The History of Calculus Who found it, who fought over it, and why your notation looks the way it does

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1734 to 1799: attack, repair, and the Enlightenment

1734 to 1799: attack, repair, and the Enlightenment. 33 entries. A date in the disputed style carries a note saying who disagrees.
Date Event Who Where Sources
1734 B​‌‍‌‌‍‍‌‍‌‍‍‌‌‍‌‍‌‍‍‌‌‍‍‍‌‍‍‌‌‌‌‍‌‍‍‌‍‍‍‌‌‌‍‌‌‌‌‌‌‍‌‍‌‍‍‍‌‍‍‌‌‌‌‍‌‍‍‍‌‌‍‌‌‍‍‍‌‌‍‌‌‍‍‌‌‍‌‍‌‍‍‌‍‍‍‌‌‌‍‌‌‌‌‌‌‌‍‌‍‌‌‌‌‍‍‌‌‌‍‍‌‌‍‌‍‌‌‍‌‌‍‌‌‌‌‌‌‌‍‍‌‌‍‌‌‌‍‍‌‌‌‌‌‌‍‍‌‌‍‌‌‌‍‍‌‍‍‌‌‌‍‌‌‌‌‌‌‌‍‌‍‍‌‍‌‌‍‌‌‌‌‌‌‍‌‍‌‍‌‌‌‍‍‌‍‌‌‌‌‍‍‌‌‍‌‍‌‌‍‌‌‌‌‌‌‍‌‌‍‌‌‌‌‍‍‌‍‌‌‍‌‍‍‍‌‌‍‍‌‍‍‍‌‍‌‌‌‍‍‌‍‍‍‍‌‍‍‍‌‌‍‌‌‍‍‍‍‌‌‍‌‌‍‌‌‌‌‌‌‍‍‌‍‍‍‍‌‍‍‌‌‍‍‌‌‌‍‌‌‌‌‌‌‍‌‌‌‌‍‍‌‍‍‌‌‌‌‍‌‍‍‌‍‍‌‌‌‍‍‌‌‌‍‍‌‍‍‍‌‍‌‍‌‍‍‌‍‍‌‌‌‍‍‍‌‍‌‍‌‍‍‍‌‌‍‍‌‌‍‌‌‌‌‌‌‌‍‌‍‍‌‍‌‌‍‌‌‌‌‌‌‍‍‌‍‍‍‍‌‍‍‍‌‌‍‌‌‍‍‌‍‌‌‍‌‍‍‌‌‍‍‍‌‍‍‌‍‌‌‍‌‍‍‌‍‍‍‌‌‍‍‌‌‌‌‍‌‍‍‌‍‍‌‌‌‌‍‌‌‌‌‌‌‍‍‌‌‌‍‍‌‍‍‌‍‍‍‍‌‍‍‍‌‍‌‍‌‍‍‍‌‌‍‌‌‍‍‍‌‌‍‍‌‍‍‌‌‍‌‍‌‌‍‌‌‌‌‌‌‍‍‌‌‌‍‍‌‍‍‌‍‍‍‍‌‍‍‌‍‍‍‌‌‍‍‍‌‍‌‌‌‍‍‌‌‍‌‍‌‍‍‌‍‍‍‌‌‍‍‍‌‍‌‌​erkeley publishes The Analyst; or A Discourse Addressed to an Infidel Mathematician, in London and Dublin, in two non-identical texts George Berkeley London and Dublin Source 310, Berkeley
1734 Jurin replies as 'Philalethes Cantabrigiensis' with Geometry No Friend to Infidelity; Robins, Walton, Pemberton, Bayes and others join in over the following decade James Jurin, Benjamin Robins London Source 310, Berkeley; Source 311, Maclaurin
1735 Euler presents his solution of the Basel problem to the St Petersburg Academy: 1 + 1/4 + 1/9 + ... = pi^2/6. He is 28. Published as E41 in 1740 Leonhard Euler St Petersburg Source 322, Monks; Source 323, Bogart
1736 The Method of Fluxions and Infinite Series published in English, trans. John Colson Isaac Newton, John Colson London Source 185, Newton; Source 192, Whiteside
1738 Du Chatelet submits her essay on the nature and propagation of fire to the Academie royale des sciences prize competition anonymously, because a submission known to be by a woman would not have been taken seriously. It does not win, and the Academie publishes it anyway - Paris Source 69, Allen
