Were you a high GPA student?

[ErGingerbreadMandude]

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I took a math course in college specifically about proofs and theorems.  In high school we were taught to memorize them, but once you get in to upper levels of mathematics, you have to work on proofs and why they are true and why they are what they are.  Toughest class I ever took.  Homework assignments were easily 10+ pages.

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I took the same stuff at the beginning of uni. I'm not exaggerating when I say that it was one of the most profoundly transformative experiences of my life. I've never learned completely new modes of thinking over the course of just two semesters the way I did then. And yes, 10+ pages, that often took as many hours to create...

But pool is right, constructing a proof often has much to do with creativity, intuition and a bit of luck. It is an art form, not a set of recipes.

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But then, isn't finding algorithms the same?

Completely different actually.

In programming(or while defining an algorithm),a programmer will know what the input will be,the procedures that will have to be done on the input and finally - the output.
The only complication is translating the procedures into an algorithm - one which a computer can understand and process.
In mathematics,one would know the start and the final result.All the procedures in the middle of the starting and the final result are unknown and they are found essentially from a process of bruteforcing - like in a jigsaw puzzle.

To represent in a form of analogy:
Output: "This is the start and end of a sentence."
In programming: "This si eth artts dna dne fo a sentence"
In mathematics: "This ............................... sentence."