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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 Atiyah–Singer index theorem
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by Daniel S. Freed HTML | PDF
Bull. Amer. Math. Soc. 58 (2021), 517-566 Request permission


The Atiyah–Singer index theorem, a landmark achievement of the early 1960s, brings together ideas in analysis, geometry, and topology. We recount some antecedents and motivations, various forms of the theorem, and some of its implications, which extend to the present.
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Additional Information
  • Daniel S. Freed
  • Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712
  • MR Author ID: 69015
  • ORCID: 0000-0003-0150-1555
  • Email:
  • Received by editor(s): June 10, 2021
  • Published electronically: July 8, 2021
  • Additional Notes: This material is based upon work supported by the National Science Foundation under Grant Number DMS-2005286.

  • Dedicated: In memory of Michael Atiyah
  • © Copyright 2021 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 58 (2021), 517-566
  • MSC (2020): Primary 58J20, 58J28, 58J52, 19K56, 81T50
  • DOI:
  • MathSciNet review: 4311554