Timeline
1665 to 1687: Newton and Leibniz
| Date | Event | Who | Where | Sources |
|---|---|---|---|---|
| 23 May 1665 (OS) = 2 June 1665 (NS) | Pocket-book entry proves Newton still resident in Cambridge | Isaac Newton | Cambridge | Source 190, Whiteside |
| 8 August 1665 (OS) = 18 August 1665 (NS) | Trinity College dismissed on account of the plague | - | Trinity College, Cambridge | Source 190, Whiteside |
| January 1664/5 (OS) = January 1665 (NS) | Newton graduated B.A. | Isaac Newton | Cambridge | Source 190, Whiteside |
| June 1665 (OS) | Newton leaves Cambridge because of plague | Isaac Newton | Cambridge | Source 190, Whiteside |
| summer 1665 (OS) | Newton computes the area of the hyperbola (i.e. a logarithm) to 'two & fifty figures' at Boothby Pagnell, Lincolnshire | Isaac Newton, Humphrey Babington | Boothby Pagnell, Lincolnshire | Source 190, Whiteside; Source 199, Cambridge University Library |
| 20 March 1665/6 (OS) = 30 March 1666 (NS) | Newton travels back to Cambridge (recorded in the Fitzwilliam notebook) | Isaac Newton | Cambridge | Source 190, Whiteside |
| October 1666 (OS) | Newton dates his first systematic tract on fluxions, 'To resolve Problems by Motion' | Isaac Newton | Lincolnshire (probably) | Source 183, Newton; Source 199, Cambridge University Library |
| c.1666 | Leibniz refused the doctorate in law at Leipzig Disputed: Reason unclear. MacTutor gives two: (a) his youth plus a quota on places, so he should wait a year; (b) a story that the Dean's wife persuaded the Dean to argue against him. No primary source obtained. | Gottfried Wilhelm Leibniz | Leipzig | Source 235, O’Connor & Robertson |
| mid-June 1666 (OS) | Newton leaves Cambridge again | Isaac Newton | Cambridge | Source 190, Whiteside |
| 1667 | James Gregory's Vera circuli et hyperbolae quadratura published at Padua, using convergent infinite series | James Gregory | Padua | Source 136, O'Connor |
| 22 April 1667 (OS) = 2 May 1667 (NS) | Newton returns to Cambridge for good | Isaac Newton | Cambridge | Source 190, Whiteside |
| February 1667 | Doctorate in law at Altdorf (De Casibus Perplexis); Leibniz declines the professorship offered | Gottfried Wilhelm Leibniz | Altdorf | Source 235, O’Connor & Robertson; Source 236, Look |
| 1668 | Gregory's Geometriae pars universalis - the first systematic calculus textbook - proves that differentiation and integration are inverse operations | James Gregory | Padua/London | Source 136, O'Connor |
| 1668 | Mercator's Logarithmotechnia prints the series ln(1+x) = x - x^2/2 + x^3/3 - ... and the term logarithmus naturalis | Nicolaus Mercator | London | Source 149, O'Connor; Source 155, Coolidge |
| 1669 | Barrow resigns the Lucasian chair and Newton succeeds him | Isaac Barrow | Cambridge | Source 140, O'Connor; Source 158, Barrow |
| 31 July 1669 (OS) = 10 August 1669 (NS) | Isaac Barrow sends De analysi to John Collins in London | Isaac Newton, Isaac Barrow | Cambridge to London | Source 184, Newton |
| 1670 | Barrow's Lectiones Geometricae; Lecture X Prop. 11 states the inverse relation between tangents and areas in geometric form | Isaac Barrow | Cambridge | Source 140, O'Connor; Source 138, Nauenberg; Source 158, Barrow |
| 12 February 1669/1670 (OS) = 22 February 1670 (NS) | Collins writes to James Gregory that Newton will probably let De analysi be printed with Barrow's Lectiones geometricae; the plan comes to nothing | Isaac Newton, John Collins, James Gregory, Isaac Barrow | London | Source 204, Guicciardini |
| 24 December 1670 (OS) = 3 January 1671 (NS) | Collins tells James Gregory that the Cambridge mathematics lecturer must either print nine lectures a year or deposit them in the public library, where copies could be transcribed | John Collins, James Gregory | London | Source 204, Guicciardini |
