I took Calc I in college but i was an economics/business major so it was probably a joke like the rest of business school. Anyway, I'm 24 and self-teaching myself now through a combination of Strangs text, khan academy, and various youtube videos/websites. So I've been self-teaching myself for 2.5 months, but in that time I started a new job, so I would say I've really only been teaching myself for 4 weeks, because 6 of those weeks I wasnt really into it because I was busy. So far, I think I have a solid grasp on limits, derivatives (power rule and chain rule), l'hopitals rule, optimization, and some on integration. Intuitively most of these things click with me. Like, for instance, regarding the second fundamental theorem of calculus; if f(t) is distance and t is time, f(b)-f(a) is distance traveled over some time. The derivative is velocity. if you add the area under the curve of the velocity graph, its every infinitesimal velocity times the amount of time for that speed, then that gives you total distance traveled, which is the antiderivative. Intuitively it makes perfect sense to me. However, if somebody were to ask me to prove l'hopitals rule, or pretty much any of these things, I would crap myself. I haven't had any formal math training in like 6 years, and even then my background is public school high school combined with one math class in college. So my question is, is this a huge problem? I 100% understand the need for rigor in math. My plan is to teach myself calc 1-3, then probability theory, then linear algebra, then partial and ordinary diffy q's, then stochastic calculus, then analysis, then number theory. So what I am wondering is, is it okay for the first time being exposed to "higher level math" to be unable to do proofs and rigor, and just get the intuition? Will I pick up on the rigor part as I move up in difficulty? Or should I not even continue on this path until I can rigoursly prove everything I am doing? Were you able to do rigorous proofs upon your first exposure to calculus?