The Role of Symmetry in Mathematics
Noson S. Yanofsky, Mark Zelcer
TL;DR
This paper explores various notions of symmetry in mathematics and their significance in addressing philosophical questions about the objectivity, ontology, and effectiveness of mathematics in relation to physics.
Contribution
It introduces multiple mathematical symmetry concepts and demonstrates their application in philosophical debates about the nature and objectivity of mathematics.
Findings
Symmetry concepts help clarify the objectivity of mathematics.
Symmetry provides insights into the role of mathematical objects.
Mathematical symmetry relates to physics and the effectiveness of mathematics.
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.
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