Physical Sciences and Mathematics Commons^™

Figure-Ground Perception: A Poem Proof, Richard Delaware

Journal of Humanistic Mathematics

This is a proof, in poetic form, of a bit of real analysis, more specifically involving the topology of accumulation points, that exploits the human optical phenomenon of figure-ground perception. Sometimes it is not a change in content, but a snap shift in point of view that yields a proof.

Mathematical Rigor From Within, Lowell Abrams

Journal of Humanistic Mathematics

There is a certain feel that is unique to the rarefied context of rigorous mathematics. These poems constitute an exploration of my experience of mathematical rigor when I am in the midst of exercising my skills as a research mathematician.

One = Zero, Eric John Gofen

Journal of Humanistic Mathematics

In this paper, I use Mathematics in addition to the three most pure sciences --- Physics, Chemistry, and Rap --- to prove that 1=0. The argument uses The Ideal Gas Law, Ohm's Law, the Definitions of Power and Velocity in addition to indefinite integrals, simple mathematical operations, and the 99 Problems Law. The intuition-crushing result can be applied to all branches of mathematics and sciences and will likely go down as one of the greatest discoveries of all time.

Does Content Matter In An Introduction-To-Proof Course?, Milos Savic

Journal of Humanistic Mathematics

Introduction-to-proof courses are becoming more prevalent in mathematics departments as more recognize the need to support students while they transition from courses focused on computation (such as calculus) to proof-intensive courses (such as real analysis). In such introduction courses, there are some common proving techniques to teach (induction, contradiction, and contraposition to name a few), but the content varies from institution to institution. This note adds to the discussion on content in such courses by analyzing two prior studies, one using a coding scheme designed to illuminate step-by-step justifications in a proof, and the other focused on interviews with course …

Every Minute Of Your Life Has Been Interesting, Susan D'Agostino

Journal of Humanistic Mathematics

In this short paper, we prove that every minute of your life has been interesting. We also provide four exercises intended to solidify understanding of this result, including one exercise related to the torturously boring family road trip you took as a child.

A Beautiful Proof By Induction, Lars-Daniel Öhman

Journal of Humanistic Mathematics

The purpose of this note is to present an example of a proof by induction that in the opinion of the present author has great aesthetic value. The proof in question is Thomassen's proof that planar graphs are 5-choosable. I give a self-contained presentation of this result and its proof, and a personal account of why I think this proof is beautiful.

A secondary purpose is to more widely publicize this gem, and hopefully make it part of a standard set of examples for examining characteristics of proofs by induction.

Prove It!, Kenny W. Moran

Journal of Humanistic Mathematics

A dialogue between a mathematics professor, Frank, and his daughter, Sarah, a mathematical savant with a powerful mathematical intuition. Sarah's intuition allows her to stumble into some famous theorems from number theory, but her lack of academic mathematical background makes it difficult for her to understand Frank's insistence on the value of proof and formality.