Relationships with Physics, Science, Arts and the Real World

The distinction between pure and applied mathematics is not scientific but only social Vladimir Arnold, in Topological problems of the theory of wave propagation,par. 1 Apology, russ. Math. Surv. 51 1 (1996)

Mathematics is that part of physics where experiments cost little Vladimir Arnold, in On Teaching Mathematics, russ. Math. Surv. 53 1 (1998)

Natural philosophy is written in this very large book which continually stands open before our eyes, I say the universe, but you can’t understand if you don’t first learn to understand the language and know the characters in which it is written. He is written in mathematical language, and the characters are triangles, circles and other geometric figures, without whose means it is impossible to humanly understand a word of it; without these it is a vain wandering through a dark labyrinth. Galileo Galilei (The Assayer, 1623)

The enormous usefulness of mathematics in the natural sciences is something that borders on the mysterious and there is no rational explanation for it…. The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift that we neither understand nor deserve. we should be grateful for it and hope that it will remain valid in future research and expand, for better or worse, to our liking, though perhaps also to our upset, to the broader branches of knowledge. Eugene Wigner (The Unreasonable Effectiveness of Mathematics in the Natural Sciences, 1960)

Mathematics, Physics and Natural Sciences

The relationship of mathematics with the natural sciences, especially physics, has always been very close.

  • Eugene Wigner - The Unreasonable Effectiveness of Mathematics in the Natural Sciences transl.it. The unreasonable effectiveness of mathematics in the natural sciences
  • Tobias Dantzig - Number-The Language of Science trad.it. Number. history of the idea that revolutionized the world
  • Roger Penrose - The Road to Reality - Complete Guide to the Laws of Universe transl.it. The road to reality: the fundamental laws of the universe
  • Gyorg Polya - Mathematical Methods In Science
  • M.Schiffer L.Bowden - The Role Of Mathematics In Science
  • V. I. Arnold - Mathematical Understanding of Nature. Essays on Amazing Physical Phenomena and Their Understanding by Mathematicians
  • Alfio Quarteroni - The equations of heart, rain and sails. Mathematical models to simulate reality
  • John N. Shive, Robert L. Weber - Similarities in Physics
  • Paul A.M. Dirac - Beauty as a method. Essays and reflections on physics and mathematics.
  • Max Tegmark - Our Mathematical Universe: My Quest for the Ultimate Nature of Reality (2015)
  • Cedric Villani - Mathematics is the Poetry of Science (2020)
  • Paul J. Nahin - Hot Molecules, Cold Electrons. From the Mathematics of Heat to the Development of the Trans-Atlantic Cable(2020)

Articles and online resources:

  • Hilary Putnam, 1975, “What is Mathematical Truth?” Historia Mathematica 2: 529-543. reprinted in his (1975) Mathematics, Matter and Method: Philosophical Papers, Vol. 1. Cambridge University Press: 60-78
  • Richard Hamming, 1980, “The Unreasonable Effectiveness of Mathematics,” The American Mathematical Monthly 87
  • Max Tegmark, 2007, “The Mathematical Universe,” arXiv 0704.0646

Mathematics and the real world

  • Apoorva Khare - Beautiful, Simple, Exact, Crazy: Mathematics in the Real World
  • Morris Kline - Mathematics and the Physical World
  • John Allen Paulos - Innumeracy. Mathematical Illiteracy and Its Consequences, 1st ed. 1988, 3rd ed. (2019)
  • W. D. Wallis - Mathematics in the Real World
  • Saul Stahl, Paul E. Johnson - Mathematics Old and New.
  • Georg Glaeser - Images of Mathematics transl.it. images of mathematics
  • Georg Glaeser - Nature and Numbers: A Mathematical Photo Shooting
  • Georg Glaeser - Geometry and Its Applications in Arts, Nature and Technology
  • Ian Stewart - What’s the Use: The Unreasonable Effectiveness of Mathematics
  • Ian Stewart - Mathematics of Life: Unlocking the Secrets of Existence transl. it. The Mathematics of Life: Solving the Secrets of Existence
  • John D. Barrow - Why is the world mathematical?

Math and Art

  • Edwin A. Abbott - Flatland
  • Georg Glaeser - Geometry and Its Applications in Arts, Nature and Technology
  • Peter Higgins - A world of mathematics. from the Egyptian pyramids to the wonders of the Alhambra
  • Eli Maor - Music by the Numbers. from Pythagoras to Schoenberg transl. it. music by numbers. music and mathematics, from Pythagoras to Schoenberg (2019)
  • Eli Maor, Eugen Jost - The Art of Geometry transl.it. The Art of Geometry
  • David Foster Wallace - Everything, and more. compact history of infinity
  • David Foster Wallace - Tennis, Trigonometry and Tornadoes
  • Jorge L. Borges - The aleph
  • Claudio Bartocci (ed.) - Mathematical Tales
  • Hans Magnus Enzensberger - The Wizard of Numbers.
  • Marco Pivato - Noverar le stelle. What scientists and poets have in common
  • Michele Emmer - Visible harmonies. art, cinema, theater and mathematics
  • Michele Emmer - Mathematical narrative. impersonal memoir with digressions
  • Douglas R. Hofstadter - Gödel, Escher, Bach. An eternal brilliant garland.
  • Bruno Ernst - The Magic Mirror of M.C. Escher
  • Bruno D’Amore - Art and mathematics. metaphors, analogies, representations, identities between two possible worlds
  • Michele Emmer - Soap bubbles. between art and mathematics
  • Guido Trombetti,Giuseppe Zollo - Mathematical Suggestions of the Divine Comedy (2021)

Mathematics and computers

Mathematics and social sciences

  • Stutely, Richard - The Numbers Guide. the Essentials of Business Numeracy - The Economist - (2014)
  • Edward T. Dowling - (Schaum Outline) Mathematical Methods for Business and Economics (2009)
  • Luca Ricolfi - Mathematics for the Humanities (2016)