April/May 1738 Daniel Bernoulli's Hydrodynamica appears in print at Strasbourg; in October his father first mentions a rival Hydraulica to Euler Daniel Bernoulli, Johann Bernoulli Strasbourg / Basel Source 333, Tou
1740 Emilie du Chatelet publishes Institutions de physique anonymously in Paris; the 1742 Amsterdam edition carries her name Emilie du Chatelet Paris Source 332, Project Vox
1740 Simpson publishes the iteration x_{n+1} = x_n - f(x_n)/f (x_n) - the form in which "Newtons method" is taught Thomas Simpson London Source 462, OConnor and Robertson
1740 Institutions de physique published anonymously, its frontispiece carrying portraits of Newton, Descartes and Leibniz; its last chapter openly attacks Mairan's 1728 memoire on forces vives - Paris Source 68, Zinsser; Source 69, Allen
1742 Maclaurin publishes A Treatise of Fluxions, 2 vols., Edinburgh; the Preface states that Berkeley's Analyst 'first gave Occasion to the ensuing Treatise' Colin Maclaurin, George Berkeley Edinburgh Source 311, Maclaurin
1744 E​‌‍‌‌‍‍‌‍‌‍‍‌‌‍‌‍‌‍‍‌‌‍‍‍‌‍‍‌‌‌‌‍‌‍‍‌‍‍‍‌‌‌‍‌‌‌‌‌‌‍‌‍‌‍‍‍‌‍‍‌‌‌‌‍‌‍‍‍‌‌‍‌‌‍‍‍‌‌‍‌‌‍‍‌‌‍‌‍‌‍‍‌‍‍‍‌‌‌‍‌‌‌‌‌‌‌‍‌‍‌‌‌‌‍‍‌‌‌‍‍‌‌‍‌‍‌‌‍‌‌‍‌‌‌‌‌‌‌‍‍‌‌‍‌‌‌‍‍‌‌‌‌‌‌‍‍‌‌‍‌‌‌‍‍‌‍‍‌‌‌‍‌‌‌‌‌‌‌‍‌‍‍‌‍‌‌‍‌‌‌‌‌‌‍‌‍‌‍‌‌‌‍‍‌‍‌‌‌‌‍‍‌‌‍‌‍‌‌‍‌‌‌‌‌‌‍‌‌‍‌‌‌‌‍‍‌‍‌‌‍‌‍‍‍‌‌‍‍‌‍‍‍‌‍‌‌‌‍‍‌‍‍‍‍‌‍‍‍‌‌‍‌‌‍‍‍‍‌‌‍‌‌‍‌‌‌‌‌‌‍‍‌‍‍‍‍‌‍‍‌‌‍‍‌‌‌‍‌‌‌‌‌‌‍‌‌‌‌‍‍‌‍‍‌‌‌‌‍‌‍‍‌‍‍‌‌‌‍‍‌‌‌‍‍‌‍‍‍‌‍‌‍‌‍‍‌‍‍‌‌‌‍‍‍‌‍‌‍‌‍‍‍‌‌‍‍‌‌‍‌‌‌‌‌‌‌‍‌‍‍‌‍‌‌‍‌‌‌‌‌‌‍‍‌‍‍‍‍‌‍‍‍‌‌‍‌‌‍‍‌‍‌‌‍‌‍‍‌‌‍‍‍‌‍‍‌‍‌‌‍‌‍‍‌‍‍‍‌‌‍‍‌‌‌‌‍‌‍‍‌‍‍‌‌‌‌‍‌‌‌‌‌‌‍‍‌‌‌‍‍‌‍‍‌‍‍‍‍‌‍‍‍‌‍‌‍‌‍‍‍‌‌‍‌‌‍‍‍‌‌‍‍‌‍‍‌‌‍‌‍‌‌‍‌‌‌‌‌‌‍‍‌‌‌‍‍‌‍‍‌‍‍‍‍‌‍‍‌‍‍‍‌‌‍‍‍‌‍‌‌‌‍‍‌‌‍‌‍‌‍‍‌‍‍‍‌‌‍‍‍‌‍‌‌​uler publishes Methodus inveniendi (E65), founding the calculus of variations and giving the first statement of the principle of least action Leonhard Euler Lausanne and Geneva Source 323, Bogart
