Univalent Foundations and the UniMath Library

The Architecture of Mathematics
  • Anthony BordgEmail author
Part of the Synthese Library book series (SYLI, volume 407)


We give a concise presentation of the Univalent Foundations of mathematics outlining the main ideas, followed by a discussion of the UniMath library of formalized mathematics implementing the ideas of the Univalent Foundations (Sect. 8.1), and the challenges one faces in attempting to design a large-scale library of formalized mathematics (Sect. 8.2). This leads us to a general discussion about the links between architecture and mathematics where a meeting of minds is revealed between architects and mathematicians (Sect. 8.3). On the way our odyssey from the foundations to the “horizon” of mathematics will lead us to meet the mathematicians David Hilbert and Nicolas Bourbaki as well as the architect Christopher Alexander.



The author would like to thank Benedikt Ahrens, Thierry Coquand, and an anonymous referee for their useful comments and suggestions.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Computer Science and TechnologyUniversity of CambridgeCambridgeUK

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