The Newton Project, 2008-13

A. The Religious Papers

Newton’s more polished religious writings are among the most original treatises on theology in the early modern period, and their publication allows researchers to see this work in its totality for the first time. Given their scope and quality, as well as their status as previously unseen works by Isaac Newton, their release constitutes a major event in the history of early modern thought. The approximately 2.2m words of Newton’s religious writings published since the start of 2008 show each stage of his creative process, from his note-taking to his idiosyncratic redrafting of various texts, and then finally on to the polished and virtually complete texts, written for a still largely mysterious audience. These texts transform what we know of the scale and nature of Newton’s researches, and make it possible for the first time to understand the links between different strands of his religious writings; the order of their composition; their putative links with other areas of his intellectual life; and their relations to the wider social and intellectual contexts in which he worked. They are available in both diplomatic and normalised form, and from November 2013 have been linked to images of the originals held by the NLI. At the time of writing, fourteen of Newton’s original Latin productions have been translated (all but one by Michael Silverthorne).^[9]

It is impossible to say exactly to what extent the religious archive as it stands was organised by Newton himself, and to what degree it has resulted from later organising efforts by his relatives, editors and owners. Fortunately, and despite the fact that the archive is now distributed across the globe, we have very good evidence that virtually nothing has been lost from the collection of papers that existed at Newton’s death. Having said that, we also know that many efforts have been made to re-order the papers by bringing together drafts or disparate documents that concern the same topic, or by joining together parts of one document that have been separated for hundreds of years.

Some of the collections that have come down to us contain a large number of much smaller documents that seem to have been put into a pile on the grounds that they belonged nowhere else. One good example is the extensive set of papers at New College Oxford (designated New College Oxford 361.2). This contains calculations associated with the second edition of the Principia, papers connected with Newton’s business at the Mint, and numerous drafts of his work on prophecy and chronology. Many of these topics can be found together on one single sheet, and often on letters addressed to Newton. Many of these pages are charred through burning, and numerous pages are genuine palimpsests whose interpretation, transcription and encoding is a monumental act of scholarly labour. For that very reason, the checking and proofing of this most resistant of documents will not occur until the spring of 2014.

The Newton Project has greatly expanded our knowledge of three aspects of Newton’s religious interests:

(i) the publication of his theological writings reveals the full range of his private religious opinions, and answers questions about his beliefs that have beguiled the curious for over three centuries. Newton’s religious nachlass has proved to be much larger and much more complex than we envisaged when we began the work fifteen years ago, and the texts available via the Newton Project are now among the largest set of religious resources for any individual. The papers demonstrate that in this field Newton was a thinker of the highest calibre and intellectual daring, though our respect for his courage may well be tempered by the fact that he published almost nothing of it in his lifetime. These would be fascinating texts if we did not know who their author was, or if we knew that they were not by Newton. As it is, the fact that they are certainly written by Newton, and that many of his most exciting non-scientific works were composed when he was at the peak of his intellectual powers (in the 1670s and 80s), allows researchers for the first time to assess the degree to which these texts are similar to his contemporary work in natural science.

Newton’s religious views covered a wide range of subjects though he did his best to avoid discussing what he thought were overly ‘metaphysical’ opinions, or those doctrines that had no basis in Scripture. He was deeply committed however, to showing how and why these same doctrines had been introduced early in the early Christian church in order to corrupt the true religion. Indeed, at every opportunity Newton used historical evidence found in the writings of the Church Fathers and others, rather than engaging in abstruse theological discussions over doctrine. It was not that he could not grasp the fine points about doctrine, but rather that he felt discussion of certain doctrines (such as the nature of God’s offer of grace, and the nature of predestination) led only to the sort of barren disputes that he condemned in the field of natural philosophy. Going far beyond what for him were permissible religious discussions, disputes over unscriptural fictions were decidedly unchristian.

Newton’s interests concerned early church history, Jewish and Christian prophecy, Scriptural exegesis, and the fate of the Noachid religion that — as he saw it — spanned the globe soon after the Flood. Some of these projects were independent of each other but from the 1670s his central interest was the rise of the Great Apostasy that (as he saw it) corrupted the Christian church in the fourth century after the birth of Jesus Christ. This had introduced the fundamental doctrines and practices of Roman Catholicism, and in his early work Newton wrote at length about how the chief perversions introduced into Christianity at this time had been engineered by the Devil himself. In assuming that Catholicism was the Devil’s own religion, Newton did not deviate markedly from the analyses offered by Anglican contemporaries such as his friend Henry More, a student of the great exegete Joseph Mede and the most prolific writer on prophecy in Restoration England. He did, however, break with almost all his contemporaries in condemning the concept of the Holy Trinity as the central doctrinal plank of that antichristian religion that came to dominate the Western world. In the domain of religion, it was his attack on the Trinity that made him cautious about revealing his true beliefs to others. The writings now published on the Newton Project website betray no evidence that Newton’s pronounced anti-Trinitarianism was engendered by contact with like-minded people, but they suggest that his deep abhorrence of the doctrine was a logical extension of his deep-seated hatred of idolatry.

