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 here?" "Oh," said the statistician, "this is pi." "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 population has nothing to do with the circumference of the circle."
An interesting essay by Eugene Wigner, published in the journal "Communications in Pure and Applied Mathematics" in February 1960. Beginning with a quote by Bertrand Russell and the above story, he launches into an exploration of why mathematics, the study of numbers and formulas, should be so darned reliable.
It's not about things like the constancy of gravity or the speed of light. It's about how engineers can use what we know about Earthbound math and physics to precisely calculate the trajectories needed to send Voyager to Jupiter, or how Maxwell's equations could predict the existence of radio waves long before Heinrich Hertz ever discovered them. It's about how we can use mathematical models to predict things that we should have no business knowing, or even guessing at, because those models underscore the entire universe no matter where we are or what we're examining.
The essay is still under copyright, but is available on the Internet at http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html, among other places.