LOOKING back from the beginning of 1666, one finds it difficult to believe that Newton touched anything but mathematics during the preceding eighteen months. Clearly mathematics did dominate his attention during the period, but it did not completely obliterate other interests. Sometime during this period he also found time to compose the “Quaestiones,” in which he digested current natural philosophy as efficiently as he did mathematics. Other natural philosophers were as ignorant of his existence as mathematicians were. To those who knew of him, his fellow students in Trinity, he was an enigma. The first blossoms of his genius flowered in private, observed silently by his own eyes alone in the years 1664 to 1666, his anni mirabiles.

In addition to mathematics and natural philosophy, the university also made certain demands on his time and attention. He was scheduled to commence Bachelor of Arts in 1665, and regulations demanded that he devote the Lent term to the practice of standing in quadragesima. Pictured in our imagination, the scene has a surrealistic quality, medieval disputations juxtaposed with the birth pains of the calculus. An investigation of curvature was dated 20 February 1665, in the middle of the quadragesimal exercises, and in his various accounts of his mathematical development he assigned the binomial expansion to the winter between 1664 and 1665. While Stukeley was a student in Cambridge over thirty years later, he heard that when Newton stood for his B.A. degree, “he was put to second posing, or lost his groats as they term it, which is look'd upon as disgraceful.”

POSSIBLY the fact that the university closed down for the better part of two years, freeing Newton from control and supervision, aided his unorthodox program of study. Such was the progressive decomposition of the established curriculum, however, that it is far from clear that his intellectual development would have differed in any respect had the plague not intervened. While the requirements prescribed an impressive array of lectures, disputations, and acts over a three-year period before a Bachelor of Arts might be admitted as an inceptor for the Master of Arts degree, most of them had ceased to be operative by the Restoration, as repeated orders from Westminster that they be observed testify. Even residence had ceased to be required. Though Newton himself was not frequently absent from Cambridge once he returned after the plague, the college Exit and Redit Book reveals that other scholars of the house felt free to come and go as they pleased, even in term time. Newton's friend Wickins, for example, who was a scholar drawing a stipend, left the college on 15 October 1667 and did not return until the middle of January. Unorthodox study was not manifestly worse than no study at all. The one discipline exerted was financial; Newton received his stipends through his tutor. Although his papers do not indicate that he again made any gestures whatever toward the established curriculum, his academic career nevertheless marched through the remaining stages to full membership in the college and university without hesitation.

The concept of the transformation of scientific ideas took its present form during the spring and summer of 1965, while I was contemplating the factors in scientific revolutions, a feature of the Wiles Lectures, on which this book is based. This concept was put to the test in the spring of 1966, while I wrote the first of the lectures, on the history of inertia (of which a portion is embodied in Ch. 4), a topic which notably displays the complexities of ways in which a scientist uses the ideas (and the names of ideas) of a predecessor or contemporary. As the reader may see for himself in this sample, the very facts of this history stridently declare that in each stage of the development of the concept and law of inertia, a scientist altered and adapted something that he had encountered in his reading and studying of the writings of a contemporary or predecessor.

The Wiles Lectures were delivered at Queen's University, Belfast, in May 1966. In the following autumn the doctrine of transformation was expounded in a privately distributed edition of the first two of the lectures, bearing the general title, Isaac Newton: The Creative Scientific Mind at Work. A revised and expanded version of the chapter on the history of inertia was presented for discussion at a symposium held in Prague on 25–29 September 1967, on the occasion of the three-hundredth anniversary of the death of Joannes Marcus Marci of Cronland, of which the general theme was ‘La révolution scientifique du 17e siècle et les sciences mathématiques et physiques’.

NEWTON'S repeated protestation that he was engaged in other studies supplied an ever-present theme to his correspondence of the 1670s. Already in July 1672, only six months after the Royal Society discovered him as a man supremely skilled in optics, he wrote to Oldenburg that he doubted he would make further trials with telescopes, “being desirous to prosecute some other subjects.” Three and a half years later, he put off the composition of a general treatise on colors because of unspecified obligations and some “buisines of my own wch at present almost take up my time & thoughts.” Apparently the other business was not mathematics, because later in 1676 he hoped the second letter for Leibniz would be the last. “For having other things in my head, it proves an unwelcome interruption to me to be at this time put upon considering these things.” He was not only preoccupied, he was almost frantic in his impatience. “Sr,” he concluded the letter, “I am in great hast, Yours …” In great haste because of what? Surely not because of ten lectures on algebra that he purportedly delivered in 1676. And not because of pupils or collegial duties, for he had none of either. Only the pursuit of Truth could so drive Newton to distraction that he resented the interruption a letter offered. Newton was in a state of ecstasy again.

