What does it mean that mathematic is a science of patterns?
I’m working on my PhD in mathematics, and while it doesn’t feel like one is studying patterns when one does mathematics it really is true. All of the abstract theory and complicated language is really just a way of describing more refined and deeper patterns. It is actually kind of an extension of the way language works in general; at some point in the history of human civilization somebody noticed something that trees, grass, and frogs had in common and invented the word “green”. Likewise, somebody later noticed that the numbers 2,3,5,7,11,13,17,… share in common and invented the word “prime”. Interesting mathematics comes about when one compares several different patterns and tries to come up with a pattern among the patterns; for example, if one thinks about prime numbers while one is thinking about numbers that can be written as the sum of two squares then one would be lead to the theorem that a prime number is the sum of two squares if and only if it leaves a remainder of 1 when
