Appendix G
Stories that check out, and stories that do not
This is the most immediately useful appendix for a classroom, because several of the debunked items are in books you may already have read. Each verdict names what was checked.
G.1 Verified from the sources
| Story | What the source shows | Sources |
|---|---|---|
| Agnesi was appointed to a chair at Bologna and never taught | True, and now documented to the day. Benedict XIV's letter of 10 September 1750; the university diploma of 5 October 1750 naming the post "Cattedra di Pubblico Lettore di Matematica"; and Mazzotti's flat statement that she "never went to Bologna to take up this teaching post" | S077 |
| Agnesi ran a poorhouse and died in it | Close, and the precise version is better. In 1771 she was asked to direct the female department of the Pio Albergo Trivulzio, about 450 patients. In 1783, having renounced everything, she moved in. She died of pneumonia in January 1799 and, with war ravaging northern Italy, was buried in a mass grave outside Porta Romana | S077 |
| Colson coined "the Witch of Agnesi" around 1760 | Name both men and the right year. Colson died in 1760, so he translated before then, but the printed book is 1801, edited by John Hellins, and the phrase at p. 222 is "which is vulgarly called the Witch". Mazzotti hedges the avversiera mechanism with "perhaps" | S077 |
| Newton used Principia Lemma 12 before anyone had proved it | False, and it is Whiston's legend from 1749. Apollonius, Saint-Vincent and La Hire had proved it, and Newton wrote his own three-line proof by hand in the margin of a book from Barrow's library, using Euclid III.36. He printed "it is clear from the Conics" instead | S076 |
| Scholars simply disagree about what Barrow gave Newton | True, and Feingold supplies the reason: Barrow was a weapon in the priority war. De Morgan saw it in 1835: the Newtonians made him "a sort of retrenched position, on which to fall back in case of defeat". Then the twentieth-century reaction against Child overcorrected. Print the dispute with its explanation | S073 |
| Newton's partisans invented the idea that Leibniz owed something to Barrow | No. It came from Leibniz's own circle. Tschirnhaus, his confidant, wrote to him in 1678 to 1679 saying he could not see much in Leibniz's calculus beyond what Barrow had published, and called Barrow "much more readily intelligible". Then he published the claim and took the credit for himself | S073 |
| The Principia's geometric style kept Continental mathematicians from using it | Not as an intelligibility problem. Fellmann: Leibniz had "not the slightest difficulty in mastering Newton's arguments in detail" and "did not find it particularly difficult to convert the substance of Newton's text into his own mathematical form". Huygens's distance from the calculus came from his own "conservative adherence to a strictly geometrical conception" | S070 |
| Newton discovered the Principia results by calculus, then hid the analysis | Still open, but now precisely located. Fellmann does not state the claim at all and corroborates only the single exception. Cohen's Guide addresses it head-on at section 5.8, and his own word for Newton's 1715 story is "Allegations" | S070, S072 |
| Sarasa discovered that the area under a hyperbola is a logarithm | True, and the context is better than the claim. He was answering a challenge problem Mersenne set partly to attack his teacher's quadrature of the circle. His sentence, in the 1649 primary: "in place of the numbers 6, 7, 8, 9, 10, 11, which were the logarithms of the magnitudes O, P, Q, R, S, T, we shall be able to take the hyperbolic quantities" | S066 |
| The result is buried in Saint-Vincent's Opus geometricum, Book VI | True, and the book's own table of contents calls those propositions admirandae, to be wondered at. But cite the range 125 to 130, not a single proposition number: the 1649 long-s scan does not render the digits reliably, and Book VI itself was not in the volume obtained | S066, S067 |
| Du Chatelet's Principia is still the standard French edition | True and understated. It is the only complete French translation of the Principia that exists | S069 |
| Du Chatelet published under her own name | Often not. The 1738 essay on fire went to the Academie anonymously, because a submission known to be by a woman would not have been taken seriously; it lost, and the Academie printed it anyway. The Institutions de physique was also published anonymously, in 1740 | S069 |
| Her Principia commentary appeared ten years late through neglect | The opposite, and the reason has a name. Clairaut, who had checked her calculations while she was alive, pressed the publisher Prault to bring it out and arranged for the illustrations to be finished | S068 |
| Galileo tried to measure the cycloid's area by weighing it | True, and the punchline is better than the story. He cut an arch and a circle from the same material, balanced them, got "about three times", and abandoned it believing the ratio incommensurable. It is exactly 3 | S064 |