| 15 February 1671 | Gregory's letter to John Collins contains what is now called Taylor's series, over forty years before Taylor | James Gregory | St Andrews | Source 136, O'Connor |
| 1670-1671 | Newton writes De methodus serierum et fluxionum (the 'Method of Fluxions') | Isaac Newton | Cambridge | Source 192, Whiteside; Source 185, Newton |
| 1672 | Sluse's general tangent rule published in the Philosophical Transactions Disputed: MacTutor (S146) gives 1672; the date 1673 is also widely cited but was not confirmed by any source read | Rene-Francois de Sluse | Liege/London | Source 146, O'Connor |
| 1672 | Leibniz arrives in Paris on a diplomatic mission for the Elector of Mainz; stays until October 1676 | Gottfried Wilhelm Leibniz | Paris | Source 230, Child; Source 236, Look |
| September 1672 | Huygens sets Leibniz the problem of summing the reciprocals of the triangular numbers; Leibniz solves it (sum = 2) by telescoping differences | Gottfried Wilhelm Leibniz, Christiaan Huygens | Paris | Source 237, Arthur |
| 25 May 1672 (OS) = 4 June 1672 (NS) | Newton tells Collins he will not print his optical lectures: he will not enjoy 'my former serene liberty' until he has done with the press | Isaac Newton, John Collins | Cambridge | Source 204, Guicciardini |
| 15 February 1673 | Royal Society meeting (Leibniz absent) at which Hooke criticizes the calculating machine | Gottfried Wilhelm Leibniz | London | Source 235, O’Connor & Robertson |
| 1673 | Leibniz acquires Barrow's Lectiones Geometricae in London; annotations suggest he read it 1674-1676 | Isaac Barrow | London | Source 138, Nauenberg |
| 1673 | Huygens's Horologium oscillatorium proves the cycloid tautochronous and introduces evolutes and involutes | Christiaan Huygens | Paris | Source 150, O'Connor |
| 9 April 1673 (Old Style) | Leibniz elected Fellow of the Royal Society Disputed: MacTutor gives 9 April 1673; 19 April 1673 is also widely printed. Royal Society register not consulted. | Gottfried Wilhelm Leibniz | London | Source 235, O’Connor & Robertson |
| January-February 1673 | First London visit: Leibniz demonstrates a model of his stepped-reckoner calculating machine at the Royal Society; meets Boyle, Hooke, Pell, Oldenburg | Gottfried Wilhelm Leibniz, Henry Oldenburg | London | Source 230, Child; Source 235, O’Connor & Robertson |
| 1674 | Newton gives John Flamsteed a set of notes on algebra, one of the earliest documented loans of a Newton mathematical manuscript outside the Cambridge circle | Isaac Newton, John Flamsteed | England | Source 204, Guicciardini |
| 11 November 1675 | Leibniz moves d from denominator to multiplier: "Idem est dx et x/d". dx, dy and the quotient dx/dy all date from this manuscript | Gottfried Wilhelm Leibniz | Paris | Source 451, Cajori; Source 452, Miller |
| 11 November 1675 (Gregorian; = 1 November Julian) | Manuscript Methodi tangentium inversae exempla: dx takes its modern position (multiplier, not divisor); Leibniz asserts d(xy)=dx.dy and d(x/y)=dx/dy, then refutes both later in the same paper | Gottfried Wilhelm Leibniz | Paris | Source 230, Child; Source 238, Miller |
| 21 November 1675 | Leibniz derives the product rule analytically, and records that "nothing new can be deduced from it, because we had already obtained it" | Gottfried Wilhelm Leibniz | Paris | Source 230, Child |
| 26 October 1675 | Leibniz, still writing omn. for "all the", produces a formula so tangled with nested sums that a new notation becomes unavoidable | Gottfried Wilhelm Leibniz | Paris | Source 451, Cajori |
| 29 October 1675 | Leibniz first writes the integral sign, an elongated S for summa, replacing Cavalieri's word omnia | - | Paris | Source 139, Miller |
| 29 October 1675 | Leibniz invents the integral sign: "Utile erit scribi [long s] pro omn." - three days after the formula that forced his hand | Gottfried Wilhelm Leibniz | Paris | Source 451, Cajori; Source 452, Miller |
