The Genesis of a Theorem

Journal of Humanistic Mathematics

article

Osvaldo Marrero¹ 

[1]Villanova University

关键词: mathematical induction;    mathematical research;    number theory;    undergraduate instruction;   

DOI  :  10.5642/jhummath.LMMV7107

学科分类：社会科学、人文和艺术（综合）

来源: Claremont Center for the Mathematical Sciences

【 摘 要 】

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.

【 授权许可】

CC BY-NC-ND