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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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