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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.


Strange new universes: Proof assistants and synthetic foundations
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by Michael Shulman
Bull. Amer. Math. Soc. 61 (2024), 257-270
Published electronically: February 15, 2024


Existing computer programs called proof assistants can verify the correctness of mathematical proofs but their specialized proof languages present a barrier to entry for many mathematicians. Large language models have the potential to lower this barrier, enabling mathematicians to interact with proof assistants in a more familiar vernacular. Among other advantages, this may allow mathematicians to explore radically new kinds of mathematics using an LLM-powered proof assistant to train their intuitions as well as ensure their arguments are correct. Existing proof assistants have already played this role for fields such as homotopy type theory.
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Bibliographic Information
  • Michael Shulman
  • Affiliation: Department of Mathematics, University of San Diego, San Diego, California 92110
  • MR Author ID: 830320
  • ORCID: 0000-0002-9948-6682
  • Email:
  • Received by editor(s): August 12, 2023
  • Published electronically: February 15, 2024
  • Additional Notes: This material is based upon work supported by the Air Force Office of Scientific Research under award number FA9550-21-1-0009.
  • © Copyright 2024 by Michael Shulman
  • Journal: Bull. Amer. Math. Soc. 61 (2024), 257-270
  • MSC (2020): Primary 68V20
  • DOI:
  • MathSciNet review: 4726991