Time comes in cycles, and we deal with it using a cyclic number system. What time is 5 hours after 10pm? Hopefully you would say 3am, not 15pm. You know 10 + 5 isn’t 3, but you also know to reset to zero when you hit 12. In mathematical terms, this is called modular arithmetic: we divide 15 by 12 and keep the remainder. We write this as 10 + 5 = 3 modulo 12.

Modular arithmetic has many applications, from cryptography to magic tricks. There is…