The Golden Ratio by Mario Livio: were mathematics invented or discovered?

The Golden Ratio, the 2003 historical analysis of the irrational number phi (~1.62) by Mario Livio, reads more like a top level review of a few thousand years of mathematical history. And so, while I enjoyed the pursuit of phi in art throughout time, I was much more taken by the top-level review of the development of math. The development, or, well, the discovery of math.

Indeed, of the various historical storylines, one theme from the book that stuck out for me more than others, I was most taken bythe ongoing debate about whether math was invented or discovered, the former of which is my persuasion to date:

Wolfman holds very similar views. I asked him specifically whether he thought mathematics was “invented” or “discovered.” He replied: “If there wasn’t much choice in selecting this particular set of rules then it would have made sense to say that it was discovered, but since there was much choice, and our mathematics is merely historically based, I have to say that it was invented.” The phrase ‘historically based’ in this context is crucial since it implies that the system of axioms on which our mathematics is based is the one that happened to emerge because of the mathematics and geometry of the ancient Babylonians. This raises two immediate questions: (1) Why did the Babylonians develop these particular disciplines and not other sets of rules? And a rephrasing of the question on the effectiveness of mathematics: (2) Why were these disciplines and their offspring found to be useful at all for physics” p. 250

An argument that I found compelling:

“For example, when one drop of water is adding to another drop or one molecular cloud in the galaxy coalesces with another, they make only one drop or one cloud, not two. Therefore, if a civilization that is somehow fluid based exists, for it, one plus one does not necessarily equal two”

The reverse argument I really loved was the idea the famed ‘God was a mathematician,’ meaning that while the relationships of maths were invented, the interrelationships of the world is driven by mathematics. That is, the coincidences and order of the world that we often subscribe to a higher being is indeed math.

A couple other essays on the concept here and here.

Watch a few kids running through the debate: