Timeline
1873 to 1913: measure, set theory, and the modern integral
| Date | Event | Who | Where | Sources |
|---|---|---|---|---|
| 1874 | Cantor proves the real numbers are not countable while the algebraic numbers are | Cantor | Halle | Source 376, O'Connor |
| 1874 | Kovalevskaya is awarded her doctorate by Goettingen in absentia, having been barred from enrolling at Berlin | Kovalevskaya, Weierstrass | Goettingen | Source 374, O'Connor |
| 1875 | Weierstrass's nowhere-differentiable function is published for the first time - by Paul du Bois-Reymond, in Borchardt's Journal | Weierstrass, du Bois-Reymond | Heidelberg / Berlin | Source 386, Johansson |
| 1875 | Darboux publishes the upper-and-lower-sum construction of the integral that textbooks call the Riemann integral | Gaston Darboux | Paris | Source 453, Miller and Aldrich |
| 1877 | Kronecker treats Cantor's dimension paper with suspicion and delays publication until Dedekind intervenes; Cantor never submits to Crelle again | Cantor, Kronecker, Dedekind | Berlin / Halle | Source 376, O'Connor |
| May 1884 | Cantor's first recorded attack of depression | Cantor | Halle | Source 376, O'Connor |
| 1885 | Mittag-Leffler persuades Cantor to withdraw a paper already in proof, saying it is 'about one hundred years too soon' | Cantor | Stockholm | Source 376, O'Connor |
| 1889 | Peano introduces the set-membership symbol in Arithmetices principia, as an abbreviation for the Latin 'est' | Peano | Turin | Source 393, Miller |
| June 1889 | Kovalevskaya becomes full professor at Stockholm, having been extraordinary professor since June 1884 | Kovalevskaya | Stockholm | Source 374, O'Connor |
| 1890 | Cellerier's independently discovered nowhere-differentiable function is published, posthumously, thirty years after its construction | Cellerier | Geneva | Source 386, Johansson |
| 1891 | Cantor gives the diagonal argument | Cantor | Halle | Source 376, O'Connor |
| 20 May 1893 | Hermite writes to Stieltjes that he turns away 'avec effroi et horreur' from the lamentable plague of continuous functions with no derivatives | Hermite, Stieltjes | Paris | Source 365, Hermite; Source 388, Kesavan |
| 1895 | Grace Chisholm is awarded a Gottingen doctorate under Klein - twenty-one years after Kovalevskaya could receive one only in absentia | Grace Chisholm Young | Gottingen | Source 419, OConnor and Robertson |
| 14 September 1901 | John Perry opens the British Association discussion on the teaching of mathematics at Glasgow, arguing that the methods of the calculus are 'easily learnt by all young boys' and should be taught in ordinary schools - the manifesto of the Perry movement | - | Glasgow | Source 492, Perry |
| 29 April 1901 | Lebesgue announces his integral in a Comptes Rendus note, 'Sur une generalisation de l'integrale definie' | Lebesgue | Paris | Source 377, O'Connor |
| 1902 | Lebesgue's thesis Integrale, longueur, aire is presented at Paris and published in the Annali di Matematica, Milan | Lebesgue | Paris / Milan | Source 377, O'Connor |
| 1905 | J. G. Leathem introduces the arrow for passage to a limit | John Gaston Leathem | Cambridge | Source 451, Cajori; Source 452, Miller |
| 1906 | Heiberg identifies and transcribes Archimedes' Method from a palimpsest in Constantinople, after following up an 1899 catalog notice | Johan Ludvig Heiberg | Constantinople | Source 2, Heath; Source 6, Miller |
| 1906 | The Theory of Sets of Points published under both Youngs' names; the other 219 joint papers carry William Young's name alone, by written agreement | Grace Chisholm Young, William Henry Young | Geneva | Source 419, OConnor and Robertson |
| 1908 | Hardys Course of Pure Mathematics and Bromwichs Infinite Series make the arrow standard; Hardy credits Leathem and Bromwich in his Preface | G. H. Hardy, Thomas Bromwich | Cambridge | Source 451, Cajori; Source 452, Miller |
| January 1913 | Ramanujan writes to Hardy - his fourth attempt, after Hill misunderstood his divergent series and Hobson and Baker did not reply | Srinivasa Ramanujan | Madras and Cambridge | Source 431, OConnor and Robertson |