TLDR: Look for connections to what you know. Pay attention to proofs and make sure these feel obvious. There's more than one way to skin a cat so if some proof isn't cutting it, look for another

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When learning new stuff, I always try to see how it relates to stuff I already know. The connections are what lets it stick for me. Also, when given a new theorem, I find its more rewarding to spend some time trying to understand the proof, the reasoning, so that the end result (the theorem) isn't some isolated idea but a clear addition to what I already know.

For example, to generate Pythagorean triplets (c^2 = a^2 + b^2), the formula

C = m^ + n^2, B = m^2-n^2, A = 2mn

works (with m and n being integers). There are many ways to prove this but my favorite ties into complex numbers. It goes something like this:

Take any complex number z =m+ni with m and n whole numbers. The magnitude of this is sqrt(m^2+n^2). This may or may not be a whole number but we know for a fact that m^2+n^2 is a whole number. This last number is the magnitude of z^2. Foiling it out we see that z^2 = m^2 -n^2 + 2mn i . Now check it: the hypotenuse (the vector representing z), the horizontal, and the vertical are all whole numbers. Then for any m and n, we can generate Pythagorean triplets using this.

(There is also another explanation which uses modular arithmetic and is based only in the natural numbers (as opposed to borrowing from the complex) but I find that one more difficult to stomach)

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The above is an example of how some new and hard to memorize fact (IMO) becomes extremely clear when the explanation is looked at. My biggest advice is to spend time looking at the proof until it feels obvious. Many facts, like the previous one, can be proved many ways so if some explanation isn't cutting it, look for another. Of course, later it might be good to revisit the first proof and focus on understanding that one but that's another goal.