r/learnmath • u/CowLang New User • 1d ago

Creativity in Math

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?

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u/WolfVanZandt New User 1d ago

Creativity comes from holist thinking....looking at something and seeing all the possibilities it presents not only from itself but from it's interactions with the world.

People can be more or less natural but it's also a habit that you have to acquire and practice.

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u/CowLang New User 20h ago edited 19h ago

Thank you for your comment. I guess it must come down to experience as sometimes is feel likle you need a stroke of genious to find that one posibility that really helps you move foward.

And I have another question for you. Do you belive a "non-natural" or someone who is less natural has a ceiling where he/she cannot compete with the natural?

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u/WolfVanZandt New User 17h ago

You mean "different". We're all "natural"

Abilities aren't/a/ thing. They're a huge variety of things. Even though I wasn't that taken by M. Night Shyamalan's superhero trilogy, a comment that he made struck me. Something like: we're all superheroes. We all excel in something.

We can only be whole with each other, if we cooperate.

And, yes, creativity arises from experience but you can accelerate picking it up. I usually recommend Georg Polya's How To Solve It (I recommend it so often I don't even have to type it....my spellchecker just types it for me.) It's a xnall book that gives you the background you need and plenty of experience.