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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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The octonions
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by John C. Baez PDF
Bull. Amer. Math. Soc. 39 (2002), 145-205

Erratum: Bull. Amer. Math. Soc. 42 (2005), 213-213.


The octonions are the largest of the four normed division algebras. While somewhat neglected due to their nonassociativity, they stand at the crossroads of many interesting fields of mathematics. Here we describe them and their relation to Clifford algebras and spinors, Bott periodicity, projective and Lorentzian geometry, Jordan algebras, and the exceptional Lie groups. We also touch upon their applications in quantum logic, special relativity and supersymmetry.
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Additional Information
  • John C. Baez
  • Affiliation: Department of Mathematics, University of California, Riverside, CA 92521
  • Email:
  • Received by editor(s): May 31, 2001
  • Received by editor(s) in revised form: August 2, 2001
  • Published electronically: December 21, 2001
  • © Copyright 2001 John C. Baez
  • Journal: Bull. Amer. Math. Soc. 39 (2002), 145-205
  • MSC (2000): Primary 17-02, 17A35, 17C40, 17C90, 22E70
  • DOI:
  • MathSciNet review: 1886087