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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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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