WELL before the contested edition of Flamsteed's Historia coelestis in 1712 brought that episode to a temporary conclusion, two new concerns, which would dominate Newton's life for more than five years, had imposed themselves upon him. In 1709, work began in earnest on a second edition of the Principia. In the spring of 1711, a letter from Leibniz to Hans Sloane, secretary of the Royal Society, inaugurated a heated controversy over claims of priority in the invention of the calculus. Moreover, a fourth problem of great import for Newton was also taking form. Already an ugly scene with Craven Peyton, the warden of the Mint, had signaled a deterioration of their relations which culminated in a major crisis in the Mint in 1714, when the battle with Leibniz was reaching its highest pitch. The Mint was the bedrock on which Newton's existence in London stood. Trouble there had to affect his whole life. In its intensity, the period from 1711 to 1716, succeeding more than a decade of relative calm, matched the great periods of stress at Cambridge, when his relentless pursuit of truth stretched him to the limit. The coincidence of these events, the demands they placed on Newton, may help to explain the furious scene with Flamsteed at Crane Court on 26 October 1711 and much else from these years not yet mentioned.

The concept of revolution

Many historians of science believe that the concept of revolution in science is of fairly recent origin, but I have found that during some three centuries there has been a more or less unbroken tradition (though by no means shared by all scientists) of viewing scientific change as a sequence of revolutions. In the eighteenth century, when this tradition appears to have taken its first rise, the word “revolution” continued to be used, as in the past, as a technical term in mathematics and astronomy; but it also gained currency in a general sense in two very distinct meanings, both of which are found in writings about scientific change and in historical accounts of political events. Of these, one which came into general usage during the eighteenth century denotes a breach of continuity or a secular (i.e., noncyclical) change of real magnitude, usually accompanied–at least in political events–by violence. The other is the older sense, used in relation both to the history of science and the history of political events, signifying a cyclical phenomenon, a continuous sequence of ebb and flow, a kind of circulation and return, or a repetition. After 1789, the new meaning came to predominate, and ever since, “revolution” has commonly implied a radical change and a departure from traditional or accepted modes of thought, belief, action, social behavior, or political or social organization. Thus in early modern times there occurred a double transformation of “revolution” and the concept for which it is the name.

THE utility of biography, Dr. Johnson argued, rests on the fact that we can enter by sympathy into situations in which others have found themselves. Parallel circumstances to which we can conform our minds shape every life. Even the great are not removed from the factors common to all: “We are all prompted by the same motives, all deceived by the same fallacies, all animated by hope, obstructed by danger, entangled by desire, and seduced by pleasure.” I must confess that twenty years devoted to the biography of Newton have not in my case confirmed Dr. Johnson's dictum. The more I have studied him, the more Newton has receded from me. It has been my privilege at various times to know a number of brilliant men, men whom I acknowledge without hesitation to be my intellectual superiors. I have never, however, met one against whom I was unwilling to measure myself, so that it seemed reasonable to say that 1 was half as able as the person in question, or a third or a fourth, but in every case a finite fraction. The end result of my study of Newton has served to convince me that with him there is no measure. He has become for me wholly other, one of the tiny handful of supreme geniuses who have shaped the categories of the human intellect, a man not finally reducible to the criteria by which we comprehend our fellow beings, those parallel circumstances of Dr. Johnson.

The origins of this book go back to 1966, when I had the honor of giving the Wiles Lectures in the Queen's University of Belfast, sponsored by the foundation established by Mrs. Janet P. Boyd in memory of her father. This foundation is remarkable in its conception. It not only provides a lecturer on an aspect of history, but ensures that each lecture will be discussed by the Belfast historians and research students and an invited group of historians from other universities. The evening discussions, following each afternoon's lecture, were of great value in helping me to make more precise certain basic issues. I am especially grateful for having thus been able to test certain primary viewpoints in an audience of colleagues and of general historians, and to profit by the reactions of Rupert and Marie Boas Hall, John Herivel, Michael Hoskin, George Huxley, D. T. Whiteside, and W. P. D. Wightman. I am indebted to my academic host, Professor J. C. Becket, to Mrs. Janet P. Boyd, and to Vice-Chancellor and Mrs. Michael Grant for much personal kindness.

The completion of a published version of these lectures occurs a decade or so later than had been expected. This delay has been caused, in the first instance, by the consuming labor of completing the Introduction to Newton's ‘Principia' and of the editing of Newton's Principia with variant readings (undertaken in concert with Alexandre Koyre and with the assistance of Anne Whitman).

