Hello guys, it's been a long while since I've last used Codeforces..

I neither have a question nor aiming to discuss a problem, it's more like a survey and I really like to listen to all of your different opinions

Do you think there are any trade-offs between Mathematics and Competitive Programming?

I mean, I've almost always thought that one cannot be great at both of the fields, though it's important to have some essential skills of the other field no matter which side you belong

My current reflection is: Mathematics is so important not only for CP but for CS and any other scientific field, but it concerns itself about some so deep low-level worries that programmers tend to take for granted, since it's almost always the case that they use some pre-built tools

and I personally think that though it's always better and more "efficient" to understand what's going on under the hood, it makes you less productive to worry so much about details and re-think about the same problems you've solved earlier, especially when you're required to re-invent the wheel in a relatively short period (which is somehow the case when one's solving CP problems)

These thoughts came to me while working on some project that requires a strong familiarity with the two fields. I was trying to solve some problem that is modeled using a certain data structure and thought that it would make the solution more efficient to solve the problem with Gaussian Elimination rather than traditional search techniques, but some problem emerged and required me to use Extended Euclid Algorithm to calculate the Modular Multiplicative Inverse of some number, and since I haven't touched Number Theory for a while I was only able (at that moment) to figure out that the solution is to calculate the mod-inv without even remembering how to do it, and though it didn't take me long to remember about the details (or re-conclude it), I just used a pre-built tool to calculate it without worrying about the tedious implementation.

I'm not an expert at any of the two fields so I don't assume that any of my reflections are correct, in fact that's why I'd like to hear all about your opinions :)