Appendix F
Disagreements between sources
An open conflict recorded is scholarship; an open conflict forgotten becomes a fact. Every claim in this book resting on an open row below carries the visible Disputed label wherever it appears.
Resolved
| ID | Topic | One source says | Another says | Resolution |
|---|---|---|---|---|
C-A002 |
Who first stated the cone = 1/3 cylinder theorem | Archimedes credits Eudoxus, naming no one else, in the preface to On the Sphere and Cylinder I (Heath 1897, p. 2) Source 1 |
Archimedes, in The Method, says 'we should give no small share of the credit to Democritus who was the first to make the assertion with regard to the said figure though he did not prove it' Source 2 |
Resolved, and the resolution is the interesting part: both are Archimedes. Eudoxus first PROVED it; Democritus first ASSERTED it. The Sphere and Cylinder preface credits the proof; The Method credits the conjecture. Nobody knew about the Democritus attribution until 1906, because The Method was lost. Method: Read both primary prefaces in full; Heath 1912 introductory note pp. 10-11 states the same resolution |
C-M002 |
Who initiated the Oxford Calculators | Kilvington's questions on physics inspired Bradwardine's rule; Kilvington is in the first academic generation but is not credited as founder Source 102 |
Bradwardine is presented as the originating figure of the Merton tradition Source 104 |
Resolved in favor of the 'both can be true' reading, now on scholarly authority rather than inference. The Stanford Encyclopedia entry on Heytesbury (E. Jung, rev. 2026 = S101) presents Bradwardine as the earlier founding figure of the Oxford Calculators, with Kilvington as Heytesbury's likely teacher in the first generation, Dumbleton and Roger Swyneshed as contemporaries, and Richard Swineshead as successor; Heytesbury is 'the second generation'. Sylla's Dictionary of Scientific Biography entry on Dumbleton (S480) independently describes Dumbleton as taking up Bradwardine's mathematization program. So Kilvington's physical questions prompted the work, Bradwardine's 1328 rule formalised it, and 'founder' properly attaches to Bradwardine. The Merton College outreach essay (S104) is an outreach page rather than an authority on priority, and nothing here rests on it for that. Method: Re-read SEP Heytesbury in full and read Sylla DSB Dumbleton in full; compared with S102 and S104 |
C-M003 |
Was the mean speed theorem proved at Merton | Truesdell: the kinematic properties 'were discovered and proved by scholars of Merton college' Source 104 |
Heytesbury 'stated the theorem as a general rule but did not provide a formal mathematical proof' Source 101 |
The geometric proof that survives is Oresme's (S107), written at Paris and not at Merton. The mean speed theorem was stated at Merton and proved at Paris. Method: primary_text_check |
C-S001 |
Occasion of Kepler's wine-barrel work | The incident occurred at Kepler's 1613 second wedding in Linz; he watched the merchant's gauging rod Source 134;Source 154 |
Framed around the abundant vintage of 1612 rather than the wedding; primary preface (S159) confirms both Source 151;Source 159 |
Resolved from the primary source: Kepler's own 1615 preface (S159) contains BOTH framings - wine delivered up the Danube to his new house in Linz, AND his duty as a newly married householder to lay in drink. The merchant measured every barrel alike 'sine discrimine, sine respectu figurae, sine ratiocinatione vel calculo'. The two secondary accounts are not in conflict. Method: primary_text_check |
C-S010 |
Pascal and the toothache | Gilberte Perier: the solution came 'during a bout of sleeplessness caused by a toothache' - but the IEP adds 'Gilberte's claims are questionable' Source 143 |
MacTutor says only that Pascal worked on the cycloid 'while bedridden with pain'; no toothache ; Whitman 1943 (S064) attributes the toothache story to W. W. Rouse Ball, not to Gilberte Pascal Source 153;Source 64 |
The toothache rests on his sister Gilberte's memoir alone, and a reference work flags her claims as questionable. Whitman (S064) traces the story to W. W. Rouse Ball's account and adds the eight-day detail, so the chain runs Gilberte to Ball to everyone else. It is a family anecdote reported by Ball, not a documented fact. Method: source_comparison |
C-S011 |
