Abstract / Synopsis
We present the story of a theorem's conception and birth. The tale begins with the circumstances in which the idea sprouted; then is the question's origin; next comes the preliminary investigation, which led to the conjecture and the proof; finally, we state the theorem. Our discussion is accessible to anyone who knows mathematical induction. Therefore, this material can be used for instruction in a variety of courses. In particular, this story may be used in undergraduate courses as an example of how mathematicians do research. As a bonus, the proof by induction is not of the simplest kind, because it includes some preliminary work that facilitates the proof; therefore, the theorem can also serve as a nice exercise in induction. Additionally, we use well-known facts from calculus to clarify and enhance what is intrinsically a discrete problem. Making an unexpected but welcome explanatory appearance, the number e is pertinent.
Osvaldo Marrero, "The Genesis of a Theorem," Journal of Humanistic Mathematics, Volume 13 Issue 1 (January 2023), pages 164-170. DOI: 10.5642/jhummath.LMMV7107. Available at: https://scholarship.claremont.edu/jhm/vol13/iss1/12