| 29 October 1675 (Gregorian; = 19 October Julian) | Leibniz writes the integral sign for the first time, in the manuscript Analyseos tetragonisticae pars secunda: "It will be useful to write [integral sign] for omn." On the same sheet d appears, but as a divisor (l = ya/d) | Gottfried Wilhelm Leibniz | Paris | Source 230, Child; Source 238, Miller |
| 29 June 1675 (OS) = 9 July 1675 (NS) | Collins reports to James Gregory that 'Mr Newton intends not to publish anything' and will only deposit his lectures in the public library | Isaac Newton, John Collins, James Gregory | London | Source 204, Guicciardini |
| 19 October 1675 (OS) = 29 October 1675 (NS) | Collins tells James Gregory that Newton and Barrow are beginning to think mathematical speculations 'nice and dry, if not somewhat barren' | Isaac Newton, John Collins, James Gregory, Isaac Barrow | London | Source 204, Guicciardini |
| 13 June 1676 (Julian) = 23 June 1676 (Gregorian) | Newton's epistola prior written for Leibniz and sent through Oldenburg | Gottfried Wilhelm Leibniz, Henry Oldenburg | Cambridge / London | Source 280, [Newton]; Source 281, Newton |
| 13 June 1676 (OS) = 23 June 1676 (NS) | Newton's Epistola prior to Oldenburg, for transmission to Leibniz | Isaac Newton | Cambridge | Source 188, Newton |
| 18/28 November 1676 | Leibniz writes to Oldenburg from Amsterdam that Slusius's tangent method "is not yet at its summit", his first reference to the tangent problem in that correspondence | Gottfried Wilhelm Leibniz, Henry Oldenburg | Amsterdam | Source 230, Child |
| 24 October 1676 (Julian) = 3 November 1676 (Gregorian) | Newton's epistola posterior, containing the two anagrams concealing his method | Gottfried Wilhelm Leibniz, Henry Oldenburg | Cambridge / London | Source 280, [Newton]; Source 281, Newton; Source 285, Dhombres |
| 24 October 1676 (OS) = 3 November 1676 (NS) | Newton's Epistola posterior to Oldenburg: the binomial series by interpolation from Wallis, and the fluxions anagram | Isaac Newton, Henry Oldenburg | Cambridge | Source 188, Newton |
| 5 February 1675/6 (OS) = 15 February 1676 (NS) | Newton to Hooke: 'If I have seen further it is by standing on the sholders of Giants' Disputed: Frequently mis-dated to 1675 because of the English civil year. Full text not yet verified by this agent (see S197). | Isaac Newton, Robert Hooke | Cambridge to London | Source 197, Newton |
| December 1676 | Leibniz enters the service of Duke Johann Friedrich of Brunswick-Luneburg at Hanover as librarian and Court Councillor | Gottfried Wilhelm Leibniz | Hanover | Source 235, O’Connor & Robertson; Source 236, Look |
| October 1676 | Second London visit, about one week: Leibniz reads Collins's papers and makes extracts headed "Excerpta ex tractatu Newtoni de Analysi per aequationes numero terminorum infinitas". He copies the series and equation-solving material, not the tangent/quadrature material | Gottfried Wilhelm Leibniz, John Collins | London | Source 230, Child |
| 5 September 1676 (OS) = 15 September 1676 (NS) | Newton tells Collins that the discourse on infinite equations he wrote about five years earlier has never been read out and he keeps it by him | Isaac Newton, John Collins | Cambridge | Source 204, Guicciardini |
| 26 October 1676 (OS) = 5 November 1676 (NS) | Newton instructs Oldenburg: 'Pray let none of my mathematical papers be printed wthout my special licence' | Isaac Newton, Henry Oldenburg | Cambridge | Source 204, Guicciardini |
| 21 June 1677 | Leibniz's reply to Newton, the first appearance of dy in the correspondence with the English | Gottfried Wilhelm Leibniz | Hanover | Source 280, [Newton] |
| 1677 | Collins makes a second transcript of De analysi and sends it to John Wallis; after Wallis's death it passes to David Gregory | John Collins, John Wallis, David Gregory | England | Source 204, Guicciardini |
