I want to give you a sense of what it’s like doing math “in the wild”. Doing mathematics is not just about learning what other people have already done: it’s about exploring and playing around with a system to figure out what’s going on. Let’s give it a go!
We are all familiar with the 12 hour system for counting time on a clock. The numbers count each digit from 1 to 12 and then circle back to 1. Since 12 is the number just before 1, we can think of 12 just like 0. We will ignore AM/PM for all of this.
We don’t usually talk about it this way, but we could say that adding 2 and 3 o’clock gives 5, in that 5 o’clock is 2 hours after 3, or 3 hours after 2.
We can ask what 7 + 7 would be. The answer is 14, but this is the same as 2, since 12 is a whole circle around the clock. That is, since 12 is the same as 0.
The next few examples are a little more complicated. Math is a much more interesting subject if you interact with it. It’s rare to find a mathematician reading without something to write on. Find a pencil and paper if you don’t have them around already.