Is It Hopeless for Me to Try to Understand the Derivations of All Formulas I Use?

Question

Recently, I've been doing some relatively more advanced math (multivariable and vector calculus) and the derivations of formulas are becoming increasingly complicated. I don't like using a formula if I don't understand why it works and where it comes from, so I have understood the derivation of all formulas I've used so far. My question is: is it hopeless for me to keep learning derivations? Will I eventually reach a point where understanding why the formulas I use work becomes too time-consuming and unreasonable? To clarify, I prefer to understand proofs in order use them, I don't memorize them. Any help is appreciated. Thank you.

Answer 1

First of all, you need very much of focus , without which all that you grasp may be lost eventually. Focus your mind when attending lectures, lessons or seminars. Keep a sharp ear.

Next, practice - deriving something once needn't always help you fix stuff in mind, so practising it as many times as you can fixes whatever you are learning in your mind.

Third - a strong heart. Never feel disheartened by the derivations you have to learn, be it complex or way above your level. Just give it a go, try again if you don't get it. Also, you can discuss it in here (I mean, the difficulties you find in trying the derivations and such stuff). As the lines in Bastille's 'Laura Palmer' goes - "Walking out into the dark, cutting out a different path, led by a beating heart..." - keep it beating, keep it brave, keep it right and you are ready to face the walls ahead of you. Never lose hope or faith in yourself.

Fourth - basics. I know you have the basics, but still it is inevitable that I say that anyone must have at least a small bit of the basics to get started.

Answer 2

Personally I don't think this is reasonable at all. You can easily spend 1 hour - 2 hours (or more in some cases) to fully understand a proof, and in multivariable calculus and linear algebra textbooks there might be a proof every 3 pages depending on how advanced the text is. In a Real Analysis text there might be a proof 2 pages. My point is, you should learn the proof if the theorem is important.