Over two million of Newton’s words on the early Christian church survive, a testament to his immense efforts to document the decline and fall of the Apostolic faith. Much of the way he thought about the corruption of Christanity was, of course, premised on his beliefs about what the original form of Christianity actually was. Newton argued repeatedly was that it was a simple religion, preached to ordinary people, whose central feature was the principle of charity (or the Golden Rule) rather than any abstruse claim about the nature of Jesus Christ or about the precise manner in which he had redeemed humanity by his suffering. There were more difficult truths to be gleaned by learned men of more mature years (such as himself), but that was a different matter.

These truths concerned the meaning of prophecy and the way in which a proper understanding of church history revealed the working of the divine hand throughout history. Newton’s mastery of the historical evidence from this period — matched by only a handful of contemporaries — was energised and wholly shaped by his radical Protestant understanding of the Apocalypse. He built his system on what he believed were the core ‘discoveries’ of Mede, who described the essentials of antichristian idolatry and who argued that it was obvious that all these signs depicted Roman Catholicism. Like Mede and others working in the Protestant tradition, Newton argued that Revelation had its own internal ‘order’, and that once this was decoded, the Revelation narrative described in detail the rise and fall of Roman Catholicism. Although he agreed with Mede about the historical guilt of popery, Newton transformed Mede’s system so that his own definition of idolatry included the doctrine of the Trinity.

(ii) aside from their status as religious writings, the publication of all of Newton’s ‘spiritual workshop’ makes it possible to understand how it fits into his larger intellectual world. When the Newton Project began in 1998, scholars at that stage belonged in two main camps. Those in the first group argued on positivist grounds that Newton’s work in the exact sciences was self-evidently more ‘valuable’ than his work in other fields, and they asserted that there could be no connection whatsoever between the gold of his mathematical and scientific effusions, and the dross of his religious fancies. In the 1960s and 70s other historians reacted vigorously to this fractured view of Newton’s work, and citing new evidence from his correspondence and other papers, they argued that all of his work was interconnected in some mysterious but coherent whole.^[10]

For many decades there has been a mutual incomprehension between both camps, each unwilling or more likely, unable to examine the documents that were the staple primary sources for the other side. The texts on the Newton Project site make it possible to address this issue using evidence rather than making crude a priori statements. Apart from his vaulting ambition, and what some scholars have unhelpfully termed his ‘quest for truth’, the papers reveal no empirical smoking gun that connects the disparate areas of all of his writings. However, the compartmentalised nature of his work gives little succour to positivists. Rather, a broad examination of Newton’s archive demonstrates his capacity (shared, it should be said, by his contemporaries) to work in a wide range of fields according to the narrative conventions, types of evidence, and styles of proof appropriate to each domain. Having said that, it is possible that future research will find much deeper consonances between ostensibly unrelated areas of his fields of study. For example, the future implementation on the site of new investigative tools such as Latent Semantic Analysis will allow researchers to search for the possible re-use of concepts and phrases in different domains (and, as it happens, make the task of conventional editing much easier).

(iii) The existence of these novel materials allows researchers to assess how Newton’s religious work was related to that of his contemporaries, as well as to the social, religious and political contexts in which he lived. The search for Newton’s links to his own world is complicated by the fact that with one or two exceptions, he showed little concern with publishing his religious writings, or in participating in any religious controversy. Apart from the issue of manuscript warrant for the doctrine of the Trinity, he evinced little interest in contemporary debates, and was primarily concerned with the interpretation of Revelation and the events that took place in the early church. Moreover, it remains hard to tie his writings to specific events, since neither internal evidence (from the publication date of his sources) nor physical documentary evidence (in the form of watermarks) has permitted us to date Newton’s writings in these areas with any precision. Although he was almost wholly reliant on editions produced by others, and was interested in the same topics and questions that captivated the energies of other early modern scholars, he was an independent thinker who set great store by that independence. To that extent, the theological writer betrayed exactly the same scholarly ethos as the author of the Principia.

