I am a bachelor student in my first year and I started a number theory course this week. My first impression is that (elementary) number theory is a very different kind of math relative to all other areas of mathematics that I know so far.
My problem is that the proofs are very easy, but I don’t know how to get any intuition about it, normally if I prove anything, my primary goal is to show why something is right, and not only that it is right, but in number theory I can prove pretty cool things without knowing why they are actually true. I think number theorie is really interesting, but I can’t enjoy proofs which do not let me feel any smarter than I was before proving a theorem.
Let me give you an example:
$a=qb+r$ with $a,q,b,r \in \mathbb{Z}$ $\Rightarrow$ gcd$(a,b)=$ gcd$(b,r)$. The proof is booth easy and boring, I can understand every step but I don't get an intuitive understanding, I just cannot see that it is true.
Does anybody may have some experience with this or at least can understand my problem?
2026-03-26 01:10:28.1774487428