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The Unreasonable Effectiveness of Mathematics in the Natural Sciences
Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959.
Communications on Pure and Applied Mathematics. 13: 1–14 (1960)
Philosophyi.e. physics is written in this grand book — I mean the universe — which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth. (Galilei, Il Saggiatore, 1623).
David Hilbert, Naturerkennen und Logik, Lecture at the Kongress der Gesellschaft Deutscher Naturforscher und Ärtze, 1930 (pdf, audio)
Michael Atiyah, Robbert Dijkgraaf, Nigel Hitchin, Geometry and physics, Phil. Trans. R. Soc. A 13 March 2010 vol. 368 no. 1914 913-926 (doi;10.1098/rsta.2009.0227)
on, conversely: The Unreasonable Effectiveness of Physics in the Mathematical Sciences
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