Is God a Mathematician_ - Mario Livio [55]
This type of logical maneuvering does not convince many philosophers, and they argue that to establish the existence of anything that is consequential in the physical world, and in particular something as grand as God, logic alone does not suffice.
Oddly enough, Descartes was accused of fostering atheism, and his works were put on the Catholic Church’s Index of Forbidden Books in 1667. This was a bizarre charge in light of Descartes’ insistence on God as the ultimate guarantor of truth.
Leaving the purely philosophical questions aside, for our present purposes the most interesting point is Descartes’ view that God created all the “eternal truths.” In particular, he declared that “the mathematical truths which you call eternal have been laid down by God and depend on Him entirely no less than the rest of his creatures.” So the Cartesian God was more than a mathematician, in the sense of being the creator of both mathematics and a physical world that is entirely based on mathematics. According to this worldview, which was becoming prevalent at the end of the seventeenth century, humans clearly only discover mathematics and do not invent it.
More significantly, the works of Galileo, Descartes, and Newton have changed the relationship between mathematics and the sciences in a profound way. First, the explosive developments in science became strong motivators for mathematical investigations. Second, through Newton’s laws, even more abstract mathematical fields, such as calculus, became the essence of physical explanations. Finally, and perhaps most importantly, the boundary between mathematics and the sciences was blurred beyond recognition, almost to the point of a complete fusion between mathematical insights and large swaths of exploration. All of these developments created a level of enthusiasm for mathematics perhaps not experienced since the time of the ancient Greeks. Mathematicians felt that the world was theirs to conquer, and that it offered unlimited potential for discovery.
CHAPTER 5
STATISTICIANS AND PROBABILISTS: THE SCIENCE OF UNCERTAINTY
The world doesn’t stand still. Most things around us are either in motion or continuously changing. Even the seemingly firm Earth underneath our feet is in fact spinning around its axis, revolving around the Sun, and traveling (together with the Sun) around the center of our Milky Way galaxy. The air we breathe is composed of trillions of molecules that move ceaselessly and randomly. At the same time, plants grow, radioactive materials decay, the atmospheric temperature rises and falls both daily and with the seasons, and the human life expectancy keeps increasing. This cosmic restlessness in itself, however, did not stump mathematics. The branch of mathematics called calculus was introduced by Newton and Leibniz precisely to permit a rigorous analysis and an accurate modeling of both motion and change. By now, this incredible tool has become so potent and all encompassing that it can be used to examine problems as diverse as the motion of the space shuttle or the spreading of an infectious disease. Just as a movie can capture motion by breaking it up into a frame-by-frame sequence, calculus can measure change on such a fine grid that it allows for the determination