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Bulletin of the American Mathematical Society

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Five stages of accepting constructive mathematics


Author: Andrej Bauer
Journal: Bull. Amer. Math. Soc. 54 (2017), 481-498
MSC (2010): Primary 03F65
DOI: https://doi.org/10.1090/bull/1556
Published electronically: October 3, 2016
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Abstract: 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
Email: Andrej.Bauer@andrej.com

DOI: https://doi.org/10.1090/bull/1556
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
Article copyright: © Copyright 2016 American Mathematical Society