how much does math change as you get further into graduate lvl + physics? More specifically, do properties like ab = ba or a(b+c) = ab + ac change? Like are there even mathematical 'structures' that governs areas in physics? Or is it more like X equation describes that relationship, Y describes that, and then you just go from there?
I was curious because I imagine in the last couple centuries we have made a lot of progress in observing phenomenon and I hear things thrown around like non commutative algebra in QFT. So, I'm guessing certain mathematical properties seem apparent in a macro scale and change when you observe different things? I told you it was vague
@Obliv I wouldn't see that as "math" changing. For instance, you certainly encounter non-commutative objects for which $ab \neq ba$ - but $a$ and $b$ are not ordinary numbers here, but e.g. matrices, so it's perfectly fine mathematically.
That is, it's not "graduate physics" that's changing the rules - mathematicians did come up on their own with many weird structures different from real numbers without any "help" from physicists ;)
@Obliv I don't think it's one way or the other - sometimes existing math inspires physicists, sometimes weird non-rigorous physics calculations inspire math.
@0celo7 They clearly mean the cohomology ring of A!
@Obliv Thanks :P I'm not sure whether I "know software engineering" but I seem to be able to produce code that works and is not more terrible than what anyone else is writing ;)
In slightly related news, @BernardoMeurer if I told you I want an easy-to-use GUI library for Python, nothing fancy, just buttons in an orderly fashion, what would you recommend?
@acuriousmind do you find software development lets you express your creativity as much as physics and math? Do you get to work on complicated algorithms and stuff?
@Obliv Not beyond answering questions here. I mostly spend my weekends with friends and/or playing video games and/or working on other little side projects (such as trying to program a Vampire - the Masquerade character generator)
@Obliv I actually find it suits me much more - I feel the short term reward cycle when programming something (you can almost always just compile what you have and see how well it works right now, especially when following a test-driven paradigm) is much more motivating than the long-term reward cycle in math&physics where you can work weeks on a difficult problem and not make any significant headway.
@acuriousmind Yeah I'm the same way. That's one of the reasons why I wanted to go more towards applied math/CS instead of physics. I haven't reached the end in either but from what I gather, it's a pretty unstable work environment when doing research in physics. On top of that, there's pressure to publish every so often etc
@Obliv I wouldn't have cared about the unstable work environment so much if I felt truly engaged with research, but I realized that the day-to-day work of a research scientist didn't really make me happy
@ACuriousMind You sure it was ambition and not just insane work ethic? Or maybe those are the same. I've had a hard time distinguishing those two sometimes. Like, when I used to go to the gym in high school, at first it was ambition/curiosity and it eventually just became routine sort of.
@acuriousmind I have a friend who had studied some basic undegrad neuroscience and he had talked to me about things related to this and I feel like understanding yourself via neuro & psychology etc is something that a lot of mathematicians and physicists lack.
I remember in math chat some guy mentioned balarka(or maybe it was someone else) being depressed. I felt bad because just because the guy is young and probably has little idea how to take care of himself, mentally and physically to avoid feeling certain ways. I think he's my age tbh.
@Obliv I think you (or at least I :P) need some form of ambition - or maybe just motivation - to generate that work ethic. For instance, I have much less trouble putting in hours at my job than I had putting in hours to read yet another paper because of the short reward cycle I outlined above.
And there's also the much more immediate feeling that other people depend on the work I do, which wasn't the case at all with the kind of physics I did
@Obliv @BalarkaSen is a regular visitor to both math and physics chat, not sure whether you mean him either, but I agree in general that self-reflection and self-care are rarer among mathematicians and physicists than they should be
