Kepler and Wiles: Models of Perseverance.

Kepler overcame 2000 years of mistaken belie , pseudo science, and downright superstition i f you have seen the videotape The Proof or read the companion book by Simon Singh (1997) called Fermat's Enigma, you know that the story of Andrew Wiles's journey toward the proof of Fermat's last theorem is a remarkable tale of hope, dis appointment, persistence, and ultimate triumph. Discovered by Pierre Fermat around 1637, the theorem is simple to state: "The conjecture that jt* + yn = zn, where n > 2, has no solution with x, y, and z positive integers" (James and James 1992, p. 163). Yet the proof of this well-known theorem eluded generations of mathematicians. Wiles spent nearly a decade attempting to prove the theorem before he finally succeeded in 1994. The videotape and the book each offer an all-too-rare glimpse into the private struggles that preceded the more formal presentation of a finished product. When reading Singh's book, my thoughts turned toward other figures in the history of mathematics who displayed the same kind of persistence, even perhaps battling their own beliefs about the way things work, finally succeeding and thereby trans forming mathematics. Among them, Johannes Kepler, of the late sixteenth and early seventeenth centuries, stands out because he left a detailed account of his attempts to understand the nature of the universe. In the process, he developed mathe matical methods that led directly to the invention of the calculus. In many ways, the paths taken by Kepler and Wiles mirror each other and offer fasci nating insights into the creative process of mathe maticians. However, Kepler was up against a chal lenge even greater than the one that Wiles faced in solving his 350-year-old mystery: Kepler had to overcome two thousand years of mistaken beliefs, pseudoscience, and downright superstition to derive his three laws of planetary motion. Kepler's first two laws of planetary motion were published in 1609; the third, ten years later. See figure 1. His best-known publication was the Mys terium Cosmographicum. Originally published in 1596, it was the only one of Kepler's works that was issued in a second edition during his life. The sec ond edition, published in 1621, contained extensive notes that reflected the ways in which Kepler's thinking changed over twenty-five years, the period during which he developed his laws of motion. first lam: Ww planets moot about the sun tn elliptical orbits mitti the sun at one focus. Second lam: WK radius nector joining a planet to the sun suieeps oner equal areas in equal intentais of time. third lam: Wat square of the time of one complete reoolution of a planet about its orbit is proportional to the cube of the orbit's semimajor axis.