# the top 10 most beautiful theorems

A 1988 poll of readers of the Mathematical Intelligencer ranked some of the most well-known theorems in mathematics thus:

1. 1.

Euler’s identity, $e^{i\pi}=-1$

2. 2.

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

3. 3.

There are infinitely many prime numbers. See Euclid’s proof that there are infinitely many primes.

4. 4.

There are only 5 regular polyhedra

5. 5.

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

6. 6.
7. 7.
8. 8.

$\pi$ is a transcendental number

9. 9.

Every plane map can be colored with just 4 colors

10. 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 TheTop10MostBeautifulTheorems 2013-03-22 18:53:52 2013-03-22 18:53:52 PrimeFan (13766) PrimeFan (13766) 5 PrimeFan (13766) Feature msc 01A60 msc 00A99