Genuinely, what is it that you get from studying mathematics?
I get that it's a hobby, but what do you even do with the knowledge you acquire?
I don't exactly fear math (even though I'm complete shit at it) but the time investment required is absolutely massive for something with questionable utility, even just for playing around with. You need a super strong base to even attempt bashing basic problems, so that's easily four or five years of study just to play around a bit.
For me, math was a way to study structure. I find this sort of thing tremendously beautiful on its own, but as it happens "finding the structure in things" turns out to be quite lucrative in the professional world as well, and I often use various ideas and strategies I chanced upon as a student of mathematics.
counterpoint to
> easily four or five years of study just to play around a bit
it depends significantly on the branch of maths you choose! I've been told by a professor of fluid mechanics that he has difficulty posing and approving subjects of undergrad dissertations because the knowledge threshold for contributing meaningful ideas reliably is so high, but in my primary interest (combinatorics) this is very much not the case.
the OEIS is replete with old sequences that no-one has considered in much detail in a decade or two, and have a lot of 'low-hanging fruit' for one willing to toy with them.
https://oeis.org/A185105 is a good example of such a sequence; "sample the elements of a random permutation of [n] in a random order and record each one's cycle (under repeated iteration), then T(n,k)/n! is the expected of the kth distinct cycle recorded," which seems like it would have been of some interest to someone in the last ≈13 years (since ie. it's well-known that the first cycle's length is uniform in [1..n]), but didn't receive any formulas until I happened upon it recently with my own toolbelt (which is quite modest and certainly could be learned in less than 4 years).
the OEIS is an excellent resource for both readinh and sharpening one's amateur teeth on novel (ie. unexplored, or at least undocumented) problems and very rewarding, if that's your goal with learninh maths
I do, yes. I won't call it a hobby because I don’t create anything, I'm just a mindless rabid stupid cunt of a consoomer who doesn't know how to differentiate his ass from a hole on the fucking ground, but I do spend a lot of time listening to music. I've spent a lot of money on audio equipment.
Even so, if you wanted to bring up time signatures, microtonality or something like math rock… I'm aware of those, but I still think the only thing that matters is that they're tools meant to allow you to express a certain message in the most appropriate ways, not so much an end in themselves.
I don't think hobby requires building anything. Spending time actively engaged is enough. One can enjoy mathematics the way one enjoys listening to music.
On the other hand if you do want to make something, and you happen to know related math then suddenly you can use it.
Building these are neither my hobby, not did I learn the relevant math for the exclusive purpose of making it. But once you acquire a few math razors you start seeing inviting fluffy yaks that were invisible before.
> but I do spend a lot of time listening to music. I've spent a lot of money on audio equipment.
This is a great domain to motivate oneself to delve deeper into Mathematics. For example;
1) What parameters do you look at in audio equipment before you buy?
2) Somebody is trying to sell you "Hi-Res" music and equipment; Are they worth the money? Why? Why Not?
All of the above need mathematics to comprehend at even a basic level. There are both complicated objective (physics/mathematics) and subjective (our auditory system) parameters to understand eg. logarithms, harmonic series, frequency modulation, tuning, impedance, human hearing frequency range and sensitivity etc.
Having some mathematical idea of the above not only saves you money but also helps you enjoy music "optimally".
The Science of Musical Sound by John R. Pierce. An old classic (also checkout his other books on Waves, Signals and Information Theory). They are all written in a semi-technical and clear manner for the general audience. - https://en.wikipedia.org/wiki/John_R._Pierce
> Genuinely, what is it that you get from studying mathematics?
GP here, I would say that I gain understanding. I know that might seem vague, but that is the truth. For example, while not technically traditional math, I have been trying to brush up on stats a bit. I like to read research journals about health, psychology, etc.. I want to be able to make my own inferences about the journals I read with an informed opinion.
I get that it's a hobby, but what do you even do with the knowledge you acquire?
I don't exactly fear math (even though I'm complete shit at it) but the time investment required is absolutely massive for something with questionable utility, even just for playing around with. You need a super strong base to even attempt bashing basic problems, so that's easily four or five years of study just to play around a bit.