NEWTON set out for Cambridge early in June. There was no greater watershed in his life. Although he would return to Woolsthorpe infrequently during the next eighteen years, with two extended visits during the plague, spiritually he now left it, and what a later commentator has called the idiocy of rural life, once and for all. Three short years would put him beyond any possibility of return, though three more years, perhaps somewhat longer, had to pass before a permanent stay in Cambridge was assured. His accounts show that he stopped at Sewstern, presumably to check on his property there; and after spending a second night at Stilton as he skirted the Great Fens, he arrived at Cambridge on the fourth of June and presented himself at Trinity College the following day. If the procedures set forth in the statutes were followed, the senior dean and the head lecturer of the college examined him to determine if he was fit to hear lectures. He was admitted – although there is no record whatever of anything but the verdict, one feels constrained to add “forthwith.” He purchased a lock for his desk, a quart bottle and ink to fill it, a notebook, a pound of candles, and a chamber pot, and was ready for whatever Cambridge might offer.

A Newtonian synthesis?

The words “synthesis” and “revolution” abound in the literature concerning the formation of modern science. The previous chapters contain testimony to the ways in which Newton's great work has been conceived to have been “revolutionary” ever since the age of Newton. The Newtonian achievement, however, is often categorized as a “synthesis” rather than as a “revolution”: as in such phrases as “The Newtonian Synthesis” or “The Great Synthesis” (for example, see Ginzburg, 1933, p. 369a; Whitehead, 1922; Butterfield, 1957, p. 106; Rosen, 1973; Gillispie, 1960, pp. 88, 144, 335, 510; Koyré, 1950b). The writers who use this word do not define exactly what they intend by it. For instance, in a brilliant essay on Newtonian science entitled ‘The Significance of the Newtonian Synthesis’, Alexandre Koyré (1950b) not only did not define what he meant by “synthesis”; he hardly used this word in the body of this text, and never in so general a context as the title would suggest.

It would appear that the Newtonian “synthesis” occurs in the literature of the history and philosophy of science as a convenient name for the Newtonian achievement taken as a whole, or the Newtonian system of the world, or the Newtonian natural philosophy. There is usually an implied sense of Newton's having put together the contributions (or, possibly the incomplete contributions) of such predecessors and contemporaries as Copernicus, Kepler, Descartes, Galileo, Huygens, and Hooke, and also John Wallis and Wren.

Some basic features of the Scientific Revolution

A study of the Newtonian revolution in science rests on the fundamental assumption that revolutions actually occur in science. A correlative assumption must be that the achievements of Isaac Newton were of such a kind or magnitude as to constitute a revolution that may be set apart from other scientific revolutions of the sixteenth and seventeenth centuries. At once we are apt to be plunged deep into controversy. Although few expressions are more commonly used in writing about science than “scientific revolution”, there is a continuing debate as to the propriety of applying the concept and term “revolution” to scientific change. There is, furthermore, a wide difference of opinion as to what may constitute a revolution. And although almost all historians would agree that a genuine alteration of an exceptionally radical nature (the Scientific Revolution) occurred in the sciences at some time between the late fifteenth (or early sixteenth) century and the end of the seventeenth century, the question of exactly when this revolution occurred arouses as much scholarly disagreement as the cognate question of precisely what it was. Some scholars would place its origins in 1543, the year of publication of both Vesalius's great work on the fabric of the human body and Copernicus's treatise on the revolutions of the celestial spheres (Copernicus, 1543; Vesalius, 1543). Others would have the revolution be inaugurated by Galileo, possibly in concert with Kepler, while yet others would see Descartes as the true prime revolutionary. Contrariwise, a whole school of historians declare that many of the most significant features of the so-called Galilean revolution had emerged during the late Middle Ages.

Kepler's laws and Newtonian principles

There are two widely held opinions concerning the development of Newton's scientific ideas: that he found the law of universal “gravitation” in the 1660s and then refrained from publishing it for twenty years, and that he found this law by “deducing” it from Kepler's “laws” (or, possibly, from only one of Kepler's laws). The analysis presented in this chapter will show that according to any reasonable definition of universal “gravitation”, Newton did not find this law until some time after November 1684, and before 1686, and then published it forthwith. It will be seen that Newton did not (and logically could not) “deduce” the law of universal gravitation from Kepler's laws. In any event, he was not consciously aware of the law of areas in a fruitful context of dynamics until somewhat later than the 1660s, possibly not until the time of a famous exchange of correspondence with Hooke in 1679–1680 (see §3.1). The clarification of the exact role of Kepler's three laws of planetary motion in Newton's thoughts about celestial motions will show Newton's successive steps and transformations leading up to the generalization of a universal force of gravity, and will reveal how the last step entailed a radical transformation of Kepler's laws.

This episode provides an example of Newton's creative mind at work, worth far more toward the understanding of whatever logic there may be in scientific discovery than a hundred precepts.