2015/06/28 by Noson S. Yanofsky, Yanofsky, Noson S.
Arts and Humanities · Environmental Science · Physics and Astronomy · #00A30 #00A69 #FOS: Mathematics #FOS: Physical sciences #History and Overview (math.HO) #History and Philosophy of Physics (physics.hist-ph) #Philosophy and History of Science #Quantum Mechanics and Applications #Science and Climate Studies
paper · pdf · doi:10.48550/arxiv.1506.08426
openalex publication_date 2015/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the physical universe? We review the well-known fact that the symmetries of the laws of physics are their defining properties. We show that there are similar symmetries of mathematical facts and that these symmetries are the defining properties of mathematics. By examining the symmetries of physics and mathematics, we show that the effectiveness is actually quite reasonable. In essence, we show that the regularities of physics are a subset of the regularities of mathematics.