Timeline
1637 to 1665: the race begins
| Date | Event | Who | Where | Sources |
|---|---|---|---|---|
| 1637 | Descartes' La Geometrie published as an appendix to the Discours de la methode | Rene Descartes | Leiden | Source 148, O'Connor |
| 1638 | Fermat communicates his method to Descartes on receiving the Geometrie; the quarrel over maxima, minima and tangents begins | Pierre de Fermat, Rene Descartes | Paris | Source 144, O'Connor; Source 151, [attributed to Jourdain, P. E. B. - UNVERIFIED] |
| August 1638 | Roberval, Fermat and Descartes each give Mersenne a different method of drawing a tangent to the cycloid; the ensuing quarrel turns partly on the fact that a tangent as the limiting position of a secant was not yet accepted | - | Paris | Source 64, Whitman |
| 1641 | Torricelli obtains the acute hyperbolic solid: an infinitely long solid of revolution with finite volume | Evangelista Torricelli | Florence | Source 131, O'Connor; Source 157, Wijeratne |
| 25 December 1642 (Old Style, Julian, England) = 4 January 1643 (New Style, Gregorian) | Isaac Newton born, Woolsthorpe Manor, Colsterworth, Lincolnshire; posthumous child, father died c. 3 months earlier | Isaac Newton | Woolsthorpe Manor, Lincolnshire, England | Source 180, Stukeley; Source 181, Conduitt; Source 200, Westminster Abbey |
| 1 January 1642/3 (OS) = 11 January 1643 (NS) | Newton baptised at Colsterworth | Isaac Newton | Colsterworth, Lincolnshire | Source 180, Stukeley |
| 1643 | Torricelli's barometer experiment, performed by Viviani | Evangelista Torricelli | Florence | Source 131, O'Connor |
| October 1643 | Torricelli writes to Roberval on the cycloid, opening the priority quarrel | Evangelista Torricelli, Gilles Personne de Roberval | Florence/Paris | Source 131, O'Connor; Source 137, O'Connor |
| 1644 | Torricelli's Opera geometrica, containing De solido hyperbolico acuto, published | Evangelista Torricelli | Florence | Source 131, O'Connor; Source 157, Wijeratne |
| 1644 | Torricelli publishes his quadrature of the cycloid and a tangent method, the earliest printed article on the curve. Roberval writes charging plagiarism; Cajori attributes Torricelli's death in 1647 to the charge Disputed: The claim that the plagiarism charge caused Torricelli's death is Cajori's, reported by Whitman, not a medical record | - | Florence | Source 64, Whitman |
| 1 July 1646 (Gregorian) = 21 June 1646 (Julian) | Leibniz born at Leipzig, Saxony | Gottfried Wilhelm Leibniz | Leipzig | Source 235, O’Connor & Robertson; Source 236, Look |
| 1647 | Gregoire de Saint-Vincent's Opus geometricum (over 1200 folio pages) contains the hyperbolic-area property equivalent to the logarithm | Gregoire de Saint-Vincent | Antwerp | Source 141, O'Connor; Source 155, Coolidge |
| 1647 | Cavalieri's Exercitationes geometricae sex, containing Exercitatio 3, his full reply to Guldin; he dies 30 November | Bonaventura Cavalieri, Paul Guldin | Bologna | Source 156, Andersen; Source 135, O'Connor |
| 1647 | Saint-Vincent publishes the Opus geometricum, ten books in over 1,200 folio pages, containing a false claim to have squared the circle and, in Book VI on the hyperbola, the propositions that make the area under a hyperbola behave as a logarithm | - | Antwerp | Source 67, Gregorius a Sancto Vincentio |
| 1649 | Sarasa recognizes that Saint-Vincent's hyperbolic areas behave as logarithms | Alphonse Antonio de Sarasa, Gregoire de Saint-Vincent | Spanish Netherlands | Source 141, O'Connor; Source 155, Coolidge |
| 1649 | Sarasa answers a challenge problem of Mersenne's, posed partly to attack his teacher's quadrature of the circle, and in the scholium states that hyperbolic areas can be taken in place of logarithms: the first identification of the area under a hyperbola with a logarithm | - | Antwerp | Source 66, Sarasa |
| 1650 | Mengoli's Novae quadraturae arithmeticae proves the harmonic series diverges and poses the Basel problem he cannot solve | Pietro Mengoli | Bologna | Source 142, O'Connor |
| 1651 | Huygens exposes the flaw in Saint-Vincent's claimed circle quadrature at Book X Prop. 39, p. 1121 | Christiaan Huygens, Gregoire de Saint-Vincent | The Hague | Source 141, O'Connor; Source 150, O'Connor |
| 1655 | Wallis's De sectionibus conicis introduces the symbol for infinity, used as a denominator: 1/infinity is an infinitely small part | John Wallis | Oxford | Source 139, Miller; Source 145, O'Connor |
| 1655 | John Wallis introduces the lemniscate for infinity in De sectionibus conicis - and uses it first as a DENOMINATOR, each of infinitely many strips having height 1/infinity of the whole | John Wallis | Oxford | Source 451, Cajori; Source 452, Miller |
| 1656 | Wallis's Arithmetica Infinitorum gives the infinite product for pi by interpolation Disputed: MacTutor (S145) gives 1656; the 1911 Britannica (S151) and Miller (S139) allow 1655 | John Wallis | Oxford | Source 145, O'Connor; Source 151, [attributed to Jourdain, P. E. B. - UNVERIFIED]; Source 139, Miller |
| 1657 | Hudde's rule published in van Schooten's Exercitationes mathematicae; fuller treatment in the 1659 Latin Geometria of Descartes | Johann Hudde | Leiden/Amsterdam | Source 147, O'Connor |
| 1658 | Pascal's anonymous cycloid prize challenge to the mathematicians of Europe; Wallis, Huygens, Wren and Fermat respond and none wins | Blaise Pascal, John Wallis, Christiaan Huygens | Paris | Source 153, O'Connor; Source 143, [author unverified] |
| 1658 | Christopher Wren sends Pascal his rectification of the cycloid, without proof, during Pascal's contest. One arch has length exactly 8a, four times the diameter of the generating circle: a curved length equal to a straight one, with no pi in it. Wallis publishes it as Wren's the following year in Tractatus duo | - | London / Paris | Source 64, Whitman |
| 1659 | Lettres de A. Dettonville, containing the Traite des sinus du quart de cercle and the characteristic triangle | Blaise Pascal | Paris | Source 143, [author unverified] |
| 5 June 1661 (OS) = 15 June 1661 (NS) | Newton admitted to Trinity College, Cambridge, as a subsizar Disputed: Conduitt's draft memoir (Keynes Ms. 129.02, f. 1v) writes 'the 5th of Iune in 1660'. Standard scholarship gives 1661. See CN-01. | Isaac Newton | Trinity College, Cambridge | Source 181, Conduitt |
| 1663 | Leibniz takes his bachelor's degree at Leipzig aged 17 (thesis De Principio Individui); summer at Jena under Erhard Weigel | Gottfried Wilhelm Leibniz | Leipzig / Jena | Source 235, O’Connor & Robertson |