| Roberval kept his methods secret because his chair was re-contested every three years | True, and Whitman states the mechanism: the incumbent set the questions, so concealment was job security. Walker: "the accident of occupying this chair caused Roberval to lose credit for many of his discoveries" | S064 |
| Christopher Wren rectified the cycloid in 1658 | True. Sent to Pascal without proof during the contest; Wallis printed it as Wren's a year later. One arch is exactly 8a, four times the generating circle's diameter, with no pi in it | S064 |
| Kerala mathematicians used ibn al-Haytham's summation identity | True and precisely located: Katz shows the identity used for k = 1 in the sine-series derivation, and notes in the same paragraph that the Indian mathematicians named no predecessor. The mathematics is shared; the citation is absent | S061 |
| Kepler invented a chunk of integral calculus because he thought a wine merchant was cheating him | True, and better in the original. His own preface: new house in Linz, wine up the Danube by barge, the merchant measuring every cask alike sine ratiocinatione vel calculo | S159 |
| Newton kept the begging letter from the counterfeiter he prosecuted | True. TNA MINT 15/17/205: "O no body can save me but you". It is still in the file | S196 |
| Newton reviewed his own anonymous report anonymously | True, and documented in his own hand: a 24,000-word holograph draft at CUL MS Add. 3968, ff. 67r to 96v | S280, S282 |
| Leibniz got the product rule wrong and corrected himself the same day | True, both on the page, 11 November 1675, with the analytic derivation following on 21 November | S230 |
| The integral sign is a long letter S for summa | True, 29 October 1675, replacing the word omnia, three days after a formula so clogged with omn. that it was unusable | S230, S238, S451 |
| "L'Hopital's rule" is Johann Bernoulli's | True. Contract of 17 March 1694, 300 pounds a year from 1 January 1694, buying exclusivity and silence | S315 |
| Jacob Bernoulli's tombstone has the wrong spiral | True. The mason carved an Archimedean spiral under a motto about a logarithmic one. Two independent sources | S328, S329 |
| Sophie Germain's parents confiscated her candles and fire | True, and they gave up when they found her asleep in the library with the ink frozen | S410 |
| Gauss corresponded with her as "Monsieur LeBlanc" and she revealed herself to save his life | True. Gauss's letter on learning the truth is verified | S410 |
| John Glenn refused to fly until Katherine Johnson checked the computer by hand | True, in NASA's own words ("get the girl") | S422 |
| Grace Chisholm Young's husband put his name on her work and promised to switch later | True, in his own letter. 220 papers later they had not switched | S419 |
| Emmy Noether lectured for four years under Hilbert's name | True | S418 |
| Seki Takakazu had determinants before Leibniz and Bernoulli numbers before Bernoulli | True, and sealed inside Japan by sakoku, so all of it had to be found again | S429 |
| Backpropagation is the chain rule in reverse | True, in two peer-reviewed surveys, with the cost argument | S436, S437 |
| Cambridge undergraduates campaigned for Leibniz notation with a punning tract title | True as a suggested title recalled by Babbage in 1864: "The Principles of pure D-ism in opposition to the Dot-age of the University". Never used | S239 |
| The Archimedes Palimpsest was read through painted-on gold forgeries using a particle accelerator | True. X-ray fluorescence at the Stanford Synchrotron detected iron in the original ink. And the first imaging attempt failed | S005, S006 |
G.2 Debunked, corrected, or unverifiable
| The story as usually told | What checking it produced | Sources |
|---|---|---|
| An apple hit Newton on the head | False. Stukeley has Newton "in a comtemplative mood" and the apple seen falling. No 18th-century source has a head strike | S180 |
| Newton spent the plague years in seclusion at Woolsthorpe | Wrong geography. Trinity commons accounts and his own pocket-book put him in Cambridge Sept 1664 to June 1665, back 20 March 1666, and back again 22 April 1667. Summer 1665 was at Boothby Pagnell, which had a library | S190 |
| Newton's dot notation dates from 1666 | False. Late 1691. The 1666 tract uses p, q, r; the 1671 autograph uses l, m, n, r. The printed dots are William Jones's 1710 substitution | S192 |
| Newton discovered the Principia results by calculus, then translated them into geometry | Contested, and the only source for it is Newton writing anonymously about himself. Whiteside finds the book built natively from limit-ratios, with one exception | S189, S190 |
| Newton said he was ashamed how many figures he carried his pi computation to | Unverifiable. Traced only to unattributed sources. The verified equivalent: his own note that he computed the hyperbola's area "to two & fifty figures", with working sheets surviving | S190 |
| Keynes said Newton left a million words of alchemy | Misattributed. Keynes said "at least 100,000 words". The million-word figure is modern cataloguing | S193 |
