I Have a problem. I mostly do mathematics because I find it fascinating and enjoy doing it. Now whenever I skim through a book a number theory I always find myself thinking 'I wish I would understand this because it seems so interesting'. So than I start at the beginning of the book, but I quickly loose interest.
The reason being that I just seem to lack any intuition for the subject. For things like combinatorics/analysis/graphs/linalg I all have at least a certain amount of intuition to help me in setting up proofs, and develop some sort of mental framework for the subject.
However for number theory I have absolutely no such intuition/framework. I can follow the proofs, I can prove most elementary stuff myself, but it's always very tedious. Even simple things like Bezout's Identity or Fermat's little theorem do not at all seem obvious to me.
Now I compare these results to results of a similar 'level' in other fields:
- The handshake lemma in graph theory
- A function being differentiable implies it's continuity in analysis
- A system of $n$ independent equalities in $n$ variables has at most $1$ solution in linear algebra
All of those seem immediately clear to me, even when I first read them. This is why I'm wondering if I'm just lacking some 'number-theory gene' or something, and I'm just not cut out to be good at number theory.
Now the question I want to ask is: to what extent is this 'normal'? Are things like Fermat's little theorem as intuitively clear to most people as for example the handshake lemma?