You know what does though? Irrigation. You know what allows you to optimally irrigate so you don't waste money that you could be spending either on growing more crops or your family? Maths.
Only a fool pretends the ground floor of a house is worthless because they live on the second floor.
I'm not saying Math is useless, I'm saying there must be tiers for topics in how useful they are such that someone can say "Hey, that's pointless!" and one can't follow with "Therefore all things are pointless". Or, that allow me to rank niche topics in their usefulness.
Irrigation is very important. Now, is Irrigation Maths more important to us as a species than Terrence Taos work on spontaneously combusting water? Probably! Would it be more useful to have PhDs be funded in optimizing food routes between countries after climate change over game theory applications for blackjack? Probably!
Unfortunately, no. Maths is so vast that what might seem a trivial and silly brain teaser can turn out to unlock a massive problem in a seemingly completely unrelated subfield of mathematics, and we won't know until someone discovers that link.
What someone might call "a silly little brain teaser" today could actually result in a breakthrough paper weeks (or centuries) from now in a different subfield because someone far smarter than us realized that part of the problem they were working was actually analogous to a number theory related problem that was simplified, even a tiny bit, by this solution. (Hell, Nash built his entire career on spotting those kind of links and then telling other mathematicians to focus on working out the individual pieces)
Maths plays out over "we don't even know how long or short" time scales. What's the use? We don't know, it's probably completely useless. Until someone suddenly realizes that it's not.
>Now, is Irrigation Maths more important to us as a species than Terrence Taos work on spontaneously combusting water? Probably! Would it be more useful to have PhDs be funded in optimizing food routes between countries after climate change over game theory applications for blackjack? Probably!
I imagine you would be equally annoyed at Euler in 1736 when he was wasting his time with bridge brain teasers (and invented graph theory in the process) instead of solving bubonic plague or optimizing irrigation. Science just doesn't (in general) work the way you propose.
Sounds like you forgot that's literally everything niche until a post doc or tenured mathematician goes "yo hold up. This tiny proof (helps) solve(s) X". And now their name's in the science history books.
The interesting thing about the question is that there really aren't any right or wrong answers.
People pointing out that maths is full of advancements that had no immediately identifiable use at the time, but that came to be useful later, is correct. Yet it doesn't even begin to answer the OP's question.
I doubt very much that many people choose to pour their lives into endeavours that they don't particularly enjoy just because some hypothetical person at some hypothetical future point in time might hypothetically find a hypothetical use (hypothetically ;P).
The answer is that "value" presupposes the question "valuable to who and why?"
Newton invented Calculus because he had an immediate use for it. Other mathematicians pour themselves into solving problems because they enjoy it and find a lot of reward in the prospect of solving a previous unsolved problem. Both are "valuable", just to different people for different reasons.
Yeah it's fine for mathematicians to amuse themselves, the problem is when they demand salaries to do that and taxpayers like OP rightfully ask "whats in it for me?" And when the answer is "IDK but maybe in a century we might have a problem this math is useful in solving" then it's not surprising that no one wants to fund pure math research. It's not the 20th century anymore when math research was going to meaningfully improve someone's life through the invention of things like electrical devices.
Yeah, if you force other people to pay for something then you had better offer them an attractive value proposition. Though public funding of mathematics and other sciences is not what I thought we were discussing :)
In which world do you think mathematicians are raking in taxpayer money? Mathematics requires very little funding: a blackboard, some chalk, a pen and paper, a desk, some coffee. That's it.
Thats a pretty myopic view of history there champ.
The pragmatic, practical perspective here is that funding the egg heads has had incredible outcomes (and its so cheap too), so dont let the simpletons shake the golden goose down just because they don't understand anything they cant fuck, fight, or eat.
They were trying to solve a real world problem using this kind of math, and then decided it'd be easier to improve upon the math itself than to continue to pound at the problem - so by definition, I'd say you're absolutely wrong here, or they never would have started this proof in the first place.
Until it's not, because someone suddenly realizes that a seemingly completely unrelated problem in a completely different subfield that's holding up a major proof is actually analogous to a problem where this result removes a bunch of roadblocks.
That's the problem with math from a "so what is this good for?" perspective: we don't know yet, but we sure have a litany of instances where seemingly useless proofs had a profound impact anywhere from weeks to centuries later.
Only a fool pretends the ground floor of a house is worthless because they live on the second floor.