Timeline
1800 to 1872: the age of rigor
| Date | Event | Who | Where | Sources |
|---|---|---|---|---|
| 1800 | Arbogast introduces D for derivation and D^-1 for its inverse | Louis Arbogast | Strasbourg | Source 451, Cajori; Source 452, Miller |
| 1806 | Ampere publishes an attempted justification that continuous functions are differentiable except at isolated points - the 'theorem' Weierstrass would refute | - | Paris | Source 386, Johansson |
| 1806 | Fearing Gauss would die as Archimedes did during the French occupation of Braunschweig, Germain sends a family-friend general to protect him, and is forced to reveal that she is LeBlanc | Sophie Germain | Braunschweig and Paris | Source 410, OConnor and Robertson |
| 21 December 1807 | Fourier presents 'On the Propagation of Heat in Solid Bodies' to the Paris Institute; referees Lagrange, Laplace, Monge, Lacroix | Fourier | Paris | Source 383, O'Connor |
| 1811 | Fourier wins the Institute prize, with a citation saying the work 'still leaves something to be desired on the score of generality and even rigour' | Fourier | Paris | Source 383, O'Connor |
| 1812 | Babbage, Herschel, Peacock and others found the Analytical Society at Cambridge to replace Newton's dot notation with Leibniz's d | Charles Babbage, John Herschel, George Peacock | Cambridge | Source 239, Babbage |
| 1813 | Memoirs of the Analytical Society published (Cambridge, 4to), written entirely by Herschel and Babbage. Babbage had suggested the title "The Principles of pure D-ism in opposition to the Dot-age of the University"; it was not used | Charles Babbage, John Herschel | Cambridge | Source 239, Babbage |
| 1815 | Germain wins the Institut de France prize for elastic surfaces - a medal of one kilogram of gold - at the third attempt; she does not attend the ceremony Disputed: Very widely printed as 1816. MacTutor says the re-opened contest of 1815. See conflict C-U410 | Sophie Germain | Paris | Source 410, OConnor and Robertson |
| 1817 | Bolzano publishes Rein analytischer Beweis: arithmetic definition of continuity, proof of the intermediate value theorem, the convergence criterion later named after Cauchy | Bolzano | Prague | Source 363, Bolzano; Source 371, O'Connor; Source 387, Ruch; Source 360, Grabiner |
| December 1819 | Bolzano suspended from his chair after Austrian government pressure; house arrest, mail censorship and a publication ban follow Disputed: MacTutor (S371) dates the suspension to December 1819; the Stanford Encyclopedia (S370) says Emperor Franz removed him from the professorship in January 1820. Probable resolution: suspended Dec 1819, formally removed Jan 1820. | Bolzano | Prague | Source 371, O'Connor; Source 370, Morscher |
| 1821 | Cauchy publishes the Cours d'analyse: verbal definitions of limit, infinitesimal, continuity and convergent series, plus the false Theorem I on sums of continuous functions (pp. 131-132) | Cauchy | Paris | Source 361, Cauchy; Source 360, Grabiner |
| 1822 | Fourier publishes Theorie analytique de la chaleur, whose claim about arbitrary functions breaks the existing concept of 'function' | Fourier | Paris | Source 383, O'Connor |
| 1822 | Fourier prints the limits of integration on the integral sign | Fourier | Paris | Source 451, Cajori; Source 452, Miller |
| 1823 | Cauchy publishes the Resume: the definite integral defined as a limit of sums and its existence proved; the preface states his aim of reconciling rigor with 'the direct consideration of infinitely small quantities' | Cauchy | Paris | Source 362, Cauchy |
| 1823 | Sarrus introduces the evaluation bar with limits attached | Pierre Frederic Sarrus | Strasbourg | Source 451, Cajori; Source 452, Miller |
