That's precisely why so many people struggle with mathematics at the beginning of their journey: the constant switch between a simplified abstraction in your head and formal, logical definition. You can't solve a problem without reverting to formalism, which requires a great mental effort. The sooner you get used to it, the faster your progress will go. Well said, Michel Talagrand!
Work hard and be open-minded when you find your "knack": you may be really interested in one field of mathematics, but discover that you have a greater aptitude in another.
There is no easy solution to what you are asking. Let's take a mathematical point of view If you are a mathematician you can of course imagine that there exist some people that should a priori stop trying because nothing proove that they don't exist. If you are asking if you should, you're probably in a interval of people including some that should and some that souldn't: but should you ? Obviously we can't answer you from the very element we have (or can we?) But it should be noted that if you ask this question is that maybe you can as I just said. The real question: do you want to do something else if you are not sure of the mathematical result ? AN obvious answer would be never stop trying but I get what you are saying. It is often say to not stop trying. I think you can ask yourself is why should I stop trying / why should I keep trying ? btw if you are an undergrad don't stop trying because I give maths classes so contact me haha !
I won’t say you should never stop trying, but generally I find that those moments of self-doubt eventually subside if what you’re trying is at all possible. If you find yourself continually failing and discouraged, seek a new perspective or try a different project. But if it truly interests you and you feel like sometimes you can pull an inch out of the problem you’re working on, keep going!
To make friends with people from academia usually comes from collabing with them in math research And if I understand right what you're talking about when you're saying "have no academic freedom" I think it really depends on where you live but since most mathematicians are usually not really implicated activists, I can't tell you for sure. Do you have examples about a mathematician being denied a prize in recent years due to political activism?
Definitely isn't for everybody, I can say that much. Some are more attuned to mathematics than others, just as others are more attuned to carpentry. We have different roles in life and one of the most important things is understanding your own and how that relates to others.
If a person wants to become a mathematician, he will do it, as long as he don't listen to people like you. Limiting beliefs are here to stop all of us all the time, and your comment is just one more proof about. As long your comment are about the people who not are playing with math because is what their soul are tell them, ok your comment can be accepted, but please try to change your way to vomit the perception about the reality to others and give a try to you to free your soul from this encapsulation you are putting yourself.
Theoretical Physicists - mathematical philosophers- have long held back physics. The Atomic Expansion Equation is well worth knowing. “The Final Theory: Rethinking Our Scientific Legacy “, Mark McCutcheon for proper physics including the CAUSE of gravity, electricity, magnetism, light and well..... everything. Mathematical ‘objects ‘, starting with Euclid’s “point” has been an abysmal descent into abstract noise.
