The unreasonable effectiveness of mathematics in the natural sciences. Richard courant lecture in mathematical sciences delivered at New York University, May 11, 1959

Abstract

“and it i s probable that there i s some secret here which remains to be discovered. ” (C. S. Peirce) There is a story about two friends, who were classmates in high school, talking about their jobs. One of them became a statistician and was working on population trends. He showed a reprint to his former classmate, The reprint started, as usual, with the Gaussian distribution and the statistician explained to his former classmate the meaning of the symbols for the actual population, for the average population, and so on. His classmate was a bit incredulous and was not quite sure whether the statistician was pulling his leg. “How can you know that? ” was his query. “And what is this symbol iere? ” “Oh, ” said the statistician, “this is n. ” “What is that?” “The ratio of the circumference of the circle to its diameter. ” “Well, now you are pushing your joke too far, ” said the classmate, “surely the pop-ulation has nothing to do with the circumference of the circle.” Naturally, we are inclined to smile about the simplicity of the classmate’s

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