# Bott-Milnor-Kervaire 1,2,4,8 Theorem

## Theorem

Let $A$ be a division algebra with real scalars.

Then the dimension of $A$ is either:

$1$: the real numbers $\R$
$2$: the complex numbers $\C$
$4$: the quaternions $\Bbb H$

or:

$8$: the octonions $\Bbb O$.

## Source of Name

This entry was named for Raoul Bott, John Willard Milnor and Michel André Kervaire.

## Historical Note

Bott-Milnor-Kervaire 1,2,4,8 Theorem was proved by Raoul Bott, John Willard Milnor and Michel André Kervaire in $1958$.