(i) Writings on the Ancient Religion

Given both the heretical nature of many of Newton’s beliefs, and his general abhorrence of print as a vehicle for his own writings, it remains unclear what the audience was supposed to be for his draft chapters and more complete tracts. In the early to mid-1680s, he turned his attention to a series of related projects concerning what he took to be the ‘true’ ancient religion that he believed was the most ‘rational’ of all. Taken as a whole, this was an enormous undertaking that would form the basis of his more mature works on chronology in the eighteenth century. The earliest of these efforts may well be his attempt to use euhemerist techniques drawn from authors such as Gerard Vossius and Samuel Bochart in order to situate his history of the ancient religion within a genealogy of the ancient peoples of Europe and the Middle East. In another related project, he examined the ancient religion in more detail and yet another series of writings he set out to show that the ancient religion was rational precisely because it embodied a series of natural, Newtonian elements. In 1685 he summarised elements of these works in the first paragraphs of the ‘ De Motu Corporum Liber Secundus’, a work that was essentially the draft of the Third Book of the published Principia. Soon afterwards he wrote a remarkable text on the religious and scientific practices of the Ancients that was related both to his more extensive treatment of the Ancient Vestal religion and also to his draft classical scholia that he was at one time intending to include in the second edition of the Principia. Over 100,000 words of notes for these projects have been transcribed over the last five years, the most interesting probably being the notes on Ralph Cudworth’s True Intellectual System and the extended excerpts that formed the basis of his ‘classical scholia’.

By the early eighteenth century Newton had greatly expanded his knowledge of the political and religious state of the ancient world. The most extensive of his drafts for a comprehensive chronology of the ancient world are now published, all for the first time. Although hyperbole about Newton’s erudition can be wearing, these texts show that he had a mastery of a vast range of sources and facts that he had brought together — using a series of interpretive principles — into one coherent whole. When these views were published in a truncated form in his 1728 Chronology of Ancient Kingdoms Amended, critics took issue with the ways in which he had used his principles — as well as evidence from astronomy — to lop off many centuries from the histories of ancient kingdoms given by historians from different cultures.^[11]

(ii) Writings on Scriptural exegesis

The fascinating analysis of textual corruption that Newton sent to Locke in November 1690 reveals both his doctrinal commitments and also his capacity to generate in a matter of months an extended, innovative tract on a particular topic. Newton argued that all putative Trinitarian proof-texts were either forgeries, inserted by ignorant or scheming priests, or had been misinterpreted by Catholics and Protestants to the present day. Newton already had a serious interest in supposed corruptions of Scripture, notably (as many of his contemporaries also did) in the history of 1 John 5:7-8 and 1 Timothy 3:16. The background to the creation of this text has been examined elsewhere, but the Newton Project now provides a rich set of resources for understanding how Newton’s various attempts to ascertain the truth about these documents were part of a much larger analysis of the general corruption of Christianity in the early Christian church. The texts on the project site include Hopton Haynes’s 1709 translation of the work.

One of the most remarkable and technically demanding documents (both to decipher and encode) published by the Project over the last five years was the result of a request to Newton made in 1693 by the Oxford divine John Mill, who had known Newton for around a decade. Mill asked Newton to send a list of variant readings of the Apocalypse from his own notes on various printed sources such as Brian Walton’s Polyglot, as well as gleanings he had noticed in two manuscripts owned by their mutual friend John Covel. Newton, who had made short records of textual variants in the past, made two lengthy sets of notes of variant readings and sent them to Mill, who recorded his gratitude for Newton’s extraordinary labours in two letters. Ultimately, he included a number of Newton’s observations in his variorum New Testament of 1707.

(iii) Writings on Prophecy and Jewish Worship

The Project has also published all the documents relating to Newton’s work on the dimensions of Solomon’s Temple and the practices of the people who worshipped within it. Newton believed that the dimensions of objects mentioned in Old Testament prophecy had a figurative or non-literal meaning (so prophetic days meant real years). Understanding Jewish religious practices, and in particular the spatial structure of worship, was crucial because it was the key to understanding the Apocalypse, whose setting was the holiest part of the Temple. The inner court, for example, represented the chosen people while the outer court represented the gentiles; specific religious rituals described in the Old Testament or the writings of Josephus and others were referenced by the account of heaven in the first chapters of Revelation. Nevertheless, Newton’s ‘ Prolegomena’, his extended analysis of Ezekiel and other books connected with the dimensions of the temple, is not primarily concerned with typology but with ascertaining the exact dimensions (in terms of cubits) and structure of the temple. The Project has also published and transcribed texts that are closely related to the ‘Prolegomena’, both offering detailed accounts of the internal structure of Solomon’s Temple and its copies. In this context it is also worth mentioning the notes Newton took from Maimonides’s De Cultu Divino, which was a major source for those contemporaries of Newton who wrote on the size and shape of the Temple.

Although the Project published three extensive prophetic treatises between 2004 and 2007, it transcribed an even greater amount of prophecy-related material between January 2008 and December 2013. On the basis of internal evidence, Newton’s small and unfinished essay on Christ’s Second Coming and the Day of Judgment can be related to the lengthy treatise on prophecy known to have been composed between 1684 and 1689. However, the largest portion of writings on prophecy was composed in the last three decades of his life. The monumental redraftings of his work on prophecy, transcribed and encoded from 2009-13, explore the relationships between Old Testament prophecy and its fulfilment both in the life and deeds of Christ and in the events of the early Christian church.

