Lately, I have been trying to prove things by own first, then read the proof. However, it is not the same. Is there any tips or advise for proving/stating things formally? I want to write on math or something, but, as I said, I'm having some trouble even before.
Should I read more first and then try to do it by my own?
Thank you
On
I forget where I read "to understand a proof, see what it proves". Sounds circular, but there is a grain of wisdom in there. Strive at understandability first, rigor second. Sure, must convince your gentle reader that no strange edge case got overlooked, that each link in the reasoning chain is solid and connects to it's neighbours. The operative word is "convince". Proofs are for people to read and understand. A rock-solid proof that nobody can understand is useless (see the brouhaha around the computer proof of the Four Color Theorem).
Proving stuff is just like other writing: There are some standard structures, known and accepted techniques, just the right balance between words and symbols. There are texts on the matter, like Knuth, Larrabee, Rogers "Mathematical Writing". Well worth a careful read.
This is how I learned proof-writing: know what your goal is and simplify it until you get something that you know is true. If this does not seem clear, check these notes: https://sites.math.rutgers.edu/~saks/300H/F16/lecturenotes.html. Sections 1,7, and 8 might help clarify things. Hope this helps.