| Newton's dog Diamond knocked over a candle and burned his papers | Not in the manuscript. A later accretion | S182 |
| Euler silenced Diderot with "(a+b^n)/n = x, therefore God exists" | Fabricated, and the fabrication is traceable page by page. Thiebault names no one and disclaims the story; De Morgan (1872) inserts Euler; Cajori repeats it; Bell says "Chinese"; Hogben says "Arabic". And De Morgan miscopied Thiebault's z as n | S313, S314 |
| Frederick the Great habitually called Euler a cyclops | One letter, 25 January 1778, to Voltaire, 29 years after the fountain job. Euler had correctly diagnosed the oversized pump in writing and been ignored. Not a standing nickname | S342 |
| Euler joked that going blind meant fewer distractions | Not verified. Widely quoted and no source located, which is why it never appears here inside quotation marks | S326 |
| Newton solved the brachistochrone in 12 hours coming home from the Mint | Wrong problem. Brewster's Mint detail belongs to Leibniz's 1716 problem, not the 1697 one | S321 |
| Johann Bernoulli said "I recognize the lion by his paw" | Attribute to Brewster, not Bernoulli. The Latin tanquam ex ungue leonem is Brewster 1831 p. 194, rendering a French original. A verifiable case of a manufactured quotation | S321 |
| Torricelli proved the horn has infinite surface area | False. He proved finite volume by indivisibles. The painter's paradox is a later overlay. Near-universal textbook error | S157 |
| Pascal thought about the cycloid to distract himself from a toothache | Originates with his sister Gilberte, and the Internet Encyclopedia of Philosophy calls her claims questionable. The transmission route is now traced: Whitman attributes it to W. W. Rouse Ball, who adds that Pascal took the relief as "a divine intimation" and worked at it for eight days. So the chain is Gilberte, then Ball, then everyone. Report it as a family anecdote reported by Ball | S064, S143, S161 |
| Cavalieri believed areas are literally made of lines | He denied it in writing, twice, to Galileo on 2 October 1634 and 28 June 1639 | S135, S156 |
| Berkeley wrote "they are the ghosts of departed quantities" as a statement | It is a question, in a chain of questions. The full stops and quotation marks come from later editors' summaries | S310 |
| Abel wrote that divergent series are "the invention of the devil" | A translation of a translation. Abel wrote noget Fandensskab, "some devilry", from Berlin not Paris, 16 January 1826, and hedged it with i det Hele, "on the whole", which English drops | S490 |
| Cauchy lost Galois' life work | Mostly myth. The lost manuscript was the Feb 1830 Grand Prize submission held by Fourier, who died that April. Cauchy's documented 1829 role was to referee and advise resubmission | S380 |
| Kronecker drove Cantor mad | Not supported. MacTutor dates the first breakdown to 1884 and treats the illness as recurrent and independent, while documenting the professional obstruction as real | S376 |
| Hermite recoiled in horror from "functions with no derivatives" | The standard English drops the word "continuous", which destroys the point. Verified from the primary: Correspondance II, p. 318, 20 May 1893 | S365 |
| Weierstrass discovered and published the nowhere-differentiable function in 1872 | He presented it 18 July 1872 and never published it (du Bois-Reymond did, 1875), and he opened by crediting Riemann. Cellerier is a third independent discoverer | S386 |
| Whewell coined "scientist" to describe Mary Somerville | Wrong book and wrong attribution. The review was of On the Connexion of the Physical Sciences, and Whewell credits "some ingenious gentleman" | S411, S442 |
| Katherine Johnson used Euler's method for the Friendship 7 orbit | Absent from NASA's biography, MacTutor, and TN D-233 itself. The report uses iterative correction of Kepler equations plus partial-derivative sensitivity | S422, S423 |
| Hilbert said "this is a university, not a bath-house" about Noether | Not in the source. Do not assert | S418 |
| Bhaskara II stated Rolle's theorem | He stated Fermat's rule for an extremum, not Rolle's theorem. Golādhyāya 4.39 | S050 |
| al-Kashi invented decimal fractions | False. al-Uqlidisi did, around 950 | S063 |
| The Kerala series reached Europe via the Jesuits | Open question, argued by serious historians on both sides. Motive, opportunity, and resemblance are documented; no transmitting document has been produced. Teach it as a dispute | S051, S052 |
| "Method of exhaustion" is what the Greeks called it | A 17th-century coinage, and misleading: the method brackets, it does not exhaust | S008 |
| Descartes chose x, y, z because a printer ran short of other letters | Unattested. He introduced the convention without comment or argument | S450 |
| The cycloid was called "the Helen of Geometers" by [someone] | CLOSED: unattributable. Whitman 1943, the leading candidate, was read in full on 14 Aug 2026 and searched: the words Helen, Troy, Trojan and discord do not occur anywhere in its eight pages. Martin (2010) uses "The Helen of Geometry" as a title with no citation. Do not attribute the phrase to anyone | S064, S161 |