| 16 January 1826 | Abel writes to Holmboe from Berlin that divergent series are 'noget Fandensskab' (a piece of devilry) and that it is a shame to base any demonstration on them; the 1902 French translation renders this 'une invention du diable', which is where the English 'invention of the devil' comes from Disputed: The 1902 editors note the letter is clearly dated 16 January 1826 'mais est certainement du 14' - Abel says he will see Die schoene Muellerin 'tomorrow', while letter VII of the same nominal date says he saw it 'yesterday'; the date was probably added when the letter was sent | Abel | Berlin | Source 490, Abel |
| 1826 | Abel publishes his binomial-series memoir with the footnote counterexample to Cauchy's Cours d'analyse p. 131 | Abel, Cauchy | Berlin (Crelle's Journal) | Source 364, Abel |
| 27 March 1827 | Lord Brougham writes to Dr Somerville asking that Mrs Somerville write up Laplace's Mecanique Celeste for the Society for the Diffusion of Useful Knowledge | Mary Somerville | London | Source 412, Somerville |
| 25 May and 1 June 1829 | Galois submits articles on the algebraic solution of equations to the Academy; Cauchy is assigned as referee | Galois, Cauchy | Paris | Source 380, O'Connor |
| 29 June 1829 | Cauchy finally reports on Abel's 1826 memoir; the report is described as hasty, nasty and superficial | Cauchy, Abel | Paris | Source 372, O'Connor |
| 6 April 1829 | Abel dies aged 26; Cauchy has still not reported on the memoir Abel submitted in 1826 | Abel, Cauchy | Froland, Norway | Source 372, O'Connor |
| February 1830 | Galois submits his Grand Prize memoir to Fourier; Fourier dies in April 1830 and the manuscript is never found | Galois, Fourier | Paris | Source 380, O'Connor |
| September 1830 | Cauchy leaves Paris after the July Revolution; he will not swear the oath of allegiance and loses all his positions | Cauchy | Paris to Switzerland | Source 372, O'Connor |
| around 1830 | Bolzano writes the Functionenlehre, containing a continuous nowhere-differentiable function built by a geometric construction Disputed: S386 dates the manuscript 1830; MacTutor (S384) says 'before 1834'. | Bolzano | Prague | Source 386, Johansson; Source 384, O'Connor |
| 1831 | Brewster's Life of Sir Isaac Newton (p. 194) puts the Latin 'tanquam ex ungue leonem' into Johann Bernoulli's mouth, creating the version quoted ever since | David Brewster, Johann Bernoulli | London | Source 321, Brewster; Source 337, Bernoulli |
| 1831 | Mechanism of the Heavens published by John Murray in an edition of 750 copies | Mary Somerville | London | Source 412, Somerville; Source 413, Somerville |
| 14 February 1832 | George Peacock writes that he and Whewell "have already taken steps to introduce it into the course of our studies at Cambridge"; the whole edition then sells chiefly at Cambridge | Mary Somerville, William Whewell | Cambridge | Source 412, Somerville |
| 1833 | Cauchy goes to Prague to tutor the grandson of the exiled Charles X | Cauchy | Prague | Source 372, O'Connor |
| March 1834 | The word "scientist" appears in print for the first time, in Whewell's anonymous review of Somerville's On the Connexion of the Physical Sciences, Quarterly Review vol. LI no. CI, pp. 54-68 - attributed by the reviewer to "some ingenious gentleman" and reported as not generally palatable | William Whewell, Mary Somerville | London | Source 411, Whewell |
| 1834-35 | Charles Whish publishes the first European account of the Kerala infinite series for pi, in Transactions of the Royal Asiatic Society Disputed: Almeida & Joseph give 1835 vol. 3; the paper is very commonly cited as 1834 | Charles Whish | London / Malabar | Source 51, Almeida; Source 52, Pearce |
| 1837 | Dirichlet states the modern definition of a function as an arbitrary rule of assignment | Dirichlet | Berlin | Source 379, O'Connor |
