Boxing Pythagoras

On Invention and Discovery

For millennia, one of the most fundamental questions in the philosophy of mathematics has plagued some of the greatest minds in history. Is mathematics something which has been invented by human beings or is it something inherent to the universe which we discover and explore? If it is something which is invented, how is it possible that surprising and often counterintuitive results in mathematics are often eerily applicable to the world around us? If it is discovered, then how is it even possible for non-physical mathematical entities to exist in order to be discovered– and how do we even have access to them that they might be discovered?

The simple fact of the matter is that mathematics is, and always has been, both. Humanity has invented rules for describing the world around us which we call “mathematics.” Then, by following the implications of those rules through to their logical conclusions, we make discoveries which may not have been originally obvious.