Kittens & Gorillas 157 and numbers had not yet been properly invented. Euclid used distances rather than numbers for all his proofs but I will use the word ‘number’ in this explanation. First a little revision. A prime number is a number that can only be divided by itself and one, for example three, five, seven, and eleven. All numbers can be split into primes using a couple of tricks. First, all numbers are divisible by a set of primes. Ten is five times two — two primes. We are also fairly sure we can form any number by adding two primes together. This is Goldbach’s Conjecture, set as a question in a letter written to Euler in 1742. It is still unproven! Euclid proved there are an infinite number of primes by using reductio ad absurdum. Imagine we have a complete list of prime numbers — James’ list of primes. It contains every prime number. (This is the setup. We are proposing something we suspect is incorrect and will lead to a paradox or contradiction. When it does, we will have proven the opposite fact. The proof relies on the fact that a number can either be prime or not prime. There is no middle ground.) Let’s make a new number by multiplying all the numbers on my list together and adding one. There are two possibilities: this new number is either prime or not prime. If the number is prime, it is a new prime number that was not on my list and I have disproved the theory. If it is not prime then it must be divisible by two prime numbers already on my list. However, neither of these numbers could have been on my list, because dividing by one of them would give me a remainder of one. Remember I multiplied all prime numbers together and added one. It must, therefore, be a new prime number, which had previously not been on my list. Once again, I disprove the theory. Since both routes fail, James’ list of prime numbers is not complete and, therefore, prime numbers are infinite. Feynman's Proof My favorite piece of logic is Richard Feynman's disproof of the