| 1841 | Jacobi reintroduces the curly d for partial derivatives, unaware that Legendre had published it 55 years before; adoption takes another half-century | Carl Gustav Jacob Jacobi | Konigsberg | Source 451, Cajori; Source 452, Miller |
| 1841 | Weierstrass writes absolute value with vertical bars, in a paper not printed at the time | Weierstrass | Munster | Source 451, Cajori |
| 1843 | Lovelace publishes her translation of Menabrea with Notes A-G; Note G contains a looping, recurrence-based algorithm for the Bernoulli numbers with a trace table for the case n=4 | Ada Lovelace, Luigi Menabrea | London | Source 415, Menabrea (trans. and notes by Lovelace) |
| 10 June 1854 | Riemann delivers the Habilitationsvortrag 'Ueber die Hypothesen welche der Geometrie zu Grunde liegen'; Gauss praises it with rare enthusiasm | Riemann | Goettingen | Source 375, O'Connor |
| 1854 | Riemann's Habilitationsschrift on trigonometric series defines the definite integral by arbitrary partitions and arbitrary sample points | Riemann | Goettingen | Source 391, Riemann; Source 375, O'Connor |
| 31 March 1854 | Koenigsberg awards Weierstrass an honorary doctorate after the Abelian functions paper, ending fourteen years of schoolteaching | Weierstrass | Koenigsberg | Source 373, O'Connor |
| October 1856 | Weierstrass takes up a professorship at the University of Berlin, aged 40-41 Disputed: Commonly reported as 'professor at 39'; MacTutor's dating makes him 40 turning 41. See conflict C-R009. | Weierstrass | Berlin | Source 373, O'Connor |
| 24 November 1858 | Dedekind, preparing his first calculus lectures at Zurich, finds the definition of continuity by cuts, and tells his friend Durege days later | Dedekind | Zurich | Source 366, Dedekind; Source 382, O'Connor |
| 1859 | Bunyakovsky publishes the integral form of what will be called the Cauchy-Schwarz inequality - in the year he retires | Viktor Bunyakovsky | St Petersburg | Source 457, OConnor and Robertson; Source 458, Kichenassamy |
| around 1861 | Riemann suggests a counterexample to Ampere's theorem in his lectures, per Weierstrass; the proof was never written down | Riemann, Weierstrass | Goettingen | Source 386, Johansson |
| 1869 | Meray publishes the first coherent rigorous theory of the irrational numbers to appear in print, three years before Dedekind, Cantor and Heine | Meray | France | Source 378, O'Connor |
| 7 November 1870 | Maxwell writes to Tait from Glenlair proposing names for the results of the nabla operator: slope, convergence, twist/turn/twirl/curl, concentration | James Clerk Maxwell, Peter Guthrie Tait | Glenlair, Dumfriesshire | Source 454, Knott |
| c. 1870 | William Robertson Smith suggests the name "nabla" to Tait, from the Assyrian harp the inverted delta resembles | William Robertson Smith, Peter Guthrie Tait | Scotland | Source 454, Knott |
| 18 July 1872 | Weierstrass presents his continuous nowhere-differentiable function to the Royal Academy of Science in Berlin, crediting Riemann with the idea | Weierstrass | Berlin | Source 386, Johansson |
| 1872 | Dedekind (cuts), Cantor (fundamental sequences) and Heine all publish constructions of the real numbers | Dedekind, Cantor | Germany | Source 366, Dedekind; Source 369, Bell; Source 378, O'Connor |
| 1872 | De Morgan's A Budget of Paradoxes names Euler in the Diderot story, adds 'algebra was Hebrew to Diderot', and miscopies Thiebault's z as n | Augustus De Morgan | London | Source 313, Brown; Source 314, Gillings |
| 20 March 1872 | Dedekind writes the preface to Stetigkeit und irrationale Zahlen; Cantor's Math. Annalen vol. 5 paper arrives that same day | Dedekind, Cantor | Braunschweig | Source 366, Dedekind |