1748 Euler publishes Introductio in analysin infinitorum (E101): analysis becomes the study of functions. S.126 adopts pi; S.138 gives e^(v sqrt(-1)) = cos v + sqrt(-1) sin v Leonhard Euler Lausanne Source 318, Euler; Source 325, Miller
1748 Agnesi publishes Instituzioni analitiche ad uso della gioventu italiana in Milan: the first surviving mathematics book by a woman and the first textbook to cover differential and integral calculus together Maria Gaetana Agnesi Milan Source 319, Agnesi; Source 327, O'Connor
10 September 1749 Emilie du Chatelet dies at Luneville, six days after childbirth, having raced to finish her Principia translation Emilie du Chatelet Luneville, Lorraine Source 332, Project Vox
26 September 1750 Pope Benedict XIV writes to Agnesi offering her the chair of mathematics at Bologna; she accepts the honor and, on Truesdell's account, never goes Maria Gaetana Agnesi Rome / Bologna Source 327, O'Connor; Source 340, Truesdell
1755 Euler's Institutiones calculi differentialis (E212) published at St Petersburg; written in 1748 Leonhard Euler St Petersburg Source 323, Bogart
1755 Euler introduces Delta for difference and Sigma for sum in one book, explicitly as a matched pair Leonhard Euler St Petersburg Source 451, Cajori
1759 Du Chatelet's complete French Principia, with her Exposition abregee du systeme du monde, published in Paris, arranged by Clairaut - ten years after her death, and still the only complete French translation Emilie du Chatelet, Alexis-Claude Clairaut Paris Source 332, Project Vox
1759 Du Chatelet's translation and commentary on the Principia appears, ten years after her death, because Clairaut pressed the publisher Prault to bring it out and arranged for the illustrations to be finished - Paris Source 68, Zinsser
c. 1760 John Colson, translating Agnesi into English, renders la versiera as 'the Witch'; published posthumously in 1801 John Colson, Maria Gaetana Agnesi Cambridge Source 320, Agnesi; Source 319, Agnesi
