Did anyone start studying mathematics late on your own or was everyone here a genius math wizard as a kid? I fell for the STEM meme and I'm starting from the very beginning as I never cared much in school, doing Khan Academy and reading books and all. But even when it's piss easy it's taking me so long and whenever I see college level stuff I lose motivation easily. I have nothing else going for me so I'm doing my best, but I worry I'm doing it wrong so does anyone have any tips? Anything could help.
>>8066873
Spivak's Calculus and Topology without tears were the most fun to read while being exceptionally good.
>>8066873
I'm doing the same. Treat it like a set of skills. Don't get discouraged by the grad students who are breezing through ant and pick pre-sheaves out of their teeth after breakfast. The hodge theaters will come later. Start with single digit addition. Don't be too proud. Since addition is easy, you have to go for speed, since you already understand the concept. Eventually, even though it seems silly, with enough repetition, you'll start getting an intuition for the numbers- you'll start seeing patterns, seeing relations between properties of them. Work your way up to larger numbers. Keep breaking them down and putting them back together- keeping track of what falls out and what doesn't. Yes, you are "just" calculating things, but the faster and more repetitive it is, the easier it will be to brainstorm while you do it, to ponder on them, to ruminate. Supplement this with non-monotonous, actual creative and critical thinking- try solving problems past your abilities- try to figure out how long it would take you to solve it if you could, figure out what you need to know. Make a five-year plan for something you can't solve yet. Fantasize about it. Keep going back and forth between the very easy and the very hard. Don't just grind on the too-hard stuff or you'll burn out. Mix in creative stuff too- try visualizing concepts, not just memorizing- actually connecting them. Write about them. Always look for patterns. Do as much as you can to immerse yourself in it.
>>8066873
Was uninterested and unexceptional in high school. Now I'm a grad student at a top 20 school. Take that however you want.
>>8066873
I was a "maths wizard" as a kid but I don't think it means much. I'd say I'm just about above average in my course so I wouldn't use early talent (or a lack of it) as any kind of gauge for your mathematical ability.
>>8066934
It all depends on how far behind you are. Test yourself on different subjects. See what you do and don't know. Use that to write a curriculum for yourself. The subject you are strongest in will serve as a place you can go back to, to use as a source for analogies for when you're having trouble understanding a concept in the harder, newer subjects. As your base grows you'll be able to think of more analogies to work from, and then eventually all the analogies will get enveloped by a simpler one, which will expand again, you'll get more and more, and then simplified again, and back and forth and so on and so forth.
Randomly pick some research papers from current math journals in different subjects and put them next to elementary school, middle school, high school and undergraduate math so you can get a feeling for what you're missing and what you'll need. Remember that undergraduate math is a means to prepare you for graduate school, and graduate school is a means to prepare you for research- assuming you haven't started doing research in undergrad. Also, read up on the history of math if you're feeling unmotivated or want a human connection/human story to contextualize a development. If that doesn't work, see how a concept is related to other fields like physics, geology, chemistry, etc. Branch out if you feel like something is missing.
>>8066952
Thank you, this is very useful to me. Sometimes I get lost just thinking about all the stuff I have yet to learn and it's both exciting and terrifying, but I just have to work hard.
Good luck to you too man, it's definitely not easy to start late at this.
>>8066873
I was stem meme.
I like math.
But its just fun, nothing I can do with it besides teach other people. Since I don't like calculus or stats, im more into the visual stuff like graph/number theory and geometry. Basically drawing things on a whiteboard to prove things.
I dropped the math major. Now doing psy with math minor. Easier. More class options. Graduate earlier.
>>8066873
I was both. I was pretty good at extracurricular math during elementary school, then when I my teenage shithead phase I didn't want anything to do with it.
After I outgrew that phase I went back to it but I was average/below average by then so I spent a while catching up.
>>8066873
You realize the M in STEM is for math, right?
>>8066873
If you're only studying pure math because you think it will make you lots of money then stop.
>>8067337
I'm only doing a math PhD for that 300k starting.
>>8067293
what does STEM means? is it and american made up career or what?
>>8067423
science, technology, engineering and math.
