Multiplication Ancient and Modern

Henry Higuera

I’ll start by explicating my title. In my opinion, the word "multiplication" has had five or so meanings in the past 2500 years, but they have been confused and mashed together.[1] This has had unfortunate results which include skull- splitting, intimidation, discouragement, demoralization and apathy, as people attempt to understand how these five are "really the same operation," as they are often told to think they are—when in fact in important respects they are not. Plus, this confusion prevents people from seeing what the operations truly have in common—for they do have important things in common—and also how the different kinds go beyond each other and can do more and different things—which in itself is a beautiful story and a worthwhile object of reflection. I am going to try and dispel some mystery and introduce what I hope is pleasing clarity.