Take the 2-minute tour ×  My main interest is physics. However,
being self-taught in mathematics for the most part, my proofs
tend to be more intuitive than it is acceptable. Yet, I
recognize my inaptitude in rigor, and I would like to proceed in
practicing my writing proofs in a more mathematical way. Having
no formal instruction, and due to my lack of experience in
writing rigorous proofs, the mistake that I make is primarily
attacking a problem directly, without being able to formulate a
sketch, which implies a, in principle, sloppy result.  I want,
if possible, to start generalizing each problem in translating a
given theorem in set-theoretical language, and form a sketch of
proof in providing the proof for the generalization of the
theorem. What are your experiences?  Example of an elementary
result:  Theorem. If $a$ and $p$ are natural numbers such that
$a^p-1$ is prime, then $a=2$ or $p=1$.  How would that be
described in formal, set-theoretical language, and proved from
there?  (I understand that the