Though he truly would not have gotten where he did had he not stood on the shoulders of giants, Isaac Newton has as good a claim as any to have begotten a new era.
I came to the Principia Mathematica, in part, through frustration at trying to comprehend Einstein. Einstein's work itself takes much too much advanced mathematices for me to ever hope to get it from the root. But even his little book on Relativity, intended for a lay audience, baffles me after a pair of readings. I think each take, alternating with different popular treatments, becomes clearer. But there is still that sense of a veil I'll never overcome.
So, I thought, if the mathematics of the 20th century is incomprehensible, maybe that of the seventeenth isn't. The Principia is daunting, to look at, but maybe, in small bites, it might yield to understanding--especially since the University of California published a new English translation a few years back.
Now let me make clear I haven't yet spent enough time yet with the thing to know if I will make any headway. But I was given to a new train of thought in learning (through introductory material) that a great deal of the second of the three parts is given to refuting Descartes' "Principles of Philosophy," and its attempts to explain celestial mechanics with a notion of whirling vortici.
Now, in my head, Newton is a scientist, and Descartes a philosopher--even though Newton called his great work "Mathematical Principles of Natural Philosophy." Part of the reason for that lies in the area of Newton's success and Descartes' failure; it was Newton whose "System of the World" successfully set out the laws that described the elliptical paths of the planets and other celestial objects in a comprehensive theory of gravity, undergirded by abstract notions of mass and force. Descartes is remembered for a more random miscellany of things: his method of doubt, his reworking of the ontological argument from the idea of "perfection," his notion of certainly as a function of clarity, his division of the world into the famous dualism of "thinking stuff" and "extended stuff." He does, granted, have a separate reputation among the mathematicians, and there I am not really ready to go.
But what strikes me as a great difference between Newton's Principia Mathematica and what I have perused of Descartes' Principia Philosophia (in the French translation of the Pleides edition) is the disabling ambition of Descartes. He goes for explaining it all, not just the motion of Jupiter, but the motion of his own hand. The same, it occurs to me, can be said for his contemporary Leibnitz, another universal genius, another master in the history of mathematics (of whom Newton boasted he had "broken his heart" in the controvery over the discovery of the calculus). Leibnitz's ambition toward comprehensiveness led him to an atomism which attempted to incorporate consciousness as a fundamental component of matter. It went nowhere (except, I suppose, into the History of Philosophy textbooks).
Newton's genius is not just his remarkable insight, his mathematical proficiency, his synthetic abilities, his geometrical talent for proof, but also his self-limitation. His "Motion of Bodies" says nothing about the motion of human bodies (except to the extent that we are dead weights when the subject of an outside force). His "System of the World" is really the system of gravitational equilibrium, an important part of the the world, but only a part. He does not lack philosophy, and the various "scholia" throughout the Principia can only be described as philosophical takes on space, time, and, toward the end, God, and something called "spirit," which may be what we call spirit, and which may be what we would call the electro-magnetic force.
Newton's fault, then, isn't so much his own as that of his followers who, dazzled by his successes, fail to see that his success is a result of his reduced scope, and his "system" a system of only part of the world, and by no means necessarily the most important. The failures of Descartes and Leibnitz remind us how far we are from a true "system of the world," when the mysteries of life and consciousness and spirit remain.