I’m reading the book Prime Obsession, by John Derbyshire, which tries to explain the Riemann Hypothesis to non-mathematicians. I got the book early in my undergraduate but never got around to reading it and then came across it in my book shelf the other day. I’m about half-way through and it has been a delightful read. Derbyshire manages to explain a lot of difficult mathematics without getting too technical and I would recommend the book to anyone starting an undergraduate in mathematics.

When I turned page 268 I was a bit surprised to see Derbyshire’s notation for the quotient rings ; he uses . The reason for his choice is that arithmetic modulo is just like adding numbers (or positions) on a (analog) clock. Let’s work this out for . We begin by replacing the on our clock by . Then we can start adding things. Say it’s and we’re starting to drive home from work which will take hours (damn commute). What will the time be when we arrive at our doorstep (late for dinner)? Well it’s of course, on the clock face. This is exactly the same as addition modulo .

February 18, 2010 at 8:16 pm

Actually, this is a fairly common way to introduce the concept to elementary-school kids. Problems: multiplication makes no sense (except to consider $\ZZ/12\ZZ$ as a $\ZZ%-module, which I believe they don’t do), and *nothing* is done with the concept later on in kids’ education. Hmmm, actually, I think there’s a problem prior to these: what’s actually happening is that the numbers on the face of the clock are a phs over the cyclic group, so it doesn’t really make sense to add four o’clock to nine o’clock.