Mathematical Proof Between Generations
Fuente:
arXiv
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| Auteurs principaux: | , , , , , , , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917601864581120 |
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| author | Bayer, Jonas Benzmüller, Christoph Buzzard, Kevin David, Marco Lamport, Leslie Matiyasevich, Yuri Paulson, Lawrence Schleicher, Dierk Stock, Benedikt Zelmanov, Efim |
| author_facet | Bayer, Jonas Benzmüller, Christoph Buzzard, Kevin David, Marco Lamport, Leslie Matiyasevich, Yuri Paulson, Lawrence Schleicher, Dierk Stock, Benedikt Zelmanov, Efim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_04779 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Mathematical Proof Between Generations Bayer, Jonas Benzmüller, Christoph Buzzard, Kevin David, Marco Lamport, Leslie Matiyasevich, Yuri Paulson, Lawrence Schleicher, Dierk Stock, Benedikt Zelmanov, Efim History and Overview Logic in Computer Science 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. |
| title | Mathematical Proof Between Generations |
| topic | History and Overview Logic in Computer Science |
| url | https://arxiv.org/abs/2207.04779 |