Is God a Mathematician?

Mario Livio's Is God a Mathematician? is a review of the history of mathematics, the philosophy behind mathematics, and the question of why it is such an accurate description of the universe. He attempts to answer the question of whether mathematics is discovered or invented. Before reading the book, I thought I knew the answer to this question.

Livio first discusses the ancient Greeks Pythagoras, Euclid, and Archimedes. Pythagoras laid down much of the framework of mathematics, and Euclid formalized many theorems of geometry. Archimedes was world-class genius who discovered/invented several major ideas but was tragically killed by an irate soldier. The Greeks, led by Plato, certainly believed that mathematics described an absolute reality, a reflection of the realm of forms.

Galileo was a brilliant mathematician as well as an experimental scientist. He disproved Aristotle's notion that heavier things fall faster than lighter ones, and proved that the Earth moves around the Sun. He even proved that sunspots were really on the Sun and not small planets revolving around it. Descartes formulated a link between mathematics and geometry which opened up whole new avenues of calculations. Descartes still believed that mathematics was a discovery that described a true world.

Livio then discusses Isaac Newton, who invented calculus, and other mathematicians of the Enlightenment. He describes how logic and set theory became formalized and some tried to describe math as a form of logic.

Throughout the book the author describes how math not only describes natural phenomena, but also predicts. Some mathematical constructs have proven useful years after they have been discovered.

While I enjoyed this book, I actually believe it was the first time I came away from a book thinking, I wish there was more math.
I know this was a book for the layperson, but I could have used more concrete examples of the elegance of math myself.

Many modern mathematicians have declared that math is invented, it's a construct of the human mind. Livio makes a convincing argument for both sides of the debate, and declares that math is both invented and discovered. He has convinced me that the math we know is shaped by our brains and our experiences. I think the question can be helped by breaking down the concept of math into: the rules of how the universe works; and our representation of it. Certainly the universe would work according to logic and mathematical formulas even if we weren't here to describe it. But the symbols and concepts we use are a human invention. So I still believe that there is a system of rules that the universe runs by, regardless of whether humans have invented language to describe it. B