Did Cavalieri believe the continuum is composed of indivisibles | Guldin's critique and the standard textbook account assume he did Source 151;Source 135 |
Cavalieri to Galileo, 2 Oct 1634: 'I absolutely do not declare to compose the continuum by indivisibles'; and 28 June 1639: 'I have not dared to say that the continuum was composed of these' Source 156 |
Cavalieri's own letters settle it: he explicitly and repeatedly denied the atomistic reading. Even the 1911 Britannica concedes 'It is possible to contend that Cavalieri did not himself hold the unsound doctrine' Method: primary_text_check |
C-S012 |
Did Torricelli prove the infinite surface area of his solid | Standard textbook claim: a finite volume with infinite surface area, proved by Torricelli in 1643/44 (no scholarly source found for this attribution) |
Torricelli proved the finite volume using indivisibles but did NOT establish the infinite surface area; that came later with integral calculus Source 157 |
S157 is the only scholarly source here and it is clear: Torricelli proved the finite volume, and the infinite-area painter's paradox framing came later. Method: source_comparison |
CN-02 |
Where the anni mirabiles work was done | Popular and traditional account: Newton did his greatest work alone in seclusion at Woolsthorpe Manor during the plague years 1665-67 Source 181;Source 182 (Conduitt, relaying Newton) and general tradition |
Whiteside, from the Fitzwilliam pocket-book and the Trinity commons accounts: Newton was in Cambridge Sept 1664-June 1665, again 20 March-mid-June 1666, and from 22 April 1667. 'The conclusion seems inescapable that Newton wrote most of them while in Cambridge (and hence with full access to university and college libraries) rather than in seclusion in Lincolnshire.' Part of the Lincolnshire time was at Boothby Pagnell, not Woolsthorpe Source 190 (Whiteside MP 1: 8, notes 20 and 21) |
Whiteside wins on documentary evidence. The plague scattered Newton between Cambridge, Woolsthorpe and Boothby Pagnell, and the October 1666 tract is the one securely dated Lincolnshire product. Method: Compared Newton's/Conduitt's retrospective testimony against contemporaneous financial and travel records as analyzed by Whiteside |
CN-04 |
What the apple did | Popular version: an apple fell on Newton's head No source. I could find no 17th- or 18th-century source for the head-strike |
Stukeley 1752, from Newton's own telling: the notion of gravitation came to him 'occasion'd by the fall of an apple, as he sat in a comtemplative mood' - he saw it fall and asked why it fell perpendicularly. Conduitt independently: 'he took the first hint of it from seeing an apple fall from a tree' Source 180 (RS MS/142, f. 15r); Source 181 (Keynes Ms. 129.02, f. 2v) |
Resolved. The apple fell; it did not hit him. Both early witnesses say 'seeing' / 'the fall of an apple ... as he sat', not impact Method: Went to the two earliest manuscript witnesses and read the exact wording |
CN-06 |
The year Newton died | Newton's own monument in Westminster Abbey: 'OBIIT XX MAR MDCCXXVI' - died 20 March 1726 Source 200 |
Modern reference works: died 20 March 1727 (Old Style) = 31 March 1727 (New Style) Source 200 (same source, explaining the convention) |
Resolved, and worth teaching. The two dates are the same day. Before 1752 the English civil year began on 25 March, so 20 March still fell in the civil year 1726; the historical year, which begins on 1 January, makes it 1727; and the Gregorian calendar, 11 days ahead by then, makes it 31 March 1727. The full form is 20 March 1726/7 (OS) = 31 March 1727 (NS). Method: Read the inscription and the repository's own explanation of the dating convention |
C-L001 |
Date of the first use of the integral sign | First written 29 October 1675, in Analyseos tetragonisticae pars secunda ("It will be useful to write ∫ for omn.") Source 230;Source 238 |
MacTutor: "21 November 1675: wrote manuscript using ∫f(x)dx integral notation for first time; manuscript also contained the product rule for differentiation" Source 235 |
The symbol dates from 29 October 1675. MacTutor is probably compressing three things into one: the symbol on 29 October 1675, the full form ∫f(x)dx with dx after the sign on 11 November 1675 per Cajori, and the analytic product rule on 21 November 1675. The primary manuscripts in Child settle it. Method: Read the primary manuscript translation (Child pp. 79-83, 90-102, 182) and cross-checked against Cajori via Miller. |
