  The tenfold way became important in physics around 2010: it implies that
there are ten fundamentally different kinds of matter. But it goes back to
1964, when C. T. C. Wall classified real super division algebras. These are
finite-dimensional real $\mathbb{Z}/2$-graded algebras where every nonzero
homogeneous element is invertible. He found that besides $\mathbb{R}$,
$\mathbb{C}$ and $\mathbb{H}$, which give purely even super division algebras,
there are seven more. He also showed that these ten algebras are all real or
complex Clifford algebras. The eight real ones represent all eight Morita
equivalence classes of real Clifford algebras, and the two complex ones do the
same for the complex Clifford algebras. The tenfold way thus unites real and
complex Bott periodicity. In this expository article we give a quick proof that
there are ten real super division algebras, and say a bit about applications of
the tenfold way.
