The numbers 8 and 24 play special roles in mathematics. The number 8
is special because of Bott periodicity, the octonions and the E_{8}
lattice, while 24 is special for many reasons, including the binary
tetrahedral group, the 3rd stable homotopy group of spheres, and the
Leech lattice. The number 8 does for superstring theory what the
number 24 does for bosonic string theory. In this talk, which is
intended to be entertaining, I will overview these matters and also
some connections between the numbers 8 and 24.

You can see the slides of this talk,
and also a video:

In my talk I mentioned these other things:

My favorite numbers:
videos of more elementary talks on the numbers 5, 8 and 24.

The tenfold way: how the 8-fold periodicity
of real Clifford algebras and 2-fold periodicity of complex Clifford
algebras combine to explain 10 kinds of matter.

The octonions: how to build
division algebras from Clifford algebras, and much more about the octonions.

Integral octonions:
using the octonions to explore of the E_{8} lattice and Leech lattice.