# Should I explore every mathematical theory myself first, or is it fine to read the proofs given?

I have read a similar question posted on MSE, but honestly, I did not get the answer to what I was thinking. Suppose I am new to conic sections. Now, my book provides me an insight to what conic sections are, and their analytical focus-directrix definition, but doesn't really give me a proof of this focus-directrix property. I searched the internet to find a proof, and saw the ideas of Dandelin's spheres. I didn't read the whole proof, I still haven't(I might after getting the answer), so that I can try to explore conics my own way, and maybe create my own proof of the property. But, provided that the property is already proved by someone, should I really do it, or reading the already existing proof is good for me? Because, if I try to do this for every mathematical theory, it would take me years to do so.
So, what is good for a mathematician or a physicist? Re-invent the wheel(because you never know, maybe you discover something new by doing so) or read the works of others and use it as a black box?

• Stand on the shoulders of giants – ÍgjøgnumMeg Oct 31 '16 at 19:32
• I think it is misleading to phrase the dichotomy as being between building the whole of mathematics on your own and using black boxes. "Black box" suggests something you are using mechanically, with no understanding of how it works. Why do that? You can learn and understand standard techniques and standard theories. Doing everything from scratch, on your own, is hopeless. Dandelin spheres, for example, weren't discovered until 1820 or so...a mere two thousand years after Archimedes introduced conic sections. – lulu Oct 31 '16 at 19:32
• Do you mean "theorem" rather than "theory"? – littleO Oct 31 '16 at 19:34
• @littleO, by a "theory", I mean a set of "theorems" related to that theory – codetalker Oct 31 '16 at 19:35
• I'm interested in this question too. It seems to me that there is a difficult "calibration" question here -- certainly we should spend some time trying to figure out some proofs before we read them, but the crucial and difficult question is "how much time?" How does one answer a calibration question like this? – littleO Oct 31 '16 at 19:38