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GustavoM your name sounds familiar, did you play Planetside? I was (technically still am) in one of the leetfits and we would have some of the aim gods try to share their knowledge and it boiled down to something similar. Don’t tense your hand (click to fire naturally tenses your hand so you have to learn to reduce that), prioritize a relaxed posture, and learn your mouse grip (try them all out!). I’ve heard OSU is very good for those that want to improve their hand eye coordination (and get comfortable with their mouse). I’ve also heard of using spacebar to shoot but only when you want to isolate aim from shooting. But you should train both together as well.
I majored in math and have so far a great career in software. I don’t think knowing math separates me out from CS grads generally. However, math majors largely chose to major in Math because we like problem solving. Plenty of CS grads major in CS because they are expected to. Being a passionate problem solver gets you pretty far.