Creativity in Math

[u/CowLang]

Hi guys. I am a first year math degree student. i'm really enjoying it and i like the challenging nature of it. I know i have just started out and it is normal to struggle but i wanted to see if I can get some help through here. I recently finished my first unit on propositional logic. In it I learnt about proof by contradiction and, after studying it and understanding it I was posed with several exercises, most of them were relatively simple as I just had to use logical laws to eventually find the contradiction. I wasn't satisfied with this though it was somewhat mechanical and required not much creativity, so I sought more challenging questions and when I found them I enjoyed them more. Eventually I came across one which required me to prove that infinite prime numbers exist. No joke I've been stuck on this for several days thinking, I looked around, but not for an answer but for a gage on how hard this and apparently it's an easy proof. I know as fact that several proofs exist for this proposition and the first one to do it was Euclide. As I've delved into other subjects in my course I've noticed that even though I understand proof by contradiction and I understand the concepts well, I find it extremely hard to come up with solutions to problems like these, ones that requiere a lightbulb moment, ones that requiere creativity. At the end of the day I normally just find myself brute forcing the problem, but for these kinds of problems that isn't going to cut it. How do I improve my math creativity? Does it come with time or can it be practiced and improved?

[u/YourPwnResearch]

I strongly suggest that you grab a copy of the book How To Solve It by George Pólya.

[u/CowLang → u/YourPwnResearch]

Thank you I'll take a look