Timeline
1914 to the present: vindication and the machine age
| Date | Event | Who | Where | Sources |
|---|---|---|---|---|
| 1916 | Hardy shows that ab >= 1 suffices for the Weierstrass function to be nowhere differentiable, weakening Weierstrass's own condition | Weierstrass | Cambridge | Source 389, Calder; Source 388, Kesavan |
| 1918 | Noether proves that to every continuous symmetry of a system there corresponds a conservation law | Emmy Noether | Gottingen | Source 418, OConnor and Robertson |
| 1919 | Noether is finally granted the habilitation after a four-year fight by Hilbert and Klein; until then she had lectured under Hilbert's name | Emmy Noether | Gottingen | Source 418, OConnor and Robertson |
| 1920 | Martin Jasek finds Bolzano's Functionenlehre manuscript in the National Library, Vienna | Jasek, Bolzano | Vienna | Source 386, Johansson |
| 3 December 1921 | Jasek gives the first lecture reporting on the rediscovered Functionenlehre | Jasek | Prague | Source 386, Johansson |
| 1922 | Schafheitlin finds and publishes, in the Basel public library, Part I of Johann Bernoulli's 1691-92 Course - proving that L'Hopital's Analyse was Bernoulli's content in L'Hopital's exposition | Johann Bernoulli, Guillaume de l'Hopital | Basel | Source 315, Truesdell |
| 3 February 1922 | Rychlik presents the correct proof that Bolzano's function is continuous and nowhere differentiable; Jarnik proves it independently at the same time | Rychlik, Jarnik, Bolzano | Prague | Source 386, Johansson |
| 1930 | Bolzano's Functionenlehre is published for the first time, edited by Rychlik, in Prague, about a century after it was written Disputed: S386's abstract says 1922, its body and MacTutor (S384) say 1930. Resolution: the proofs were published in 1922, the manuscript in 1930. See conflict C-R017. | Bolzano, Rychlik | Prague | Source 384, O'Connor; Source 386, Johansson |
| 1930 | Nikodym completes the Radon-Nikodym theorem, the abstract form of "one measure has a density with respect to another" | Otton Nikodym, Johann Radon | Poland | Source 435, OConnor and Robertson |
| 1931 | Banach and Mazurkiewicz independently prove that in the space of continuous functions, the nowhere-differentiable ones are generic | - | Poland | Source 388, Kesavan |
| 1934 | Skolem constructs the hyperintegers by the ultraproduct method and proves the analogue of the Transfer Principle - the machinery of nonstandard analysis, 27 years before its application | Thoralf Skolem | Norway | Source 440, Keisler |
| 1934-1935 | The Bourbaki group forms in Paris, initially to write a better analysis textbook than the one they were teaching from | Nicolas Bourbaki, Henri Cartan | Paris | Source 434, OConnor and Robertson |
| 1936 | Sotheby dispersal of the non-scientific Newton papers; J. M. Keynes reassembles about half Disputed: Keynes says 'dispersed in the auction room in 1936'; the sale is usually given as 13-14 July 1936, which this agent did not verify. | John Maynard Keynes | London | Source 193, Keynes |
| 1937 | Stone generalises the Weierstrass approximation theorem to compact Hausdorff spaces | Marshall Stone | USA | Source 435, OConnor and Robertson |
| 1942 | B. H. Brown publishes 'The Euler-Diderot Anecdote' in the American Mathematical Monthly, the first proper debunking; Gillings extends it in 1954 | - | Hanover, New Hampshire | Source 313, Brown; Source 314, Gillings |
| 1944 | Laurent Schwartz conceives the theory of distributions during a night of insomnia in occupied France, and runs next door to tell Henri Cartan | Laurent Schwartz, Henri Cartan | Nancy or Grenoble, France | Source 433, OConnor and Robertson |
| July 1946 | 'Newton, the Man' read at the Royal Society tercentenary by Geoffrey Keynes; J. M. Keynes had died in April 1946 | John Maynard Keynes | London | Source 193, Keynes |
| 1955 | The College Board dates the establishment of the Advanced Placement Program to this year ('The Advanced Placement Program was established in 1955') Disputed: This is the College Board's own institutional date. Other accounts date the pilot examinations to 1954 (run by the School and College Study of Admission with Advanced Standing) and the first examinations under the College Board to 1956. Neither was verified in this project - see S444 | - | United States | Source 448, Commission on the Future of the Advanced Placement Program |
| 1958 | Mary Jackson becomes NASA's first black female engineer, having needed the City of Hampton's permission to attend the required classes in a segregated high school | Mary Jackson | Hampton, Virginia | Source 425, Shetterly |
| 1960 | NASA TN D-233 published: given a chosen landing point and a number of orbits, solve for the launch azimuth. First author credit for a woman in Langley's Flight Research Division | Katherine Johnson, Ted Skopinski | Langley Field, Virginia | Source 423, Skopinski and Johnson; Source 422, Shetterly; Source 424, OConnor and Robertson |
| 1961 | Robinson introduces nonstandard analysis | Abraham Robinson | USA | Source 381, O'Connor |
