An early cosmology placed the earth on the backs of four elephants, all standing on a turtle. The question, “On what did the turtle stand?” always was answered, “It’s turtles all the way down.” Calculus and all of 19th century analysis worked because the functions studied are more closely approximated by their tangent lines the more closely we look. When we zoom in, the curves appear simpler. By the start of the 20th century, mathematicians knew some examples where this was false, but these were regarded as monsters. Benoit Mandelbrot recognized the mathematics of these monsters described much of nature, and expanded this idea into fractal geometry. Very often, nature does not get simpler under magnification; Benoit gave us a way to quantify the fact that it’s complicated all the way down.
Michael Frame, a Yale University professor, worked alongside Benoit Mandelbrot, a world renowned mathematician and IBMer, known for coining the word fractal and developing the Mandelbrot set. Read the rest of Frame’s article, here.