Maybe it’s just because my father used to teach a course about the History of Calculus, but I’m continually amazed by the mathematicians of the ancient world. Consider someone like Archimedes, for example; a brilliant geometer whose law of buoyancy is still taught in introductory physics courses around the world. Now just think for a minute about how much he accomplished–not only without modern technology, obviously, but also without the benefit of calculus, Cartesian graphs, algebra, or even a numeral system good for anything besides basic addition. We think of science as being built upon the shoulders of giants–each generation making new discoveries based on those of the last, but one thing which I feel is often overlooked is the act of taking that which is already known and expressing it in such a way that it becomes easily manageable. To use more modern examples, I shudder to think what Quantum Mechanics would be like without Dirac notation, or what particle physics would be without Feynman diagrams.
It makes me realize that whereas right now I may be struggling with my work, chances are there’s probably some enormously easier way to do it that I can’t even think of yet.