The Utility of Recreational Mathematics

Prelude and Vademecum

This article is an amplification with illustrations of a write-up of my talk at the University Mathematics Teaching Conference at Sheffield Hallam University, 7 September 1999 [Singmaster 2000]. That talk was based on earlier talks that I had given on this topic, notably at the European Congress of Mathematicians in 1992 [Singmaster 1992; 1996]. Some topics discussed there were skipped in my talk at Sheffield, and some brief remarks on a few topics not mentioned at Sheffield were added in the write-up of that talk [Singmaster 2000]. I have now combined the material from all of these talks into the following, accompanied by suitable images.

The Nature of Recreational Mathematics

To begin with, it is worth considering what is meant by recreational mathematics. An obvious definition is that it is mathematics that is fun. However, almost any mathematician enjoys the work, even in studying eigenvalues of elliptic differential operators; so this definition would encompass almost all mathematics and hence is too general. There are two, somewhat overlapping, definitions that cover most of what is meant by recreational mathematics.