. Cool. Then a faster solution may or may not exist. But the programmer doesn’t generally know if the solution they found is the fastest one possible, so they probably will still try to find a better one. Nothing really changes for the programmer whether or not P equals NP. The programmer will keep looking for a faster solution to the extent they are willing or able to, unless they know the solution they found is the fastest possible, which is not something P versus NP can tell you alone. Oh, also forgot to mention that even if P=NP, a large number of problems won’t have solutions which can feasibly be solved in polynomial time anyways due to other restrictions.
It is an example of something that SOUNDS like it has important applications but doesn’t really in itself. This is similar to Navier-Stokes. The act of trying to solve NS will probably give immensely valuable insight into turbulence etc, however in terms of practical applications a strict solution of NS is not particularly important, because the systems involved are massively chaotic and real fluids don’t truly obey NS anyways. In Mathematics existence and smoothness of solutions in many kinds of differential equations is a big problem, but anyone who does anything practical just ends up approximating them anyways.
The other argument you make is the same kind of hand wavy thing that people say and never convinces anyone. Some things you can tell are gonna have practical consequences, including Rutherford’s model. Others maybe not but they do turn out to have some. But then there’s all the other stuff.
Not extensively comp sci in particular except for a few classes (idk if that counts), but applied math in general.
This opinion is not unique to me. Like, many people who actually solely do research on the field will say as much. If P!=NP, well, that’s what everyone kind of expects already and nothing much changes. If P=NP but no one finds a polynomial time solution of an NP hard problem, that’s big news, but it still doesn’t change anything practically. If someone DOES find that, well, it might be useful, or it might not be, depending on a few other things, but just proving P=NP won’t give you that.
EDIT: I just saw your edit, hold on a while.
118 comments
You nerds really gonna have a struggle session about math?!
This serves as the arbitrary nth example in my inductive proof that Hexbear will struggle session about any topic. Now I just need the n+1 case to exist.
I’ll be publishing my paper shortly in the American Journal of Mathematics.
They’re not necessarily an actual troll. I know people like that and I’ve experienced music that way for brief periods.
It’s a little silly to get angry/surprised when you say inflammatory or just straight up wrong things at the beginning of your post and don’t clarify until near the end. Like, no kidding people don’t want to read the whole thing when the first paragraph makes it look like you have zero clue what you’re talking about
We’ve gone over this. The first paragraph is not wrong. Assuming this is what you are referring to, the process of solving P vs NP may bring something important for practical work, or it may not. But the actual answer to the question, which is considered extremely important theoretically and for good reason, won’t change much. IF it turns out that P=NP and IF the proof actually involves finding an algorithm to solve NP hard problems in polynomial time and IF that algorithm is of a practicable form and not something insane like telling you that you can solve NP hard problems but in n^666 time, then alright, yeah. But that’s a lot of ifs, and it’s not directly linked to whether or not P=NP is solved. I brought this up specifically because it is one of the famous problems that the solution sounds like it may be massively important practically, but in reality kind of isn’t.
Also I didn’t “only” clarify near the end, the point is more or less contained in the first paragraph. It’s just that for some reason this subject instantly pushes the buttons of people.
While the P=NP thing is a bad take for reasons people with more understanding than me have already explained, the worst part IMO is
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.
This is a ridiculously presumptuous and weird thing to say, particularly given how fast computing is expanding and making it more relevant than ever.
If I’m understanding your argument correctly, the better way to approach this is to say that all fields of study are useful. Non-STEM things like art and music are important, as are mathematics and physics that are too experimental to find an immediate use for. Like, modern art does not improve people’s material conditions in any significant way, does that mean it should be tossed out? Should history? Should philosophy? For all his writing, Marx hasn’t improved my life one bit so far, toss him out too.
I know this kind of slippery slope argument sounds silly, but that’s the point. It’s a really bizarre way to come around to your final point, which seems to be that it should be studied despite being useless.
The P=NP thing isn’t my personal take. Many people working in the field more or less agree. P=NP is about whether all NP hard problems can be solved in polynomial time. The answer doesn’t necessarily tell you how to do it if it is even possible (and most don’t believe it is). If it’s not true, then not much changes practically. If it is, then there’s many many reasons why it may still not really make a difference practically speaking. It could make a difference in some kind of optimal case where it turns out that the proof actually gives an algorithm, that algorithm is something practicable, and it isn’t some kind of horribly unwieldy thing that renders any kind of practical solution in exponential time more practical for a typical problem (which is also possible, “fast” means something different to comp sci people and to programmers, for comp sci people fast is asymptotic, but in the real world you don’t always care about the asymptotic behavior of something, in the real world many problems in polynomial time are practically not solvable), and a best case scenario solution is getting more unlikely by the day. Mathematical comp sci people don’t care if they get that P!=NP or if they get a non constructive proof of P=NP or if they give some kind of independence proof or if they actually do find a constructive proof of P=NP but it is horribly impractical. Just getting any kind of proof is amazing news because it’s such a deep result and such an important question theoretically, even though it probably won’t change much in practical terms.
This is a ridiculously presumptuous and weird thing to say, particularly given how fast computing is expanding and making it more relevant than ever.
Well computing is expanding a lot but most relevant math is still relatively simple, bar a few niche contexts.
If I’m understanding your argument correctly, the better way to approach this is to say that all fields of study are useful.
See, I kept putting useful in scare quotes for a reason. I also said this in the first paragraph:
[…] this stupid idea that scientific research should have “practical application” (which generally means “someone can sell it for money”)
Usually when presented with something that seems far fetched or hard to apply, people say “why is that useful? What can someone do with this? What can you make? How can you sell it? Why do we need this? Why are we spending time on this if it isn’t useful?”. This is a consequence of capitalism. Practically useful and valuable are different things. I think all the miscommunication arises from people uncharitably or hastily interpreting what I mean by useless.
Why do people just come here and just comment while having seemingly not read what I said, my post very, VERY explicitly argues AGAINST the idea that is should have an immediate or even non immediate benefit.
You literally say ‘most of modern math is useless’.
Which is entirely irrelevant to what you said. Also I said most PURE math, not most math in general.
then try and absolve the post with a high level meta-analysis in the last paragraph, sure
What? I made the same point in like 3 different paragraphs:
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.
This is literally the first paragraph.
This of course is usually don ** 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”
This is the 3rd paragraph.
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.
This is literally the ENTIRE last paragraph.
but the entire post itself postures itself on the assumed uselessness and lack of immediacy of modern math.
Which is entirely irrelevant to what you said.
shoving every participant in this thread into a locker
