Because even if you can't literally rattle off the stuff o to a 10th grade algebra exam, you remember the general gist and some of the details. I could not do a line integral right now but I know it exists, what it's for, and if I ever had a programming problem that was a line integral, I would remember it and be able to Google "line integral Wikipedia".
There is also, in my opinion, great benefit to just training your brain. Even if you forget all the details, I think someone who learned calculus and then forgot it is going to generally be in a better place to handle any general mathematics than someone equal who never learned calculus at all.
Because we've inverted the pyramid. School enables people to work and make money. Education is a side effect of the daycare, and unless you go home to motivated and curious parents, likely the best you can hope for is they get socialized enough to not chronically get fired in pretty monotonous careers.
Ask the folks who set the math curriculum. If it were up to me nearly all math in school would be application-first and exceptions would be carved off into separate classes, presented very differently, and mostly not required.
Do you think high school students are qualified to decide for themselves whether they'll need math later in life? I never imagined having the kind of career I ended up with. I always thought I'd work as a writer. I ended up as a software engineer.
No, but I think we could make math more useful and less unpleasant for most students by focusing on applications with just a little time for proofs or whatever in case that really piques some student’s interest. I doubt this would discourage many kids who’ll go on to become math majors, and it’d serve everyone else much better. You could still cover a lot of the same stuff.
People use different aspects of their education and it’s vastly faster to pick something up the second time. So you may have never used a given lesson, but other people in your class may have found it really helpful.
Sometimes going a few steps deeper helps you retain some useful bit of info. I ended up making useful of various bits of chemistry decades after taking the class, but understanding the basics was still helpful.
Finally basing things on utility is just a prediction. Some things that seemed useful turn out less so as technology filled in a gap.
The difference is that if you knew it and lost it, you can relearn it pretty fast. If you never knew it, it takes massive amount of effort.
The person who would fail that math or French conversation right now, would be able to get up to speed in days, weeks or months depending on what exactly you want if needed. However, learning French from nothing would take years again.
I mean… I don’t know that many people but, even so, I know a couple who are in most ways smarter than me and who’d be very-capably contributing a ton more to the economy if math classes hadn’t blocked them from it. They’d have been way above median at a ton of important jobs, but weren’t allowed to do that because they were bad at, specifically, some math they didn’t need for those jobs. No degree, so, life path permanently altered in a way bad for both them and all the rest of us.
If I know a couple, there are probably many such folks.
I’ve not seen the same thing happen with any other subject.
I used to be Ok at math. I would now fail any math test past 10th grade (forget college), and I’m not so confident about 8th or 9th either.
I also used to be pretty good at French. I’ve lost most of it. Rarely having a reason to use a skill means you lose it.