What is the most beautiful math result in your opinion?*

*Can't be

Personally, I usually like approaches that allow you to solve a problem in an indirect way.

My favorite result is probably the uniqueness of the Poisson equation (I don't see why this wouldn't hold for other differential equations too, but as a physics guy this is the area I saw it applied so I'm just going with that) as it allows for the method of images. I don't think there is any other result which when I first saw applied made me go WTF.

For similar reasons, I think the residue theorem is quite cool too. Who would have thought that to solve real integrals you would need to move off the real line and look for singularities

*elsewhere.* I mean, it's quite amazing if you think about how that must have developed historically.

An unrelated result which I quite like, which you introduced me to Chruser, are the Borwein integrals.