(iv) Writings on the early Christian church

Among the vast range of textual fragments that make up Newton’s oeuvre are a series of fascinating individual chapters on the early church whose inter-relationships are as yet undetermined. One of these is an extraordinary Proemium to a multiple volume work on early church history. As an account of the rise of the monastic orders it is unique among Newton’s writings for its explicit treatment of the ascetic practices carried out by the first monks, and for those interested, it gives the best evidence of Newton’s sexual proclivities. Another stray chapter offers a detailed account of the way Athanasius (as Newton saw it) had corrupted the writings of the ante-Nicene writers in order to make the early Church Fathers more orthodox, and a lengthy essay deals with the discussions at Alexandria between the bishop of the city, Alexander, and the presbyter Arius, which gave rise to the great Arian controversies in the 320s and 30s. Newton gave vent to his dislike of the morals and machinations of Constantine, whose personal behaviour and interference in religious affairs he condemned in the harshest terms. Finally, in a much longer tract Newton brought together many of the analyses found in draft chapters elsewhere in his writings to provide a large and coherent narrative of the nature and origins of the Arian controversy.

The relationship between the hundreds of thousands of raw notes that remain in his archive, and the more polished writings on prophecy, chronology and church history will take many years to study — though this undertaking is made much easier by the fact that the writings are in digital form. There are a number of documents that contain the raw materials of Newton’s key work in these areas, including some of his notesfrom Book One, Tome 2 of Petavius’s (Petau’s) Dogmata Theologica, and a vast reservoir of excerpts (NLI Yahuda Ms. 14) from Baronius’s Annals and various editions of the Church Fathers. Another set of documents, now classified under one heading (NLI Yahuda Ms. 2.5b), is made up of a number of different notes from primary sources along with parts of longer tracts composed by Newton. Occasionally Newton’s writings either degenerate into notes or they are in fact composed of lengthy quotations from original sources, with the odd bridging sentence that indicates that the text is in fact to be classed as one of Newton’s own texts.

(v) Calendrical reform and natural theology

The Project has published a number of texts related to calendrical reform, a subject in which Newton took a keen interest when he moved to London in 1696. This was in connection with the irregularities regarding the dating of Easter created by the Julian calendar, which Protestant England and Scotland still used. Some of Newton’s ideas for making religious festivals more consistent across Christendom (allegedly twice as accurate as was possible within the Gregorian calendar) were radical for the time, but some of them were adopted when the Julian calendar was finally abandoned in 1752.

Although the scholar of Newton’s working practices is drawn to the most heavily re-worked and intractable documents, many provide much easier pickings. At the start of 2008 the Project published full diplomatic transcriptions of the short but fascinating correspondence that Newton conducted with Thomas Burnet in the winter of 1680-1. Burnet sought reassurance from the Lucasian Professor in connection with his Telluris Theoria Sacra (Sacred Theory of the Earth), the first volume of which appeared in 1681. Burnet offered a sophisticated, physical account of the creation of the cosmos, arguing that Moses had delivered a false theory of Creation that was rendered acceptable to the inferior mental and physical faculties of the vulgar. Newton responded politely but negatively, arguing that Moses’s account had been ‘accommodated’ to the vulgar but was not for that reason false. Burnet’s story, he said, was plausible but in key places he had effectively exchanged his own views in the place of what was clearly stated in Genesis. As evidence for Newton’s interest in natural theology, the Burnet correspondence should be examined alongside Newton’s exchanges with Richard Bentley in the winter of 1692-3, which the Newton Project published early on in its existence.

(vi) The notes of Barnabas Smith

Lastly, among of the highlights of the series of texts published over the last three years are writings that are not by Newton himself, but which were composed by his step-father, Barnabas Smith. Those acquainted with the history of Newton’s childhood will be aware that his mother left the home at Woolsthorpe Manor to become the wife of Smith, the rector of the local parish of North Witham. Of the ten year period during which Newton was brought up at the Manor by his maternal grandmother, he left only one direct piece of evidence. This testimony, in which he remembered wanting to burn down the house that his mother and step-father slept in, is all the more remarkable in that he recorded it almost ten years after the thought must have occurred. William Stukeley told John Conduitt that Newton inherited the 200 or 300 volumes of theological texts left by Smith at his death, but he also managed to acquire Smith’s theological notebook.

As we shall see below, Smith’s notebook became the ‘Wastebook’ in which Newton expressed many of his most important early mathematical discoveries. Smith listed a large series of theological topics alphabetically; the date of these mainly Latin entries is unknown, and they could have been made at any time in the half-century before his death in 1653. In his own theological notebook, Newton organised his theological notes in a similar form (as did most others), but he seems to have drawn nothing from his step-father’s jottings. A detailed study of these notes, and of Smith’s theological views is yet to be made, and as a result of this we may be in a better position to understand whether Smith, or Newton’s maternal uncle William Aiscough, played a larger role in Newton’s religious upbringing. In any case, it is obvious that Newton’s mature radical doctrinal commitments left him with little in common with Smith’s orthodox concerns. However, it is the jarring disjunction between the theological content of Smith’s notes and the innovative mathematical work of his step-son, with a line drawn between the two sets of entries, that is the most visually striking.