1766 E​‌‍‌‌‍‍‌‍‌‍‍‌‌‍‌‍‌‍‍‌‌‍‍‍‌‍‍‌‌‌‌‍‌‍‍‌‍‍‍‌‌‌‍‌‌‌‌‌‌‍‌‍‌‍‍‍‌‍‍‌‌‌‌‍‌‍‍‍‌‌‍‌‌‍‍‍‌‌‍‌‌‍‍‌‌‍‌‍‌‍‍‌‍‍‍‌‌‌‍‌‌‌‌‌‌‌‍‌‍‌‌‌‌‍‍‌‌‌‍‍‌‌‍‌‍‌‌‍‌‌‍‌‌‌‌‌‌‌‍‍‌‌‍‌‌‌‍‍‌‌‌‌‌‌‍‍‌‌‍‌‌‌‍‍‌‍‍‌‌‌‍‌‌‌‌‌‌‌‍‌‍‍‌‍‌‌‍‌‌‌‌‌‌‍‌‍‌‍‌‌‌‍‍‌‍‌‌‌‌‍‍‌‌‍‌‍‌‌‍‌‌‌‌‌‌‍‌‌‍‌‌‌‌‍‍‌‍‌‌‍‌‍‍‍‌‌‍‍‌‍‍‍‌‍‌‌‌‍‍‌‍‍‍‍‌‍‍‍‌‌‍‌‌‍‍‍‍‌‌‍‌‌‍‌‌‌‌‌‌‍‍‌‍‍‍‍‌‍‍‌‌‍‍‌‌‌‍‌‌‌‌‌‌‍‌‌‌‌‍‍‌‍‍‌‌‌‌‍‌‍‍‌‍‍‌‌‌‍‍‌‌‌‍‍‌‍‍‍‌‍‌‍‌‍‍‌‍‍‌‌‌‍‍‍‌‍‌‍‌‍‍‍‌‌‍‍‌‌‍‌‌‌‌‌‌‌‍‌‍‍‌‍‌‌‍‌‌‌‌‌‌‍‍‌‍‍‍‍‌‍‍‍‌‌‍‌‌‍‍‌‍‌‌‍‌‍‍‌‌‍‍‍‌‍‍‌‍‌‌‍‌‍‍‌‍‍‍‌‌‍‍‌‌‌‌‍‌‍‍‌‍‍‌‌‌‌‍‌‌‌‌‌‌‍‍‌‌‌‍‍‌‍‍‌‍‍‍‍‌‍‍‍‌‍‌‍‌‍‍‍‌‌‍‌‌‍‍‍‌‌‍‍‌‍‍‌‌‍‌‍‌‌‍‌‌‌‌‌‌‍‍‌‌‌‍‍‌‍‍‌‍‍‍‍‌‍‍‌‍‍‍‌‌‍‍‍‌‍‌‌‌‍‍‌‌‍‌‍‌‍‍‌‍‍‍‌‌‍‍‍‌‍‌‌​uler returns to St Petersburg at Catherine II's invitation, aged 59; he goes on to produce almost half his life's output there, most of it after losing his sight Leonhard Euler, Frederick II of Prussia Berlin to St Petersburg Source 326, O'Connor
1768-1770 Euler's Institutiones calculi integralis published in three volumes at St Petersburg Leonhard Euler St Petersburg Source 323, Bogart
1770 Condorcet first uses the 'curly d' partial-derivative symbol; Legendre gives it its modern form in 1786 Nicolas de Condorcet, Adrien-Marie Legendre Paris Source 325, Miller
1771 Euler undergoes cataract surgery; sight is briefly restored, then lost entirely. He dictates for the remaining twelve years and his output increases Disputed: MacTutor records Calinger's view that the standard chronology of Euler's sight loss (1738 strain, 1740 one eye) is unreliable Leonhard Euler St Petersburg Source 326, O'Connor
1772 Lagrange uses 'fonction derivee' in the Nouveaux Memoires of the Berlin Academy - the origin of the English word 'derivative' Joseph-Louis Lagrange Berlin Source 324, Miller
1773-1774 Diderot visits St Petersburg at Catherine II's invitation; the alleged confrontation with Euler is placed here by the anecdote and is unsupported by any Russian source Disputed: Thiebault, the only source, does not name Euler and declines to vouch for the story Denis Diderot, Leonhard Euler St Petersburg Source 313, Brown; Source 314, Gillings; Source 339, Thiebault
