TITLE: Branches of mathematics not having a general method to solve
QUESTION [9 upvotes]: I studied applied math, so each course (except abstract algebra) was dedicated to solution of a similar problems. After those courses it seems that every branch of mathematics has a developed theory with a few unsolved problems. I believe that is wrong. I found out that there is no general approach to Diophantine equations (the 10th Hilbert problem), to problems like "Collatz conjecture" and to nonlinear differential equations. 
And so the question is: what is the other branches of mathematics (collections of similar problems) without a general method to solve them?

REPLY [4 votes]: Irrationality of certain numbers is still though problem for mathematics. Even though irrationality of some numbers like square roots of integers that are not perfect squares and irrationality of $\pi$ and $e$ has long been known, it is still unknown whether $\pi + e$, $2^e$, $\pi^{e}$, $\pi^{\sqrt{2}}$,  $\pi \cdot e$ , $\pi / e$, Catalan's constant, Euler-Mascheroni constant, etc. are irrational or not, even though all are highly suspected to be.