Galileo was born in 1564, the same year as Shakespeare and Marlowe. By 1609, Marlowe was famous and seventeen years dead; Shakespeare had written all the major plays except The Tempest; Galileo had done nothing in particular. He had dabbled in literary criticism and many other genres, occupied an undemanding post as a professor of mathematics, and supported his relatives and hangers-on largely through a sideline making his “military compass.” This was a complex calculation device that, like modern software, cost for the package and cost again for the training. Besides that, Galileo’s intellectual capital consisted of some disorganized jottings on mechanics and an unshakable conviction of his own genius.

Then opportunity knocked, and Galileo was ready to move fast. Rumors reached Italy of a Dutch invention involving glass lenses in a tube that magnified objects at a distance. Galileo’s knowledge of geometry and experience in instrument-making came together. By the winter he had a version that magnified twenty times. On January 7, 1610 he turned the telescope on Jupiter. It had three unknown stars next to it, in itself not surprising as many new stars were evident. The next night, the tiny stars seemed to have got ahead of Jupiter instead of being left a little behind. January 9 was overcast. On January 10, the stars were still with Jupiter but in a different position. Galileo realized he had discovered moons, the first celestial discovery in recorded history (except for transient events like comets). A fast enough printing job would ensure his priority, and he had the naming rights. Graciously seeking the permission of his hoped-for patron (and former pupil) Duke Cosimo de Medici of Florence, he named them the Medicean stars in the book announcing the discovery, which appeared on March 12. Galileo was appointed grand ducal mathematician and philosopher at Florence on July 10, with an increase in salary acceptably huge.

The moons of Jupiter and further discoveries with the telescope, notably the phases of Venus and rotating sunspots, strongly suggested—although did not definitively prove—that Copernicus’s heliocentric theory of the universe was true. The Catholic Church believed the theory contradicted Scripture and tradition. When Galileo visited Rome in 1616 talking up the Copernican theory, the Inquisition declared it heretical and commanded him not to teach or defend it. He did the exact opposite, publishing the polemical Dialogue Concerning the Two Chief World Systems, which, though not explicitly favoring Copernicanism, made the alternatives look implausible. One of the alternatives made to look particularly ridiculous was a purely hypothetical interpretation of astronomical hypotheses in general, a theory suggested to Galileo in a quiet, conciliatory talk by his former friend, Pope Urban VIII. That did not prove to be a prudent move. Galileo, then aged nearly seventy and ill, was dragged before the Inquisition, found guilty of disobeying its previous orders, and ordered to recant his theory and live thereafter under house arrest.

Heilbron’s approach is biographical, telling Galileo’s life story interspersed with explanations of his ideas. There is not much on Copernicanism, the science of motion before and after Galileo, or on the significance of his contribution as compared with others’—all this is taken as read. That being said, the reader who has some initial sense of the point of Galileo’s work will find Heilbron’s treatment excellent, both as a definitive biography and as a guide to Galileo’s discoveries (and errors). There is more personal correspondence available than for most early modern figures, notably the letters to and from his daughter in a convent, Maria Celeste (the subject of Dava Sobel’s Galileo’s Daughter). This allows Heilbron to sketch Galileo’s personality convincingly—self-centered but usually generous, aggressive but in person friendly, regularly ill, restless but with great powers of concentration. And above all, sure of his own rightness and contemptuous of opponents: “Galileo’s particular genius, his literalness, black-and-white judgments, hypochondria, and shallow psychological depth perception made a Manichean personality.”

Heilbron’s discursive treatment allows certain things to become clear that are easily missed in briefer studies. One is that there really was conflict between the Copernican hypothesis and the Catholic faith as it stood at that time. Although the aggressive personalities involved brought the conflict to a head, they were locked into a preexisting collision course brought on by the logic of their positions. There was only one non-negotiable contradiction, but there was no way around it. According to Joshua 10:13, Joshua was aided by a miracle in which “The sun stopped in the middle of the sky.” Plainly that is impossible unless the sun is normally moving, which contradicts Copernicus’s theory that it is motionless in the middle of the universe. Galileo gamely, indeed rashly, launched into Biblical hermeneutics, and by modern standards did an excellent job. Like attributions of emotions to God, Galileo says, such expressions are not to be taken literally but are to be read as accommodations to the understanding of the ancient Israelites. He suggests, in effect, a different setting on the literal-to-metaphorical spectrum of interpretation, and his position is more or less that of most modern Biblicists. Unfortunately, the Catholic position was and is that this setting is not a matter to be decided by individuals, but by the Church. Since the Catholic Church chose a position more to the literal end, the contradiction between Copernicanism and existing Catholicism was genuine. Galileo’s condemnation was then logically inevitable.

