I saw this comment on a Facebook math group recently and ended up leaving a wordy reply.
Some people say "math is part of the Humanities" and I disagree strongly. It seems that in some sense mathematics is related to science as just like science, math attempts to discover universal truths outside of human opinion. This isn't to say that it can't also be related to philosophy as it gets more abstract or that it cant be seen as a type of art (after all, we know some elegant proofs).
If we came across an alien civilization, their art, music, philosophies, and ideas will be different from ours. But their mathematics, just as their science will be the same as ours. Because it needs to be. Their pi would be our pi, they would just have a different way of expressing it.
My response below:
I'm honestly okay with math being humanities. Makes it feel more warm and approachable, as it should be. A de-humanization of mathematics (i.e. viewing it as some kind of universal entity external to the human realm) would be detrimental to mathematicians and non-mathematicians alike.
In my humble opinion, mathematics is created as needed by human minds through an intense series of abstractions -- but abstractions nonetheless, of real, human experiences and learned patterns.
Yes, there's a kind of universality to mathematics, but mathematics within the human context is expressed in terms of human thoughts. It is written by humans, to humans, and at the end of the day for (often extremely abstracted) human purposes and interests.
Yes, you can always extrapolate and say that mathematical theorems "exist" as some kind of objective "thing" and that we're just discovering them in a very selective and human way... but that's neither here nor there. I guess that interpretation is not that interesting to me. In a sense everything is "discovered" -- poetry, literature, what have you.
To me, mathematics as we know is a distillation of human thought. It's a human activity that serves a higher-order need for truth, without regard to specific application. We package and serve this in the form of results: lemmas, theorems, definitions. If philosophy can be considered a "humanities" subject, I'm okay with math being one.
You do hit upon an interesting idea when you mention "universal truths outside of human opinion". Although it seems a little offensive to the humanities to imply that they seek truths subject to human opinion (lol)... There are certainly different approaches within the humanities vs mathematics as it is done today. Tickles different parts of the brain, so to speak... so maybe there is some kind of hard distinction to be made along those lines.