C-L002 |
When Leibniz corrected his wrong product rule | He asserted d(xy)=dx.dy and d(x/y)=dx/dy, and refuted both LATER IN THE SAME MANUSCRIPT of 11 November 1675: "although just above I stated that this was the case, and it appeared to be proved" Source 230 |
Popular accounts (and the common textbook telling) say he corrected the error "days later", pointing at the 21 November 1675 manuscript Source 230;Source 235 |
Both events are real and they are two different events. On 11 November 1675 Leibniz made the error, then recognized it and retracted it on the same sheet. On 21 November 1675 he derived the correct rule analytically for the first time. The pair is worth more than either one alone. Method: Read Child pp. 100-102 (the manuscript) and p. 182 (Child's own chronological summary). |
C-L004 |
Length of Nova Methodus | Six pages common secondary description |
pp. 467-473 of the October 1684 Acta Eruditorum; the article ends part-way down p. 473, where L. Strauss's article begins Source 231 |
The article runs pp. 467-473 and stops part way down p. 473, where L. Strauss's article begins, which is where the shorter counts come from. 'Six pages' is a rounding rather than an error, and 'six and a half pages' is closer, but the page range is the exact form. Method: Counted from the running heads and the start of the following article in the 1684 volume scan. |
C-L006 |
Whether Leibniz saw Newton's De analysi | Yes, but in OCTOBER 1676, on his second London visit, from Collins's papers; his surviving extracts (found by Gerhardt) copy the series and equation-solving material, not the tangent/quadrature material Source 230 |
The dispute-era claim (and much popular retelling) that he saw it on the 1673 visit and took the calculus from it Source 280 |
Resolved: 1676, not 1673, and the content of what he copied shows he took series methods, not the differential calculus, which he already had (the notation is dated to 1675). Method: Read Gerhardt's account of the two folios of extracts in Child's translation, pp. 167-170, against Newton's own narrative in the 1715 Account. |
C-L007 |
The altered date on the 11 November manuscript | The sheet reads "11 November 1673"; the 5 was altered to a 3 in darker ink, apparently by Leibniz Source 230 |
Child argues the alteration was an honest later misreading by Leibniz of his own phrase superiore anno, and that "The date 1675 is incontestable" Source 230 |
Resolved on the internal evidence: the paper develops the manuscript of 1 November 1675 directly, so 1675 is the year. The alteration on the sheet is real and Newton's side used it against Leibniz. It is a genuine ambiguity honestly resolved, not a forgery. Method: Read Child pp. 90-91 including Gerhardt's ink observation. |
C-L008 |
Year of Newton's anonymous Account | 1714: Philosophical Transactions no. 342 is for January and February, which concluded the year 1714 in England's Julian calendar Source 280 |
1715: the same months were the first two months of 1715 on the Continent's Gregorian calendar Source 280 |
Both years are correct, because the English legal year began on 25 March. The issue is no. 342 (January and February 1714/5), pp. 173-224, and the double year is the honest form of it. Method: Wilkins's editorial note to the TCD edition states both explicitly. |
C-L009 |
Date Newton's De analysi reached Barrow and Collins | Child's text reads "the paper which Newton sent in June, 1699, to Barrow, from whom Collins received it on July 30, 1699" Source 230 |
The universally accepted dates are June 1669 and 31 July 1669 general scholarship |
Resolved: 1669. The '1699' in the Child text is a typographic or OCR corruption, and Barrow died in 1677, so the sentence as printed cannot be right and no quotation of it appears here. Method: Internal inconsistency: De analysi could not have been sent to Barrow in 1699, since Barrow died in 1677. |
C-L010 |
When the English legal year began | Child, p. 171 n. 82: "the commencement of the legal year in England was altered from May 25 to January 1" Source 230 |
The English legal year began on 25 MARCH (Lady Day), not 25 May general scholarship / Source 280 editorial note |
