Galileo was a physicist who confined himself to his study of mechanical and astronomical phenomena, and hesitated to generalize his methods and principles. Descartes, his contemporary, brilliant mathematician, formulator of optics, was able to see with startling distinctness the wider significance of these things. He it was who first brought to the learned world a realization of the consequences of the scientific work we have been examining, and sketched out in clear words the full outline of the new universe into which men had been ushered.

In 1637 he published his first works, his Discourse Upon Method and the first fruits of its application in geometry, optics, and general physics. At his death in 1650 he had spread the fame of the mathematical interpretation of nature through the length and breadth of Europe, given confidence to many a lonely investigator to pursue his work…
The ground was prepared for Newton, who may almost be called the greatest of the Cartesians, to effect his great synthesis, and for the public to receive with awe and reverence his harmonious world-machine.

The vision that was Descartes’ was well expressed in the epitaph written by his closest friend Chanut: “In his winter furlough comparing the mysteries of nature with the laws of mathematics he dared hope that the secrets of both could be unlocked with the same key.” The reference is to the incident that determined the course of his whole life. After the best education that France afforded, disgusted with all that had been taught him save mathematics, he had turned to “the great book of the world.”

…The diversity he found in men’s beliefs taught him to distrust custom and listen only to reason. One day, confined to his room by the cold, he resolved to discard speculating much on mathematical problems, and now there came to him the vision that here, in combining the best in geometrical analysis and algebra, lay the source of all true science. “As I considered the matter carefully it gradually came to light that all those matters only are referred to mathematics in which order and measurement are investigated, and that it makes no difference whether it be in numbers, figures, stars, sounds or any other object that the question of measurement arises. I saw consequently that there must be some general science to explain that element as a whole which gives rise to problems about order and measurement, restricted as these are to no special subject matter. This, I perceived, was called universal mathematics… Such a science should contain the primary rudiments of human reason, and its province ought to extend to the eliciting of true results in every subject. To speak freely, I am convinced that it is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency, as being the source of all others.”

That night Descartes seems to have had an intense vision in which the Angel of Truth appeared and bade him trust his new science; it would indeed give him all knowledge. He rose on fire to carry out his analysis in geometry, and soon had perfected the branch we now call analytical geometry. This meant nothing less than the complete correspondence between algebra and the realm of space — that is, the real world. By algebra man could hope to discover the secrets of the universe; this was the key to the great cipher of nature, this the new method men had been seeking.

To Descartes thenceforth space or extension became the fundamental reality in the world, motion the source of all change, and mathematics the only relation between its parts. It is significant that this Cartesian faith, so similar to that of the pioneers in astronomy and physics, lacked any trace of the mystic Platonism that had marked all of them. He had made of nature a machine and nothing but a machine; purposes and spiritual significance had alike been banished. Descartes himself worked out the principles of optics in detail; but his significance lies rather in his general conception. He had reached the notion of seeking an explanation of all things in the world in purely mechanical terms.

Intoxicated by his vision and his success, he boasted, “Give me extension and motion, and I will construct the universe.” The whole working-out of mechanical physics in the next two centuries is but the development of this idea. All energy is reduced to kinetic energy, the energy of motion; all qualitative differences in the world to quantitative differences of the size, shape, and speed of motion of particles of matter. Living beings form no exception; life becomes a mere matter of chemical and physical changes, all animals are mere automata, even the body of man is a purely physical machine. The world of the Middle Ages has been explicitly and entirely rejected for the world of modern physics.