Modern Catholics can only conclude that the condemnation of Galileo, and the centuries it took for the Church to dig itself out of the impasse, are God’s way of reminding the faithful not to take Vatican pronouncements with 100 percent seriousness. Heilbron concludes the book by wondering if another four hundred years will see the astronomer’s canonization.

The second thing that becomes clear as the story proceeds is just how often Galileo was wrong about science. He did not like forces, but it is impossible to do mechanics without them. His attempt to explain motion with pure geometry and occasional reference to “natural motions” cannot work and misled him many times. One of the main objections to the theory of a rotating earth is that things should fly off, like mud from a rotating wheel. The true theory is that the earth’s gravity keeps them stuck on, but would not be sufficient to do so if the earth rotated much faster than it actually does. Galileo’s attempted geometrical explanation implies that they would stay stuck on no matter how fast the earth rotated, which is nonsense. Similarly far off target was Galileo’s theory of the tides, which he was convinced was a knockdown argument for Copernicanism. The true tidal theory involves the gravitational attraction of the moon, which explains why the tides follow the lunar months. Galileo, dismissing all such “astrological” influences, believed the tides were caused by the earth’s shaking due to its daily motion and yearly rotation around the sun. That implausibly implied that the tides were unrelated to the moon; even when he later adjusted the theory to include the moon, his hypotheses remained unlikely. Needless to say, Galileo pugnaciously defended this theory just as strongly as he did all his true theories. “If the earth is immobile,” he writes, “tides cannot occur; if it moves with the motions already assigned to it [by Copernicus], they follow necessarily.” That is completely wrong.

Heilbron is rather disparaging of Galileo’s mathematical talents. His first sentence of the preface is “It will be useful and perhaps reassuring to state that this is not the biography of a mathematician.” That is missing something important. Galileo’s talent in mathematics certainly had its limitations; for example, he ignored algebra and failed to understand Kepler’s discovery that the orbits of the planets are elliptical. But he had an extraordinary ability to deploy two of the most basic mathematical concepts, symmetry and proportion, and make them reveal nature’s secrets. One of his mathematical insights of genius paved the way for his crucial discovery that heavy bodies dropped from rest are uniformly accelerated, that is, their speed increases proportionally with time (at two seconds after dropping, their speed is twice what it was at one second, and so on). Prior to time-lapse photography, that would have been very hard to observe, since bodies fall so fast. It was clear that bodies fall faster as they go (since a body that has fallen farther makes a bigger crunch than one dropped a short distance), but in what way? Galileo considered the two simplest theories: the more natural one that speed is proportional to the distance fallen, and the slightly more abstract one that speed is proportional to the time since start. He showed that the first theory cannot be right—there is no need to observe anything, because it is completely impossible, for purely mathematical reasons, that speed should be proportional to distance. It is not very difficult to do that with the calculus methods developed later by Newton and Leibniz, but Galileo’s “bare hands” way of doing it is very smart. Heilbron mentions it only in an obscure half a sentence.

After his condemnation and confinement to house arrest, Galileo became blind within five years and died four years after that. Heilbron calls this period “end games” and treats it briefly as a twilight phase in which the old master declines and dies. That is not the truth. The old lion was not curled up and expiring. Galileo’s four years after the condemnation are better compared to the late Proust, shut in his cork-lined room and weaving the memories of his youth into his masterpiece. Galileo’s surpassing contribution to science is not the Copernican polemic of the Dialogue Concerning the Two Chief World Systems, nor his discoveries with the telescope, which would have been achieved by others soon enough (perhaps with less Sturm und Drang). His true crowning achievement is the late Discourse on Two New Sciences, published in Leiden (to be on the safe side) in 1638. In that work, he sorts out the mass of his youthful efforts to create a science of motion to replace Aristotle’s powerful but flawed start. Modern mathematical science had begun.

Galileo died in January 1642. The science of motion was established, but not complete. On December 25 of the same year, Isaac Newton was born. As Alexander Pope said, “all was light.”