Thread: How do you lot remember SO much math???

I mean there is so much math to be learnt and many of you for example (Plato) seems to know everything. I'm guessing he is a physics professor or something but even still how can you keep track and remember accurately so many different types of math like long division, fractions, algebra, integrals, functions and calculus.... and then on top of that many of you know all kinds of physics! It just seems like an incredible amount to remember.

Don't get me wrong if I focused on 1 topic for awhile I would be able to remember it so long as I sat down and practiced it every other day.

So how the hell do you lot remember every topic you ever learn???

The same way you remember your name or address- use it a lot. Do lots of exercises. In other words, practice just like you say- don't stop practicing!

Just by practice....

i don't. i've forgotten a lot. but one thing helps me remember: understanding what it is i've learned. i'll try to give a simple example:

with functions, an "inverse function for f" is a function g such that f(g(x)) = g(f(x)) = x.

so it kind of acts like a reciprocal, like when (a)(1/a) = 1. now the "function x" that is, the function h(x) = x is just a line at 45 degrees. so, geometrically, its clear to me that if f does something above the line y = x, then g should do the "opposite thing" below the line y = x, and vice versa.

put another way: suppose y = f(x). then if x = g(y) (i switched the roles of x and y, which is what mirroring across the line y = x does):

g(f(x)) = g(y) = x, so the function g must be the inverse function for f. i no longer have to "remember" this, it's firmly wrapped up in my mind with the MEANING of "inverse function". i could no more forget this fact, than i could forget that i have five fingers on my left hand.

understanding is harder than just "learning". it's hard to explain, but there comes a point where you are convinced of the certainty of something. not just that "it works" but you can take it apart, and you see how and why it works. at that point, you finally "own" the knowledge, and it can no longer be stolen from you by the passage of time. now, it is true that familiarity and constant exposure keeps certain channels of thought "fresh" in your mind. and this is the sort of thing that practice can help with. but understanding....you have to look deeper, to see a fact from more perspectives than just one, how it interlocks with other things you know. and i find that mere "exercises" aren't enough...depth requires contemplation. thinking about something on your own terms. not because its homework, or to solve a problem (in real life, on the job, or even just as a puzzle), but to "be at home with the ideas".

an analogy: you can learn to follow recipes, and be able to prepare many kinds of meals. or: you can learn to cook, and no recipe memory is necessary.

There is only one method to remember math is just doing practicing, keep on trying solving the problems several times and also try to learn new method along with it.

no.

doing something wrong 20 times, does not suddenly give you the understanding to do it right. if you can solve a problem correctly 5 times out of 5, doing it 15 more times is just a waste of time.

repetition breeds either boredom, or frustration. neither is conducive to learning anything. "wax on, wax off" does not work for mathematics.

what does work? playing, for one. fooling around, and seeing what happens. discovering things for yourself.

the best teachers only tell you where to look. the seeing is up to you.

Practice. Also, try deriving the formulas/theorems on your own. Then you'll understand them much better.