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?