As I progress through Codeforces and competitive programming in general, I've noticed that the most advanced users tend to apply mathematical proof thinking and don't start coding until they've convinced themselves the solution is correct, even for greedy non-exactly-math problems.

For me, these insights usually come intuitively, but intuition alone isn't always reliable.

Do you recommend practising this more rigorous approach? If so, how would you go about learning it? Is there any resource you'd suggest, or is it something that develops naturally over time out of necessity? I'm also curious whether it's more common here simply because there are more mathematicians than programmers on the platform. Thanks in advance.