Eugene Paul Wigner
EUGENE PAUL WIGNER  Macroknow Library

The Unreasonable Effectiveness of Mathematics in the Natural Sciences.

"What is Mathematics? . . . I would say that mathematics is the science of skillful operations with concepts and rules invented just for this purpose. The principal emphasis is on the invention of concepts."1a

" . . . [T]he mathematician could formulate only a handful of interesting theorems without defining concepts beyond those contained in the axioms and that the concepts outside those contained in the axioms are defined with a view of permitting ingenious logical operations which appeal to our aesthetic sense both as operations and also in their results of great generality and simplicity."1b

"What is Physics? The physicist is interested in discovering the laws of inanimate nature. . . It is, as Schrödinger has remarked, a miracle that in spite of the baffling complexity of the world, certain regularities in the events could be discovered. . . The laws of nature are concerned with such regularities. . . This property of the regularity is a recognized invariance property . . ."1c ARISTOTLE BOOLE PLANCK EINSTEIN CRICK BROMLEY WATSON

"Every empirical law has the disquieting quality that one does not know its limitations."1d

" . . . [F]undamentally, we do not know why our theories work so well. Hence their accuracy may not prove their truth and consistency."1e PENROSE

"The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve."1f

Interesting Link
  • Eugene Paul Wigner, Princeton University; b. 1902, Budapest, Hungary. The Nobel Prize in Physics 1963, "for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles"

* Italics in the original.

1 Eugene P. Wigner. The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Richard Courant Lecture in Mathematical Sciences delivered at New York University, 11-May-1959. Communications on Pure and Applied Mathematics, Vol. XIII, 001-14 (1960). New York, NY: John Wiley & Sons, Inc., 1960.
a Ibid., at 2.
Ibid., at 3.
Ibid., at 3-4.
Ibid., at 11.
Ibid., at 14.
Ibid., at 14.