What are the most overpowered theorems in mathematics? [closed]
Solution 1:
I would include the pigeonhole principle in such a list. This principle is one that is easy to explain to a 4 year old, and at the same time it is used throughout all areas of mathematical research. As an example see Proof of Van der Waerden's theorem (in a special case).
Solution 2:
Look into complex analysis. You have insanely powerful theorems all stemming from a function being analytic :).
Solution 3:
Orbit-stabilizer. There's so many things that can be described as group actions, and tons of counting arguments reduce to it.