Cox's theorem

Cox's theorem is like a recipe for how to use math to make good guesses about what's going to happen. Imagine you want to know what's going to happen if you put a rock in a pond. You might guess that it will make ripples that will spread outwards. Using Cox's theorem, you would try to find the most accurate way to make this guess.

First, you would gather information about everything you know: the size and shape of the rock, how high you're dropping it from, how big the pond is, and any other details that might affect the result. Then, you would use math to guess what's going to happen based on that information. But there are lots of different ways you could use math to make that guess.

Cox's theorem helps you figure out which method of using math is most accurate. It says that you should use something called "probability theory" to make your guess. Probability theory is like a set of rules for how to make good guesses about what's likely to happen. You might think of it like a referee in a soccer game, making sure everyone plays fair.

By using probability theory to make your guess about what will happen when you drop the rock in the pond, you're more likely to get an accurate result. Cox's theorem proves that using probability theory is the best way to use math to make guesses about what's going to happen.