Introduction

An introduction to the life and work of John Napier while introducing students to logarithms will bring the “dry” material to life.

Napier was a Scottish mathematician who lived from 1550 to 1617.  He worked for more than twenty years to develop his theory and tables of what he called logarithms, a word he derived from two Greek roots:  logos, meaning word, or study, or reasoning, or in Napier’s use, “reckoning”, and arithmos, meaning “number”.  Much of our mathematical terminology, and indeed our English vocabulary, derives from Greek and Latin roots.  It is a useful exercise to take a few moments when new terms are introduced to explore the etymology of the word and to have the class try to name other words also deriving from these roots.  For example, you might ask “Where else have you seen a word derived from arithmos? 

If etymology is not your strong suit, you will find The Words of Mathematics by Steven Schwartzman an excellent resource.  It is published by the MAA.

Napier chose the name “logarithms” because he thought of them as “reckoning numbers”.  Their use could save computational time, especially the time of beleaguered astronomers.  These men had to carry out computations involving very large numbers.  Any simplifying devices were welcomed with joy.  In fact, the French mathematician Pierre Laplace (1749-1833) said that Napier’s new tool “doubled the life of the astronomer.”  Come back to this idea after students have seen that logarithms are exponents and after they have learned the rules for working with logarithms.  Then the students will be able to appreciate the computational improvements – especially when the lack of computers and calculators is borne in mind!