B. The Mathematical and Scientific Papers

By the end of 2007, it had become obvious that in order to make use of the full power of the digital medium, and to allow the religious materials to be understood in the contexts of Newton’s other work, the Project was obliged to incorporate into the edition the totality of his work in the exact sciences. The Newton Project accordingly made a series of bids to fund the transcription of Newton’s key writings in these areas and as a consequence, the project has published in full his key notebooks in science and mathematics, along with his subsequent enhancement of the key ideas contained within them. The significance of these texts for the history of the exact sciences cannot be overestimated. The transcribed notebooks and early writings in mechanics and mathematics contain all the documentary remains of Newton’s pioneering work on the calculus, the binomial theorem and the value for acceleration due to gravity. Newton wrote down his most important mathematical discoveries in these texts, and to some extent he made these discoveries through the acts of writing them. For the first time they are available in their entirety, with links to high quality images of the originals at CUDL. In many cases these documents have been embedded in the digital infrastructure at Cambridge that permits the side-by-side viewing of the transcription and the image.

(i) Component JISC projects

The transcription and publication of these documents has been made possible by two awards from JISC in 2009 and 2011. In ‘Enlightening Science’ the project used Enlightenment popularisations of Newton’s scientific work to convey basic principles of physics to modern day audiences. We worked with a number of schools and other institutions and pioneered the use of videos both to record interviews with historians of science and to capture the recreation of core Newtonian experiments from the eighteenth century. Directed by Iliffe, the project published a series of podcasts and a wide range of lectures and popular texts from the eighteenth century that now constitute one of the most popular parts of the site.

The second JISC project, ‘Windows on Genius’, designed and directed by Iliffe, allowed us to publish in full the texts of all of Newton’s pioneering work on the method of series and fluxions (as he named the differential and integral calculus), the binomial theorem, and the genesis of the Principia Mathematica. JISC-funded work on this project was carried out between March and December 2011, and it remains an on-going and highly successful collaboration with Cambridge University Digital library to make images of Newton’s foundational scientific and mathematical works accessible alongside searchable transcriptions of the materials. The transcriptions of Newton’s two Cambridge mathematical notebooks alone took two and a half years, and presented unprecedented encoding problems both in terms of representing the original features of Newton’s notation, and also of displaying the layout of the mathematics systematically and precisely across different browsers. About 45% of the content of each of these documents is now published for the first time, and in unprecedented detail. The availability of these documents, along with later texts that develop their ideas, allows researchers to examine all the contexts necessary for understanding the evolution of his ideas. Secondly, and for the first time, researchers can see specific arguments and projects that have previously been uprooted from their original contexts setting now replaced in their correct position within the document.

(ii) The Optical Papers

The Newton Project now offers unrivalled resources for studying Newton’s pioneering studies in the field of optics. The last of his letters on optical subjects were published in 2012-13, but it is now possible to track the development of Newton’s optical thought in its entirety. His undergraduate philosophy notebook and his subsequent essay ‘ Of Colours’ show in detail the development of his theory of light and colours, according to which white light was understood to be composed of more basic (primary) colour-making rays. Initially he discovered that individual rays each had their own specific index of refraction (or as he put it, ‘degree of refrangibility’), so that given the same angle of incidence of a ray of sunlight entering a given prism at minimum deviation, red rays would always be refracted at a specific angle, and so would yellow and purple rays. Then, in a dramatic assault on all previous theories (whether Aristotelian or ‘mechanical’), Newton argued that colour did not arise from the transformation or modification of light as it passed from one medium to another, but instead it was an original property of specific ‘colour-making’ rays. Bodies possessed the colours they did only because they were ‘disposed’ to reflect some colours and to absorb others. When primary rays were brought together again by a subtle arrangement of prisms or by introducing a lens, white light would result. This was essentially the theory of the heterogeneity of white light that Newton announced in his famous paper on light and colours of February 1672.

