Which Came First, Mathematics or Physics?


ChickenEggChickenEgg......? Physics is the fundamental study of Nature, in other words, in physics we want to find out how stuff works. Mathematics, on the other hand, is harder to pin down since it exists only in the human mind. Mathematics epitomizes the word "abstract." But still this can't be the complete story because many mathematical structures can be used to describe how physical objects interact and the nature of the relationships among them. In physics we use mathematics as a tool to understand Nature. In mathematics, the pure notions of numbers and other structures do not need physics to exist or explain or even justify them. But the surprising thing is that often some newly discovered abstract formulation in mathematics turns out, years later, to describe physical phenomena which we hadn't known about earlier. When, as a student of physics, you see this for the first time, it is truly overwhelming. The only conclusion I can bring myself to is that mathematics is not just a tool of physics; it must be much, much more. Since mathematics is a product of our imagination, then somehow the structure of the universe itself seems to be imprinted on the human mind. And if that is the case, the relationship between mathematics and physics does indeed boil down to the chickenandtheegg question. A One Way Street But if you start from basic mathematical concepts alone, it is not possible to derive the existence of gravity or any of Newton's laws. Doesn't it seem to you that something strange is going on here? It's as if you can go from A to B but not from B to A, and we're left to wander around in a oneway street. Here are some discussion questions you might think about ==> ? Let's see..... The following stories will require some concentration on your part, but if you stick with it, you will come away with a whole new view on how mathematics and physics are intertwined. The first two examples show how some abstract mathematical ideas preceded the physics they ended up describing. The third example shows the reverse: a physical concept that forced mathematical progress (a much rarer thing!).







