Best Equations

In the spirit of the best constants thread, post what you think is the best (most beautiful, useful, elegant, etc) equation from math and physics.

My suggestion: Euler's formula:

e^(ix) = cos(x) + i sin(x)

especially because when x=π, e^(iπ) + 1 = 0 (Euler's identity)

proving 1=2 is the best
if a = b
a^2 = ab   [for purpose of writing a^2 = aa)
aa + (aa-2ab) = ab + (aa-2ab)
2aa - 2ab = -ab + aa
2 (aa-ab) = 1 (aa - ab)
2 = 1

by far the best equations / maths ever