During what was later termed his ‘annus mirabilis’ of 1666, Newton composed an essay on refraction, which he entered into his mathematical notebook (see below). At the outset of his 1672 paper, Newton claimed that he had begun to grind non-spherical (hyperbolic, parabolic or elliptical) lenses at the start of 1666. Probably inspired by reading Hooke’s Micrographia, he had bought a triangular prism to reproduce the experiment in Descartes’s Dioptrique (Newton used the Latin edition of 1650), where the latter had reproduced the colours of the rainbow by shining a white light through a prism. In his earlier essay on refraction, his interest in improving refracting telescopes took him back to Descartes’s equally important remarks on the sine law of refraction where Descartes had announced that because of the law, spherical lenses could not bring parallel rays to an exact focus. ‘Of Refractions’ recorded Newton’s practical efforts to grind glass in non-spherical conic sections.^[12]

In the end, if we are to believe Newton in his 1672 paper, it was his discovery that primary coloured rays have intrinsically different indexes of refraction, and that there were constraints on the exactitude of images that could be produced by even the most perfectly ground non-spherical lenses, that made him end his “Glass works”. The text shows Newton’s immense self-confidence and his talent for building practical devices, a continuation of the early tendency noted by his school friends and much later, by William Stukeley. It was this proclivity, of course, along with his understanding of the limits to simple refracting telescopes caused by chromatic aberration, which would lead him to make the first working reflecting telescope some time in 1668.

In December 2013 the Project published a diplomatic transcription of an earlier version of the optical lectures that Newton delivered as his first Lucasian lectures from January 1670. Neither these, the ‘ Lectiones Opticae’, nor a later version (designated by Alan Shapiro as ‘Optica’) are the verbatim accounts of the lectures Newton gave in 1670-1 and indeed they are different versions of a longer tract that he was intending (at one stage) to publish alongside a magnificent treatise on calculus and infinite series. By giving lectures on the topic of optics, Newton was following the path laid out by Isaac Barrow, his predecessor as Lucasian Professor. The first two lectures proved that sunlight consists of rays that have different indexes of refraction, and then from lecture 3 Newton discoursed at length on the nature of colours. It was in the third lecture that Newton for the first time pleaded that mathematics should play a central role in natural philosophy — and that there could be a mathematical science of colours. Lecture 9 as having been given in July 1670) was the first of three lectures on the subject of measuring refractions, and the remainder of the lectures concerned various propositions that followed from his analysis to that point. In the ‘Optica’ (which is being transcribed by the Newton Project throughout 2014), Newton reversed the order of the sections on colour and measuring refractions.^[13]

In 2007, a substantial grant from the Royal Society enabled us to begin work on transcribing the extensive manuscript drafts of the ‘Queries’ that Newton appended to the successive editions of his Opticks, along with full transcriptions of all the printed editions of that text ( 1704, 1706 and 1717/18). The transcription and encoding of the drafts were completed in 2008 and they were published online in the same year. The published ‘Queries’ were presented by their ultra-cautious author in a tentative and hypothetical form, but there is no doubt that they, and their drafts, represent his private views on various philosophical subjects such as the nature of life, electricity, gravity, force, the mind-body problem, and the relationship between God and his creation. Whatever Newton’s views about their epistemic status, the ‘Queries’ appended to the 1717/18 edition of Opticks cast in a more acceptable language his long held views about the existence of an ‘aether’, to which he had been committed since he was a student. The topics of the ‘Queries’ show a substantial degree of continuity with earlier projects conducted within alchemy, and many of them contained results from experiments on electricity and light that were conducted under Newton’s direction while he was president of the Royal Society. Many of the claims articulated in them are impossible to reconcile with the doctrines and general approach of the Principia Mathematica, but his views on the aether would exert an immense influence on natural philosophy throughout the eighteenth century.

(iii) The ‘Mathematical Notebook’ and the ‘Waste book’

The first of two major student documents published in full for the first time, the so-called ‘ Mathematical notebook’, records Newton’s initial engagement with the works of Johannes Hudde, François Viète, René Descartes, Frans van Schooten and John Wallis. Some of these researches may have been inspired by the lectures of the first Lucasian professor, Isaac Barrow (which began in the spring of 1664), though it is more likely that Newton had guidance on what books to read from Barrow himself. In any case, the content of his first notes shows that he was quickly able to engage in independent and original research. Later accounts of his initial problematic encounter with Euclid’s Elements and then his engagement with Descartes’s Géometrie (in van Schooten’s Latin edition) and Wallis’s Arithmetica Infinitorum — based on the memorandum of Abraham de Moivre (and Newton’s own recollections) — have become famous. However, the documentary history of Newton’s early researches is now for the first time available in its entirety. The first excerpts in the notebook concern the extraction of square, cube and higher roots and are from Schooten’s 1646 edition of Viète’s Opera Mathematica. Nothing in theseearly notes indicates that their author was about to engage in one of the most fertile bursts of creativity in the history of mathematics. ^[14]

