Appendix D
Whose name is on it, and who did the work
Stigler's law of eponymy says no scientific discovery is named after its original discoverer. Stephen Stigler proposed it in 1980 and joked that Robert Merton had discovered the law first. The 1980 paper sits behind a paywall, so the Merton joke is unverified here and Appendix K.1 lists it (Source 460, Stigler).
Every row below was verified against a source. This table is a ready-made lesson on its own.
| Named for | Who had it first | The evidence | Sources |
|---|---|---|---|
| L'Hopital's rule | Johann Bernoulli | Contract of 17 March 1694: 300 pounds a year from 1 January 1694, buying exclusivity and silence. L'Hopital's preface does thank the Bernoullis generally; the body text never credits him | S315, S316 |
| Maclaurin series | James Stirling, 1717 | Lineae Tertii Ordinis p. 32, twenty-five years early. Stirling said in 1730 it was Taylor's; Maclaurin (art. 751) credited Taylor too | S312, S451 |
| Taylor series | Gregory, Leibniz, Johann Bernoulli (1694) | Gibson 1921. Bernoulli's priority claim was about Prop. XI, not Prop. VII Cor. 2 | S312 |
| Rolle's theorem | Rolle 1691, but unproved and only about polynomials | And Rolle called the calculus "a collection of ingenious fallacies" in print from 1700 to 1705 | S459 |
| Cavalieri's principle | Zu Geng, c. 500 CE | 緣幂勢既同，則積不容異. About 1,100 years earlier. The name is not Cavalieri's either; it is his Prop. II.4 | S023, S135 |
| Riemann integral | Darboux, 1875, for what is taught | Riemann's own definition uses arbitrary partitions and arbitrary tags. The upper and lower sums students learn are Darboux's reformulation | S391 |
| The Fundamental Theorem of Calculus | Gregory 1668, Barrow 1670, Cauchy for the modern statement | The name itself dates only to 1942 (Sherwood and Taylor) | S136, S158, S362 |
| Cauchy-Schwarz inequality | Bunyakovsky, 1859 | Integral form with the equality case, 26 years before Schwarz 1885. Bunyakovsky retired the same year he published it and lived another thirty years watching other names go on it | S457, S458 |
| Holder's inequality | Rogers, 1888 | Holder 1889 | S458 |
| Jensen's inequality | Holder, 1889 | And Jensen said so himself, and was ignored anyway | S458 |
| Simpson's rule | Kepler 1615, Cavalieri 1639, Gregory 1668, Newton | Simpson said so himself | S451, S462 |
| Newton's method | Simpson, 1740, for the iteration taught | Newton's own version was algebraic and derivative-free | S451, S462 |
| Stirling's approximation | De Moivre, disputed | Not settled from the primary sources | S451 |
| The Witch of Agnesi | Curve named by Guido Grandi (1718) as versoria, a sail rope | Agnesi wrote "che dicesi la Versiera", "which is called", at Vol. 1 p. 381. The English "witch" is Colson's translation, edited by John Hellins and published in 1801, p. 222: "which is vulgarly called the Witch". Colson's synopsis went further and made it hers: "which she calls the Witch". The confusion with avversiera (she-devil) is Mazzotti's "perhaps", so write "probably", not "because" | S077, S319, S320 |
| The Leibniz series for pi | Madhava, c. 1400 | Roy 1990. Note that the Madhava attribution itself rests on Nilakantha's testimony | S062 |
| Gregory's series | Madhava, c. 1400 | Same | S062 |
| Pascal's triangle | Halayudha, al-Karaji, Khayyam, Jia Xian, Yang Hui, Zhu Shijie | Cajori already wrote "known in the West as Pascal's arithmetical triangle" in 1919. The correction is over a century old | S456 |
| Vandermonde determinant | Nobody | Vandermonde never discussed it | S451 |
| The enri (Japanese circle principle) | Takebe Katahiro, not Seki | Credited to the teacher for two hundred years, handed back to the pupil recently | S430 |
| Backpropagation | Linnainmaa, 1970 | 1986 was popularization. Reinvented at least four times | S436, S437, S438 |