Whenever I read about the theory of evolution, I’m always struck by the juxtaposition of complexity and simplicity. The theory of evolution is simple: change in the inherited characteristics of biological populations over time leads to new, generally more successful, populations. It’s pretty damn simple. If you’re not equipped genetically to handle the environment you’re born into, you’ll most likely die and leave few descendants. Others who are better genetically equipped will live long fruitful lives and leave many descendants, thus altering the genetic landscape of the population.
The complexity comes into how nature goes about the whole evolutionary process. In the theory of evolution, there’s no guiding plan; there’s no pinnacle that nature is striving towards. Rather nature is discovering various ways of achieving different ends using a variety of similar, but not identical (and in some cases, very different), proteins and atomic structures. Really, what evolution is doing is gradually mapping out the the physical constraints imposed chemically on the universe by the laws of physics, while simultaneously dealing with ever-changing environments and needs.
So when I think of mathematics, it seems to me a very similar process. Continue reading