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Birkhäuser

Primes and Particles

Mathematics, Mathematical Physics, Physics

  • Book
  • © 2024

Overview

Authors:
  1. Martin H. Krieger

    1. University of Southern California, Los Angeles, USA

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  • Presents many analogies between physical objects and mathematical structures
  • Shows how mathematics works in mathematical physics and how physics exemplifies mathematics
  • Argues that the mathematical rigor in physics is motivated by various aspects of the physical description of nature

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About this book

Many philosophers, physicists, and mathematicians have wondered about the remarkable relationship between mathematics with its abstract, pure, independent structures on one side, and the wilderness of natural phenomena on the other. Famously, Wigner found the "effectiveness" of mathematics in defining and supporting physical theories to be unreasonable, for how incredibly well it worked. Why, in fact, should these mathematical structures be so well-fitting, and even heuristic in the scientific exploration and discovery of nature? This book argues that the effectiveness of mathematics in physics is reasonable. The author builds on useful analogies of prime numbers and elementary particles, elementary structure kinship and the structure of systems of particles,  spectra and symmetries, and for example, mathematical limits and physical situations. The two-dimensional Ising model of a permanent magnet and the proofs of the stability of everyday matter exemplify such effectiveness, and the power of rigorous mathematical physics. Newton is our original model, with Galileo earlier suggesting that mathematics is the language of Nature.

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Introduction

    • Martin H. Krieger
    Pages 1-20

  3. Why Mathematical Physics?

    • Martin H. Krieger
    Pages 21-27

  4. Learning from Newton

    • Martin H. Krieger
    Pages 29-39

  5. Primes and Particles

    • Martin H. Krieger
    Pages 41-55

  6. So Far and in Prospect

    • Martin H. Krieger
    Pages 57-61

  7. Creation: When Something Appears Out of Nothing

    • Martin H. Krieger
    Pages 63-69

  8. Packaging “Spectra” (as in Partition Functions and L/ζ-Functions) to Reveal Symmetries in Nature and in Numbers

    • Martin H. Krieger
    Pages 71-76

  9. Legerdemain in Mathematical Physics: Structure, “Tricks,” and Lacunae in Derivations of the Partition Function of the Two-Dimensional Ising Model and in Proofs of The Stability of Matter

    • Martin H. Krieger
    Pages 77-92

  10. Mathematical Physics

    • Martin H. Krieger
    Pages 93-96

  11. Back Matter

    Pages 97-102
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Authors and Affiliations

  • University of Southern California, Los Angeles, USA

    Martin H. Krieger

About the author

Martin H. Krieger was trained as an experimental physicist at Columbia University. He is a Fellow of the American Physical Society. Krieger has taught in policy and planning and management at the University of California (Berkeley), Minnesota (Twin-Cities), MIT, University of Southern California, and University of Michigan (Ann Arbor). He has been a fellow at the Center for Advanced Study in the Behavioral Sciences and the National Humanities Center. Krieger is professor emeritus at the University of Southern California. Primes and Particles is his twelfth book. His earlier books include Doing Physics (Indiana, 1992, 2012), Constitutions of Matter (Chicago, 1996), and Doing Mathematics (World Scientific, 2003, 2015).

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