Which gets closer to my real point, mathematics is inherently philosophical and I’d argue it is a kind of analytic philosophy. A close reading of late 19th/early 20th-century history of mathematics, I believe, shows us how closely mathematics developed alongside analytic philosophy, such that at the foundational level at least, they seem to be the same branch of knowledge. It wasn’t too long ago that in some parts of the world mathematics was (rightfully in my opinion) considered a branch of philosophy and there was no clear separation between a philosopher and a mathematician. So, in my mind, mathematics is the way it is, or is beneficial to humans because, or is worth pursuing ourselves instead of handing most of it to machines because of the same reason as philosophy is all of these things: human beings are naturally curious and we satisfy our curiosity by trying to learn and understand things, it’s a natural drive and it’s among the things which help us grow as individuals and as a collective.
Personally, I consider the above a very practical value, so I’d argue that pure mathematics does have “applied” value at a more basic level than what engineering or science disciplines are usually concerned with.
Bureaucracy has no direct value, but it may have indirect value, if it helps us achieve things that are more directly useful. Pure mathematics has had a lot of indirect value until now. It turns out that training people to do mathematics for the sake of doing mathematics, at any level from schoolkid to mathematics professor, teaches skills that transfer to other domains. If human thinking becomes obsolete, that indirect value may be gone, but the direct value will remain.
The results in pure mathematics are largely irrelevant, except as means of acquiring transferable skills. Sometimes they have practical implications, but such situations are exceptional. And there is not much correlation between the practical value of a result and its value as seen by mathematicians.
Why does anything have value? Ultimately because we can use them to get something we need or want. For the former, there is some sense in trying to reach an objective definition of value. The latter is inherently subjective. Some things are valuable to some people, because those people find those things valuable. That circular definition is the root of subjective value that cannot be reduced any further.
PS: @calf, I've re-read your message above a few times and I must agree with others elsewhere in this thread that incoherence is afoot. Please review your own comments before sending, from the point of view of a reader who doesn't yet know what you want to say.
He simply said what pure mathematics is. You brought the "ought" part in. By what standard do you determine what pure mathematics ought to be good for?
If you disagree (as the GP does, apparently), I ask you--what value do you see in it?
The only reason most pure mathematics research exists right now is because it is interesting to the mathematicians who conduct it. I think a black box is not interesting to mathematicians and therefore has little worth. That's the argument.
they're really not because clearly their sole method of engaging with this discourse is projection.
> Being purely for the sake of improving human understanding
no matter what anyone tells you, there is absolutely no working mathematician that wakes up every day and goes to work based off that desire. it's not a priesthood, it's a job.
>As someone who did math professionally for a long time, I agree with you. I think it has as much value as chess (a game we made up which we play for fun).
I mean, I don't see how this is much different from what I argued, no? Nobody really cares about computer chess all that much at this point except as a benchmark of technological achievement, and except to the extent that it helps human players better understand the game and improve their own play. We still play chess, even though computers can do it better than we can, because we find it interesting.
people are making this comparison so often it's borderline embarassing. yes we do and there's seemingly a possibility that math goes the way of chess. now answer this: do we award doctorates in chess? do people get paid to study and teach and publish on chess on the same scale that they do with math today?
i'm not an asshole for pointing out that your argument is by now a trope and also wrong <shrug>
> but I will say that a large amount of that activity is financed by demand from students in one shape or another
you couldn't be more wrong - tuition pays for almost none of researchers' salaries, neither phd students nor faculty.