We tend to think of a mathematical function as an operation. A number goes in one end, things are done to it and then another number comes out the other end. This definition is nice but not all inclusive, there are many functions that fall outside its umbrella. Technically a function is a relation between two sets. One set is all the numbers that can go into the function, and the other is all the numbers that can come out the other side. The function can (hypothetically) be defined by drawing a line between every number in the first set to the resulting number in the second set. I've been saying numbers but, and this is key, it doesn't actually have to be numbers. Being a relationship between sets is all that really matters, not what those sets are. The crucial discovery, and when mathematics really took off, is that the members of those sets can be other functions. As soon as we begin to analyze functions working on functions, things can take off exponentially. And, as in so much, what was true in mathematics is true all the way up the chain to our workday universe. If you're talking about physics or programming or even art, as soon as new inventions can work seamlessly off the old you hit the inflection point and things begin to explode. Because no one, not even the best of us, can really build all that much by themselves. In science they call it 'standing on the shoulders of giants' and in the art world there is always the old adage about great artists and stealing. Real progress only starts when we all begin to build off each other.