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One thing I've been having trouble with as I'm learning math is to coalesce new concepts into a broader context. When learning things I usually assume there's a
by ad404b8a372f2b9 6y ago
One thing I've been having trouble with as I'm learning math is to coalesce new concepts into a broader context. When learning things I usually assume there's a tree of knowledge that I can travel back up, but with math it seems like a tangled graph of concepts which can be grouped into many different permutations to form different theories, also it's not entirely clear at what level of abstraction one should stop digging.
I'm beyond lost.
- zomglings 6y agoJust want to offer some help. If you are interested in math, don't get disheartened about how tangled things seem. Even if you can't find any external references to a broader context, you will find that, given enough time and effort, a broader context emerges in your mind. Dig until you get tired or bored - because you could really keep digging forever. If you ever feel lost, read the masters - Euler and Dirichlet are two favorites. Here is a great book: https://www.amazon.com/Euler-Master-Dolciani-Mathematical-Expositions/dp/0883853280 https://www.amazon.com/Euler-Master-Dolciani-Mathematical-Ex... If you get tired of that, read about the greats. MacTutor has a great archive. I especially like their biographies: https://mathshistory.st-andrews.ac.uk/ https://mathshistory.st-andrews.ac.uk/ The most important thing (only my opnion) is to not lose the sense of wonder at the beauty of the universe as seen mathematically. I don't know what your particular situation is - are you in university or school and studying math or learning math as you juggle a career? Any more specific advice depends on your circumstances and your objectives, but I really hope I was able to help somewhat.
- zomglings 6y agoRe: masters. Also Shelah: https://arxiv.org/abs/math/0211398 https://arxiv.org/abs/math/0211398