When Newton joined the Royal Society in 1672, Robert Hooke was one of its most celebrated members, possessing a brilliant if somewhat scattered mind, that leaped from discipline to discipline and discovery to discovery. He and Newton had opposite personal temperaments and approaches to scientific research, and both craved the spotlight, so a rivalry may have been inevitable. The rivalry began when Newton presented his first paper to the Royal Society, detailing his work on the nature of light and advancing his theory that white light was a composite of all the colors of the spectrum. Hooke, who had his own ideas about the nature of light, criticized Newton's work, and Newton took offense, claiming huffily that his own discovery was "the oddest if not the most considerable detection which hath hitherto beene made in the operations of Nature," and threatening, in March of 1673, to withdraw from the Society over the quarrel. He was dissuaded from this course, but his rivalry with Hooke persisted, despite attempts to patch things up in the late 1670s. In the 1680s, with the publication of Newton's Principia, it flared anew; Hooke claimed that he had worked out one of Newton's key mathematical formulae a decade earlier. Thereafter, as Newton grew famous and Hooke slid into obscurity, the older man became embittered, and developed a loathing for his rival that endured until his death in 1703.

The French philosopher and scientist René Descartes declared that everything in nature, from the working of the human brain to the weather over Europe, could be explained by the motion and interaction of tiny, invisible particles that filled the universe. He applied this to the solar system to explain the motion of planets and moons: the swirling interaction of these particles, he explained, created a whirlpool-like effect of "vortices" that carried the planets around the sun. It was a logical system, but it was entirely based on supposition, since Descartes could not demonstrate the existence of his tiny particles. Newton, recognizing that such an all-encompassing scheme was unverifiable, chose to focus his energies upon what he could prove, using experiments and the iron laws of mathematics. This led to his theory of gravity, the force of attraction between objects that binds planets into their orbits, and which he proved, mathematically, in the Principia. Descartes' defenders objected that Newton had not shown how gravity worked, and that his system thus lacked the explanatory power of Descartes' vortices. Newton admitted that this was true: Descartes' model explained the "why" and "how" of everything, whereas his did not. But Descartes' vortices, however complete and philosophically satisfying, did not make mathematical sense; only gravity could be proven to be truly extant.

The law of gravity, as propounded in the Principia, had amazing explanatory power. Gravity explained why the planets orbit the sun, as well as the orbit of our moon, and of Jupiter's moons. Fifty years before, the astronomer Kepler had discovered all of these orbits to follow elliptical paths; gravity now explained why the paths took this particular shape. Gravity is also responsible for the movement of comets, which, Newton revealed, transcribed orbits around the sun just as planets did. He also discovered that the force exerted on the earth by the sun's gravity is responsible for the flattening of the earth at the poles and for the bulge at the equator. Finally, gravity explains the tides: the weak gravitational pull that the moon exerts on the earth combines with the pull of the sun to form what Newton termed a "lunisolar" effect and create the daily rhythm of the seas.