# Branches of mathematics not having a general method to solve

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?

• There's still no unified way to represent solutions to transcendental equations in closed form, IIRC. – J. M. is a poor mathematician Sep 20 '10 at 21:53
• You are mixing two things: being «underdeveloped» and «not having a general method to solve» are completely different things! – Mariano Suárez-Álvarez Sep 21 '10 at 11:07
• @Mariano Suárez-Alvarez, thank you I've change the title. – rystsov Sep 21 '10 at 12:16

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.