John Baez

Quantum Matter in Mathematics and Physics

2023/8/24

Two of My Favorite Numbers: 8 and 24

The numbers 8 and 24 play special roles in mathematics. The number 8 is special because of Bott periodicity, the octonions and the E₈ 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 E₈ lattice and Leech lattice.

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