| from 1678 | Leibniz begins the Harz mountains project to drain the silver mines with windmills; the schemes run for years and all fail | Gottfried Wilhelm Leibniz | Harz mountains | Source 235, O’Connor & Robertson |
| 24 November 1679 (OS) = 4 December 1679 (NS) | Hooke writes to Newton proposing the compounding of tangential motion with a central attraction | Robert Hooke, Isaac Newton | London to Cambridge | Source 203, Chin |
| c. 1680 | Newton reworks the synthetic addendum to De methodis as Geometria curvilinea, the geometric version of the fluxional calculus later used in the Principia Disputed: Guicciardini hedges: he dates the Geometria curvilinea 'c. 1680' and places the synthetic addendum 'just after completing the De methodis' (1671), giving no year for either | Isaac Newton | Cambridge | Source 204, Guicciardini |
| 1683 | Seki Takakazu is the first to study determinants - ten years before Leibniz, and in a more general form | Seki Takakazu | Edo, Japan | Source 429, OConnor and Robertson |
| October 1684 | Nova methodus pro maximis et minimis published in Acta Eruditorum, pp. 467-473; the first publication of the calculus. Signed only "per G.G.L."; no proofs; contains printer's errors including concavity/convexity interchanged | Gottfried Wilhelm Leibniz, Otto Mencke | Leipzig | Source 231, Leibniz; Source 232, Leibniz (trans. Walker) |
| 1684 | Newton's Lucasian lectures on algebra are deposited in the Cambridge University Library and become public in principle; they are printed in 1707 as Arithmetica universalis | Isaac Newton | Cambridge | Source 204, Guicciardini |
| 9 June 1684 (OS) = 19 June 1684 (NS) | David Gregory sends Newton his Exercitatio geometrica de dimensione figurarum, which contains series quadrature theorems already in De analysi and which Gregory credits to his uncle James's papers | David Gregory, Isaac Newton, James Gregory | Edinburgh to Cambridge | Source 204, Guicciardini |
| 1684 or 1685 | John Craig visits Newton at Cambridge and is allowed to transcribe part of De methodis and of the Epistola posterior to Leibniz Disputed: Guicciardini dates this visit 1684 at pp. 460 and 462 and 1685 at p. 465, in the same article. The 1685 passage carries the fuller account (Wallis's 1683 Proposal, Craig's letter, the meeting, the report to Pitcairne and David Gregory); the 1684 statement cites Whiteside, Mathematical Papers vol. 7, pp. 3-4 | John Craig, Isaac Newton | Cambridge | Source 204, Guicciardini |
| 1685 | Newton communicates his 'prime theorem' on quadratures to John Craig; excerpts from his letters and manuscripts appear in print in Wallis's Treatise of Algebra | Isaac Newton, John Craig, John Wallis | England | Source 204, Guicciardini |
| 1686 | The integral sign reaches print (Acta eruditorum, pp. 297, 299) with its descender cut off, looking like a small s | Gottfried Wilhelm Leibniz | Leipzig | Source 451, Cajori |
| 20 June 1686 (OS) = 30 June 1686 (NS) | Newton writes to Halley about Hooke's claim to the inverse-square law; threatens to suppress Book III of the Principia | Isaac Newton, Edmond Halley, Robert Hooke | Cambridge to London | Source 203, Chin |
| June 1686 | De geometria recondita et analysi indivisibilium atque infinitorum, Acta Eruditorum p. 292 onward; the first appearance of the integral sign in print | Gottfried Wilhelm Leibniz | Leipzig | Source 233, Leibniz; Source 232, Leibniz (trans. Walker) |
| July 1687 | Philosophiae Naturalis Principia Mathematica published, London Disputed: Precise publication day not verified by this agent; Halley paid for the printing. Imprimatur dated 5 July 1686. | Isaac Newton, Edmond Halley | London | Source 186, Newton; Source 191, Whiteside |
| November 1687 - June 1690 | Leibniz's archive journey through Bavaria, Austria and Italy researching the history of the House of Brunswick | Gottfried Wilhelm Leibniz | Central Europe / Italy | Source 235, O’Connor & Robertson |