Mathematical Proof Between Generations

Faculty/Professorship: AI Systems Engineering 
Author(s): Bayer, Jonas; Benzmüller, Christoph  ; Buzzard, Kevin; David, Marco; Lamport, Leslie; Matiyasevich, Yuri; Paulson, Lawrence; Schleicher, Dierk; Stock, Benedikt; Zelmanov, Efim
Publisher Information: Bamberg : University of Bamberg Press
Year of publication: 2022
Pages: 1-17
is version of: 10.48550/ARXIV.2207.04779
Language(s): English
Licence: Creative Commons - CC BY - Attribution 4.0 International 
DOI: 10.48550/ARXIV.2207.04779
URN: urn:nbn:de:bvb:473-irb-545931
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into peril. Now may be the time to reconcile theory and practice, i.e. precision and intuition, through the advent of computer proof assistants. For the most time this has been a topic for experts in specialized communities. However, mathematical proofs have become increasingly sophisticated, stretching the boundaries of what is humanly comprehensible, so that leading mathematicians have asked for formal verification of their proofs. At the same time, major theorems in mathematics have recently been computer-verified by people from outside of these communities, even by beginning students. This article investigates the gap between the different definitions of a proof and possibilities to build bridges. It is written as a polemic or a collage by different members of the communities in mathematics and computer science at different stages of their careers, challenging well-known preconceptions and exploring new perspectives.
GND Keywords: Beweis; Mathematische Logik
Keywords: mathematical proof
DDC Classification: 510 Mathematics  
004 Computer science  
RVK Classification: SK 130   
Type: Preprint
Release Date: 9. November 2022

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