The Role of Symmetry in Mathematics
History and Overview
2016-04-04 v2 History and Philosophy of Physics
Abstract
Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce several notions of symmetry in mathematics and explain how they can also be used in resolving different problems in the philosophy of mathematics. We use symmetry to discuss the objectivity of mathematics, the role of mathematical objects, the unreasonable effectiveness of mathematics and the relationship of mathematics to physics.
Keywords
Cite
@article{arxiv.1502.07803,
title = {The Role of Symmetry in Mathematics},
author = {Noson S. Yanofsky and Mark Zelcer},
journal= {arXiv preprint arXiv:1502.07803},
year = {2016}
}
Comments
25 pages. arXiv admin note: substantial text overlap with arXiv:1306.4235