Geometry and the Real World

Abstract

Mathematics is important in understanding nature. By mathematics we create models, which provide explanations for the phenomena we observe. If a mathematical model yields a result which is in contradiction to the observations we make, then the theory will have to be scrapped, no matter how beautiful the mathematics in it should be. But can mathematics guide us in finding new knowledge about nature itself? In other words, not just arrange the knowledge we already have in a nice and orderly model, but actually predict observations which we have not yet made? The answer is, of course, affirmative. In fact this phenomenon is the reason for the usefulness of working with models in the first place.