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 \mathbb{Z}/n \mathbb{Z}; he uses \mathbb{CLOCK}_n. The reason for his choice is that arithmetic modulo n is just like adding numbers (or positions) on a (analog) clock. Let’s work this out for n = 12. We begin by replacing the 12 on our clock by {0}. Then we can start adding things. Say it’s 11 and we’re starting to drive home from work which will take 2 hours (damn commute). What will the time be when we arrive at our doorstep (late for dinner)? Well it’s 1 of course, 11 + 2 = 1 on the clock face. This is exactly the same as addition modulo 12.

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