This is one of the exercises in my abstract algebra book (Nicholson) and it's just the title:
Show that $\pi$ is not algebraic over the field $\mathbb A$ of algebraic numbers.
All I know what to do is to set up an equation like $a_0 + a_1 \pi + \cdots + a_n \pi^n = 0$ where $a_i \in \mathbb A$ and then try to show a contradiction like $\pi$ is algebraic over the reals. My guess is that the proof would somehow involve the polynomials $f_i \in \mathbb Q[x]$ of $a_i$ such that $f_i(a_i)=0$, but I simply don't know where to go from here. I've been here for well over an hour. Can anyone give me some hints?
When I mean hint, don't just do 90% of the proof and leave the last step to me, I just want a vague hint.