5 May 1777 Euler presents 'De formulis differentialibus angularibus', introducing the letter i for sqrt(-1); published only in 1794 Leonhard Euler St Petersburg Source 325, Miller
1779-1785 Samuel Horsley uses both the Jones and the Wilson transcripts for his edition of Newton's Opera omnia Samuel Horsley, William Jones, James Wilson London Source 204, Guicciardini
1786 Legendre publishes the modern partial-derivative symbol - and abandons it the following year Adrien-Marie Legendre Paris Source 451, Cajori; Source 452, Miller
1786 Simon LHuilier writes "lim." for the first time, in the essay that won the Berlin Academy prize on the nature of infinity Simon LHuilier Berlin/Geneva Source 451, Cajori; Source 452, Miller
c. 1795 S​‌‍‌‌‍‍‌‍‌‍‍‌‌‍‌‍‌‍‍‌‌‍‍‍‌‍‍‌‌‌‌‍‌‍‍‌‍‍‍‌‌‌‍‌‌‌‌‌‌‍‌‍‌‍‍‍‌‍‍‌‌‌‌‍‌‍‍‍‌‌‍‌‌‍‍‍‌‌‍‌‌‍‍‌‌‍‌‍‌‍‍‌‍‍‍‌‌‌‍‌‌‌‌‌‌‌‍‌‍‌‌‌‌‍‍‌‌‌‍‍‌‌‍‌‍‌‌‍‌‌‍‌‌‌‌‌‌‌‍‍‌‌‍‌‌‌‍‍‌‌‌‌‌‌‍‍‌‌‍‌‌‌‍‍‌‍‍‌‌‌‍‌‌‌‌‌‌‌‍‌‍‍‌‍‌‌‍‌‌‌‌‌‌‍‌‍‌‍‌‌‌‍‍‌‍‌‌‌‌‍‍‌‌‍‌‍‌‌‍‌‌‌‌‌‌‍‌‌‍‌‌‌‌‍‍‌‍‌‌‍‌‍‍‍‌‌‍‍‌‍‍‍‌‍‌‌‌‍‍‌‍‍‍‍‌‍‍‍‌‌‍‌‌‍‍‍‍‌‌‍‌‌‍‌‌‌‌‌‌‍‍‌‍‍‍‍‌‍‍‌‌‍‍‌‌‌‍‌‌‌‌‌‌‍‌‌‌‌‍‍‌‍‍‌‌‌‌‍‌‍‍‌‍‍‌‌‌‍‍‌‌‌‍‍‌‍‍‍‌‍‌‍‌‍‍‌‍‍‌‌‌‍‍‍‌‍‌‍‌‍‍‍‌‌‍‍‌‌‍‌‌‌‌‌‌‌‍‌‍‍‌‍‌‌‍‌‌‌‌‌‌‍‍‌‍‍‍‍‌‍‍‍‌‌‍‌‌‍‍‌‍‌‌‍‌‍‍‌‌‍‍‍‌‍‍‌‍‌‌‍‌‍‍‌‍‍‍‌‌‍‍‌‌‌‌‍‌‍‍‌‍‍‌‌‌‌‍‌‌‌‌‌‌‍‍‌‌‌‍‍‌‍‍‌‍‍‍‍‌‍‍‍‌‍‌‍‌‍‍‍‌‌‍‌‌‍‍‍‌‌‍‍‌‍‍‌‌‍‌‍‌‌‍‌‌‌‌‌‌‍‍‌‌‌‍‍‌‍‍‌‍‍‍‍‌‍‍‌‍‍‍‌‌‍‍‍‌‍‌‌‌‍‍‌‌‍‌‍‌‍‍‌‍‍‍‌‌‍‍‍‌‍‌‌​ophie Germain submits observations on Lagrange's Ecole Polytechnique analysis course under the name of a real former student, M LeBlanc Sophie Germain Paris Source 410, OConnor and Robertson
1797 Lagrange publishes Theorie des fonctions analytiques, founding the calculus on power series 'freed from every consideration of infinitely small or vanishing quantities, of limits or of fluxions', and introducing f'x, f''x and the primitive/derived pair Joseph-Louis Lagrange Paris Source 317, Lagrange; Source 325, Miller
1797 Lagrange introduces f prime and f double prime, "pour plus de simplicite et duniformite" Joseph-Louis Lagrange Paris Source 451, Cajori; Source 317, Lagrange