The other great research notebook published in full by the Newton Project for the first time is the ‘ Waste Book’. Originally his step-father Barnabas Smith’s theological notebook (see above), Newton recorded his earliest investigations into reflection and refraction and at some point wrote down a fascinating list of all the problems he believed remained to be determined by mathematicians of his generation. He would go on to tackle nearly all of them, mostly with great success. From the summer of 1664 Newton immersed himself in Descartes’s great mathematical work Géometrie, available to him in van Schooten’s second Latin edition. In a number of research projects beginning the winter of 1664/5 (ff. 30v-33v and 47r-50r), he examined equations for both basic and complicated curves. At the start of 1665, in research written down in the mathematical notebook (ff. 93v-116r and 120r-149r) he extended Descartes’s techniques for constructing subtangents and subnormals to curves. By the summer of 1665 he had mastered these, and could derive the tangent to any curve by assuming that two lines converged to meet at a single point on a circle whose circumference coincided with the curve in question. These researches would culminate in Newton’s expression of the fundamental algorithm for determining the tangent at any point (“An universall theorem for tangents to crooked lines”) to a wide variety of curves — what we now call the differential calculus.^[15]

Among the most important entries in the Mathematical notebook are the notes that start on fol. 15r, which record Newton’s reading of Wallis’s Arithmetica Infinitorum in the winter of 1664/5. Momentously, Newton soon developed various techniques published in Wallis’s book and discovered the generalised binomial theorem that allowed him to expand expressions of the form (a + x) m/n for negative and fractional powers. Newton later developed these foundational researches on the binomial theorem. Further notes from Arithmetica Infinitorum represent his initial confrontation with ‘the theory of indivisibles’, ‘squaring’ or ‘quadratures’, an approach to the calculation of areas under curves and volumes of that would evolve into the nascent version of what we now term the integral calculus. At about the same time, if not before, Newton began to use integral tables to solve anti-differentiation problems, in what was known as the ‘inverse problem of tangents’. Newton would be the first mathematician to understand and express the inverse relationship between the differential and integral calculus, articulating this in his great 1666 paper discussed below.^[16]

(iv) Mathematical tracts

Another collection of texts represent extensions and more polished versions of work already done in the notebooks. Newton’s justly famous mathematical tract of October 1666, is made up of a series of propositions giving procedures for resolving increasingly complex problems by motion, that is, by treating various points that mark out various curves as if the points moved with a ‘velocity’ in time through a virtual space. Newton had developed this technique while in Lincolnshire the previous Autumn (again conceivably gleaned from Barrow’s lectures), and it was as a result of this that he coined the term ‘fluxion’ (its instantaneous rate of change, or what we now call a derivative), which became the general term he used to describe his method. The approach blurred the division between mathematics and mechanics, and many early propositions in the 1666 tract deal with rotations of planes and figures, and with the location of centres of gravity. In this work Newton wrote down for the first time in a systematic way the basic rules for finding the ‘tangent’ to a curve at any point and for finding the areas of surfaces bounded by curves and the volumes of three-dimensional figures. He also expressed his finding that the methods of tangents and quadratures (differentiation and integration) were inverse operations.^[17]

Newton’s early ‘ Laws of Motion’, which date from about the same time, are unrelated to the more famous laws that formed the basis of the Principia Mathematica. They extend and attempt to formalise studies already carried out under the heading ‘ Of Reflections’ in the ‘Waste Book’ on rules concerning the impact of two bodies. As earlier, Newton was more interested in analysing the total force required to keep a body revolving around a central point. This fact betrays his underlying interest in the analysis of orbital dynamics, and shows his commitment to the view that such motion was to be analysed in terms of infinitesimally small ‘impacts’ that prevented an orbiting body from moving in a straight line along its tangent (and away from the centre of revolution). In the later work Newton generalised earlier findings that were based on various conservation principles and was the first to express the area law for central force motion (what we nowadays identify as the principle of conservation of angular momentum).

Newton first came to prominence when his paper on the analysis of equations by infinite series was circulated in the summer of 1669 to a group of London mathematicians by Barrow and the mathematical intelligencer John Collins (see below). This, Newton’s most notorious mathematical work on account of its key role in the priority dispute with Leibniz, summarised and extended the results of his work to that point and was effectively his first publication, albeit in a non-printed or ‘scribal’ form. Although its contents went unheralded at the time, probably because none of its readers could grasp the magnitude of what he had done, Newton expressed three basic ‘rules’ for integrating simple curves. Collins made a point of contacting Newton and meeting him when the latter, now enshrined as Barrow’s successor in the Lucasian chair, travelled to London in late November. Newton initially impressed Collins by showing that he had contrived infinite (converging) series for log (1 + x) as well as for a number of other curves or ‘crooked lines’. Others, most notably Nicolas Mercator, had developed series that enabled them to determine the areas under various curves by creating infinite series for various curves and integrating them term-by-term. Despite his reticence in revealing his underlying methods, or indeed any of his work at all, Newton was however, far ahead of contemporaries. De Analysi was the result of Newton’s reading of the work (passed to him via Barrow, who had received it from Collins) and his recognition that he had to write something fast in order to secure his own priority.^[18]

