In many of my science classes over the years, I found myself extremely confused about the intuition behind theorems and proofs. I would ponder, how could you possibly figure that out? This pervasive thought did not only apply to complex topics. There are so many simple things that this could refer to. How about long division? We all employ that technique all the time, an elementary and systematic approach to dividing any two real numbers that seems trivial. But, would I have come up with such an elegant way of doing it? Maybe, but I cannot know for sure, for it is something I have already learned.
In my algorithms class the last semester, I thought the same things when learning Dijkstra’s algorithm, Kadane’s algorithm, and binary search. These are relatively simplistic algorithms, but I was always thinking whether I would have ever figured them out on my own. Looking back, I would say that this is a relatively naive way of looking at things. The reason these algorithms and ideas have names is because we see them as great discoveries. They’re named after the phenomenal scientists that discovered them. They needed an immense understanding of the topics before they even knew where to begin. These ideas were not discovered over night. They may have taken years. They were not proved in the span of a 45 minute lecture in a college class.
The reason we have education is to quickly teach us the principles that took thousands of years to discover. If we were meant to re-discover everything that’s already known, we would never have made it past the stone age. We build on the foundation our predecessors left behind. It allows us to focus on the now instead of the past. It allows us to continuously innovate on the knowledge we have been given. It’s okay for you and I not to immediately understand Stokes’ Theorem. He walked so we could run. He laid down the path for us to forge on ahead. It’s our responsibility to embrace and iterate on the ideas that have been passed down to us. We need not spend an eternity on the past. It is our duty to build on it and leave a greater foundation for the future to inherit.