Mathematics: What is the most beautiful theorem proof, and why?

Late 1700s, in a German elementary school, as a punishment for misbehaving with the teacher, he was asked to sum 1 to 100.
The teacher was astonished when a kid solved this within seconds as:

S = 1 + 2 + .......+ 100
S= 100 + 99 +....+ 1
---------------------------------
2S = 101 + 101 + ....+ 101 (100 times)
= 101x100

=> S = 101x100/2 = 5050

The student was the famous mathematician and physical scientist Carl Friedrich Gauss.