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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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Five stages of accepting constructive mathematics
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by Andrej Bauer PDF
Bull. Amer. Math. Soc. 54 (2017), 481-498 Request permission


On the odd day, a mathematician might wonder what constructive mathematics is all about. They may have heard arguments in favor of constructivism but are not at all convinced by them, and in any case they may care little about philosophy. A typical introductory text about constructivism spends a great deal of time explaining the principles and contains only trivial mathematics, while advanced constructive texts are impenetrable, like all unfamiliar mathematics. How then can a mathematician find out what constructive mathematics feels like? What new and relevant ideas does constructive mathematics have to offer, if any? I shall attempt to answer these questions.
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Additional Information
  • Andrej Bauer
  • Affiliation: Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
  • MR Author ID: 640857
  • Email:
  • Received by editor(s): July 1, 2016
  • Published electronically: October 3, 2016
  • Additional Notes: This material is based upon work supported by the Air Force Office of Scientific Research, Air Force Materiel Command, USAF under Award No. FA9550-14-1-0096
  • © Copyright 2016 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 54 (2017), 481-498
  • MSC (2010): Primary 03F65
  • DOI:
  • MathSciNet review: 3662915