| February 1962 | Before Friendship 7, John Glenn asks engineers to "get the girl" to re-run by hand, on a desktop mechanical calculator, the same equations programmed into the IBM computers: "If she says they are good, then I am ready to go" | Katherine Johnson | Cape Canaveral and Langley | Source 422, Shetterly |
| 1964 | Wengert essentially discovers forward-mode automatic differentiation | Robert Wengert | USA | Source 436, Baydin, Pearlmutter, Radul and Siskind |
| 1966 | Robinson publishes Non-standard Analysis, giving infinitesimals that obey the same laws as ordinary numbers, as Leibniz had claimed | Abraham Robinson | USA | Source 381, O'Connor |
| 1970 | Linnainmaa's master's thesis gives the first published description of the reverse mode of automatic differentiation - the algorithm now called backpropagation - with no reference to neural networks; the 1976 BIT paper is titled "Taylor expansion of the accumulated rounding error" | Seppo Linnainmaa | Helsinki | Source 436, Baydin, Pearlmutter, Radul and Siskind; Source 437, Schmidhuber |
| 1970 | Seppo Linnainmaa conceives the reverse mode of differentiation - the ancestor of backpropagation - 'on a sunny afternoon in a Copenhagen park'; G. M. Ostrovskii and co-workers had used the same technique about five years earlier, and it was independently rediscovered repeatedly into the 1980s Disputed: Griewank's whole point is that there is no single inventor: Ostrovskii et al. c. 1965 (published 1971), Linnainmaa 1970, Speelpenning 1980, Werbos 1982, Baur-Strassen 1983, Griewank himself 1987 | - | Copenhagen / Helsinki | Source 438, Griewank |
| 1974 | Bishop's lecture at the Workshop on the Evolution of Modern Mathematics, Boston; the phrase 'debasement of meaning' is in the draft but not in the audio of the lecture as delivered | Bishop, Abraham Robinson | Boston | Source 390, Katz |
| 1974 | Werbos's thesis Beyond Regression casts the reverse mode in formal discrete-time terms | Paul Werbos | Harvard, USA | Source 436, Baydin, Pearlmutter, Radul and Siskind; Source 437, Schmidhuber |
| 1975 | Sabetai Unguru publishes 'On the need to rewrite the history of Greek mathematics' (Archive for History of Exact Sciences 15, 67-114), denying that Greek geometry is algebra in disguise; van der Waerden (1976), Freudenthal (1977) and Weil (1978) reply in the same journal - the debate that governs whether 'why did the Greeks not invent calculus?' is even a well-posed question | - | - | Source 491, Katz |
| 1976 | Keisler publishes Elementary Calculus: An Approach Using Infinitesimals, the first calculus textbook built on Robinson's hyperreals; Bishop reviews it hostilely in the Bulletin of the AMS in 1977 | H. Jerome Keisler | Wisconsin, USA | Source 440, Keisler; Source 441, OConnor and Robertson |
| 1976 | About 76,000 students sat nearly 100,000 Advanced Placement examinations in the United States, all subjects combined - against 3,079,134 students and 5,744,259 examinations in 2024 | - | United States | Source 493, Coleman; Source 446, College Board |
| late 1970s to early 1980s | Gladys West leads a five-person team computing the geoid on an IBM 7030 Stretch - the Earth-shape model that satellite positioning is measured against | Gladys West | Dahlgren, Virginia | Source 426, OConnor and Robertson |
| 1977 | Bishop reviews Keisler's Elementary Calculus in the Bulletin of the AMS | Bishop | USA | Source 395, Bishop; Source 390, Katz |
| by 1977 | AP Calculus already consisted of two examinations, 'calculus AB' and 'calculus BC'; the booklet lists 'Calculus (two courses)' among fourteen AP subjects Disputed: This fixes only an upper bound: the AB/BC split predates 1977. The year it was introduced, and the meaning of the letters, remain unsourced - see S444 | - | United States | Source 493, Coleman |
| 1980 | Speelpenning gives the first genuinely automatic implementation of reverse-mode AD | Speelpenning | Illinois, USA | Source 436, Baydin, Pearlmutter, Radul and Siskind |
| 1986 | Rumelhart, Hinton and Williams popularise backpropagation; the PDP group had not read Parker, and Parker had not read Werbos | - | USA | Source 436, Baydin, Pearlmutter, Radul and Siskind; Source 437, Schmidhuber |
| 1997 | Grabiner's 'Was Newton's Calculus a Dead End?' argues that Maclaurin's Treatise transmitted improved Newtonian calculus to the Continent | Colin Maclaurin | Claremont, California | Source 335, Grabiner |
| 28 or 29 October 1998 | The Archimedes Palimpsest is sold at Christie's for $2 million to an anonymous collector, who deposits it at the Walters Art Museum Disputed: Walters gives 28 October 1998; the project website gives 29 October 1998 | William Noel | New York | Source 4; Source 5; Source 6, Miller |
| 2002 | Netz, Saito and Tchernetska publish a new reading of Method Proposition 14 in which Archimedes calls two infinite collections 'equal in multitude' | Reviel Netz, Archimedes | Stanford / Osaka / Cambridge | Source 3, Netz |
| 2024 | 426,848 AP Calculus examinations taken in one year in the United States - 278,657 Calculus AB and 148,191 Calculus BC - out of 5,744,259 AP examinations sat by 3,079,134 students | - | United States | Source 446, College Board; Source 447, College Board |