Physical Sciences and Mathematics Commons^™

A Short Walk Can Be Beautiful, Jonathan M. Borwein

Journal of Humanistic Mathematics

The story I tell is of research undertaken, with students and colleagues, in the last six or so years on short random walks. As the research progressed, my criteria for `beauty' changed. Things seemingly remarkable became `simple' and other seemingly simple things became more remarkable as our analytic and computational tools were refined, and understanding improved. I intentionally display some rather advanced mathematics as it is my contention -- as with classical music -- that one can learn to appreciate and enjoy complex formulas without needing to understand them deeply.

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.