Newton did not accede to Collins’s requests to publish ‘De Analysi’ in print, but despite himself, he almost became a mathematical author in the early 1670s. One project would have shown that Newton was a master of modern algebra while the second would have demonstrated beyond question that he was the greatest mathematician of the modern world. The first was a result of Collins’s invitation to Newton to write an introduction to Gerard Kinckhuysen’s Algebra, which Collins had recently had translated (by Mercator) from Dutch into Latin. Despite initial confusion about his precise role in the business, Newton spent some time composing ‘Observations’ on the work, sending Collins an extensive text in July 1670. Although the level of sophistication Newton brought to his task went far beyond what he found in the object text, the project was never completed — in part because Newton was uncomfortable with features of his authorial role, and in part because he did not believe he had ‘finished’ the work. Having made a swift copy, Collins returned the work at Newton’s request, but despite revising it over the Autumn, Newton was never satisfied with the project. This did not, however, stop the high quality of his performance from becoming known to others such as John Wallis, who recommended its publication.^[19]

The second of these projects was much more substantial. Newton completed the ‘Observations’ over the winter of 1670/1 but at some point he considered that his reputation would be better served by revealing the extent of his mathematical accomplishments. In July 1671 he told Collins that on Barrow’s advice he had completely reworked or ‘methodiz’d’ ‘De Analysi’ over the previous winter, working on it continuously until being called back to family business in Lincolnshire in mid-April. Continuing to frame his object of study as a point carving out a curve by moving through a space over time, he extended and systematised his work in the 1666 tract and in ‘de Analysi’.^[20]

(v) Principia -related texts

Finally, as part of ‘Windows on Genius’, the Newton Project transcribed and published all the texts relating to the initial publication of the Principia Mathematica in 1687. Famously, Newton sent a small tract entitled ‘De motu corporum in gyrum’ to Edmond Halley some time in November 1684, three months after being prompted to do so by a visit from Halley. At the start of the year Halley had discussed orbital dynamics with Robert Hooke and Christopher Wren. All of them agreed that planets moved in regular conic sections and that the force that kept planets in orbits around the sun was inversely proportional to the square of their distance from it. The problem that Halley brought to Newton was whether and how one could demonstrate that planetary orbits arose from the inverse-square law; Newton claimed that he had such a demonstration but had been unable to give it to Halley at their meeting.^[21]

The original ‘De motu’ offered embryonic versions of the first two of what are now known as Newton’s Three Laws of Motion. Beyond this, Newton introduced the notion of ‘centripetal force’ and showed that an elliptical orbit implied an inverse-square law. He also noted that the same law implied an elliptical orbit when the velocity of the orbiting body fell between certain parameters. He extended his approach to other heavenly bodies, in that the analysis applied to the Moon, the satellites of Jupiter, and the orbits of planets around the sun. It used a combination of techniques that allowed him to investigate centrally directed force (to the focus of an ellipse) in terms of continuously exerted force away from a tangential/ inertial path. Newton made use of the Galilean law for terrestrial acceleration due to gravity, as well as Kepler’s so-called Second Law, which held that with respect to one of two foci, the areas swept out by orbiting bodies were proportional to the time taken. Although the treatise dealt in the main with motion through void spaces, a small part of it did deal with motion in resisting media. This topic would swell to take up the entire second book of the 1687 Principia.

Newton revised the tract in early 1685, and statements that had been ‘hypotheses’ now became ‘laws’. He now dealt more seriously with the conceptual basis of his physics and referred to an immense immovable space that existed as what we would call a privileged frame of reference. Having realised that the issue of whether moving objects were in a state of ‘moving’ or ‘at rest’ depended on the frame of reference, Newton’s invocation of absolute space allowed him to pick out absolute or real motion. This left his treatment consistent with the denunciation of the Cartesian account of real motion he had expressed in his ‘ De Gravitatione’ of the previous decade. Further revisions of ‘De motu’ were carried out in the spring of 1685, and Newton strove to define much more clearly key terms in his physics such as ‘inertia’, ‘force’, ‘density’, and the pairs of absolute and relative space and time. These texts contain the dynamic thought processes behind what would become the most important contribution to modern science.^[22]

Throughout the summer and autumn of 1685 Newton developed a two book treatise whose second part was entitled De motu Corporum Liber Secundus. By now Newton had realised that there had to be mutual attraction between the heavenly bodies he had analysed in earlier versions of ‘De motu’, and from this he arrived at the momentous conception that all bodies in the cosmos attracted every other body. Elements of ‘body’, which Newton would define as mass, attracted other bodies according to the product of the masses divided by the square of the distance between them (and multiplied by a constant). Now he began to use universal gravitation to explain the phenomena of tides and comets, as well as the complex issue of the motion of the moon. The ‘liber secundus’ was written in a ‘popular style’ (as Newton would later put it), but this, and the analysis of comets within it, proved unsatisfactory. After an altercation with Hooke that occurred in the summer of 1686, Newton transformed the content and presentation of the liber secundus so that the published version (Book Three) in the Principia was far less accessible, and far more technically demanding than what he had produced in the draft.^[23]