the top 10 most beautiful theorems
A 1988 poll of readers of the Mathematical Intelligencer ranked some of the most wellknown theorems in mathematics thus:

1.
Euler’s identity, ${e}^{i\pi}=1$

2.
Euler’s formula for a polyhedron, $V+F=E+2$

3.
There are infinitely many prime numbers^{}. See Euclid’s proof that there are infinitely many primes.

4.
There are only 5 regular polyhedra

5.
The sum of the reciprocals^{} of the squares of the positive integers is $\frac{{\pi}^{2}}{6}$. See the Basel problem^{}.

6.
A continuous mapping of a closed unit disk into itself has a fixed point^{}

7.
The square root of 2 is irrational

8.
$\pi $ is a transcendental number^{}

9.
Every plane map can be colored with just 4 colors

10.
Every prime number of the form $4n+1$ is the sum of two square integers in only one way
References
 1 David Wells, The Penguin Book of Curious and Interesting Mathematics. London: Penguin Books (1997): 126  127
Title  the top 10 most beautiful theorems 

Canonical name  TheTop10MostBeautifulTheorems 
Date of creation  20130322 18:53:52 
Last modified on  20130322 18:53:52 
Owner  PrimeFan (13766) 
Last modified by  PrimeFan (13766) 
Numerical id  5 
Author  PrimeFan (13766) 
Entry type  Feature 
Classification  msc 01A60 
Classification  msc 00A99 