Resolved: Child is wrong; it is 25 March. His worked example (November 18/28 1676) is nonetheless correct. Method: Cross-checked against the Wilkins note on Phil. Trans. no. 342 and the standard rule for double-dating between 1 January and 25 March. |
C-L011 |
The "D-ism / Dot-age" title | Babbage: "I suggested that the most appropriate title would be: The Principles of pure D-ism in opposition to the Dot-age of the University" Source 239 |
It is often quoted as though it were the actual title of an Analytical Society publication common secondary usage |
Resolved: the title was a suggestion, recalled by Babbage in 1864, and nobody used it. The volume appeared as Memoirs of the Analytical Society (Cambridge, 1813), so the line is Babbage's joke rather than a title page. Method: Read Babbage, Passages from the Life of a Philosopher, pp. 28-30 and his own bibliography of the 1813 Memoirs. |
C-L012 |
Whether Newton wrote the anonymous 1715 Account | Yes: Wilkins's edition states "This Account appeared anonymously, but is known to have been written by Sir Isaac Newton"; Newton's holograph draft survives as CUL MS Add. 3968 ff. 67r-96v (c. 24,000 words), cataloged by the Newton Project Source 280;Source 282 |
The article itself carries no author and speaks of Newton in the third person throughout Source 280 |
Resolved beyond doubt by the surviving manuscript: the holograph draft is in Newton's own hand, CUL MS Add. 3968 ff. 67r-96v. It is the single most damning documented fact in the affair and it needs no hedging. Method: Read the published text in full and checked the Newton Project catalog record for the holograph. |
C-L014 |
Composition and dates of the 1712 Royal Society committee | Conventionally: Arbuthnot, Hill, Halley, Jones, Machin, Burnet, Robartes, Bonet, de Moivre, Aston, Brook Taylor; appointed 6 March 1711/12, reported 24 April 1712 common secondary accounts |
Newton, anonymously: "The Committee was numerous and skilful and composed of Gentlemen of several Nations"; he names nobody. Kollerstrom names only Halley, as secretary "for the three months of its existence" Source 280;Source 284 |
Resolved for membership. De Morgan, Essays on the Life and Work of Newton (1914), pp. 27-29 (S288), names all eleven: Halley, Jones, De Moivre and Machin (mathematicians and Newton's friends); Brook Taylor (mathematician, friend of Keill); Robartes, Hill, Burnet, Aston and Arbuthnot (non-mathematicians, Aston and Arbuthnot 'intimate personal friends of Newton'); and Bonet, the Prussian minister in London. They were appointed 'at different times in March' 1712 and reported in April 1712. De Morgan states that the names were never officially published with the report, which is exactly why Newton's anonymous Account (S280) could say only 'numerous and skilful and composed of Gentlemen of several Nations', the several nations being Bonet. Still open: the day-level dates conventionally given, appointed 6 March 1711/12 and reported 24 April 1712, are not confirmed by any full text obtained, so the dates read March 1712 and April 1712 until somebody reads the Royal Society Journal Book. De Morgan's verdict: 'the Committee ... were not judges at all'; the members were 'unscrupulous partisans'; Leibniz was given no notice and never invited to produce documents. Method: Read De Morgan 1914 in full text on archive.org (public domain); cross-checked against S280 and S284 |
C-R001 |
Cauchy's death year | Cauchy (1789-1867) Source 360 (matharticles.com reprint of Grabiner 1983, p. 185) |
Cauchy died 23 May 1857 at Sceaux Source 372 |
1857 is correct; the 1867 in the reprint is a typographic error and not a scholarly claim Method: cross-check against biography; the error appears only in this reprint |
C-R002 |
Wording of Cauchy's 1823 methodological motto | 'avec la simplicite que produit la consideration directe des quantites infiniment petites' Source 367 n.11 |
'avec la simplicite qui resulte de la consideration directe des quantites infiniment petites' Source 362 (1823 first edition, Avertissement) |
The 1823 first edition reading stands. The other wording changes the phrasing and not the meaning, and the primary is what this book quotes. Method: read the primary scan |
C-R003 |
Abel's 'invention of the devil' quotation | 'The divergent series are the invention of the devil, and it is a shame to base on them any demonstration whatsoever', commonly attributed to a letter to Holmboe of 16 January 1826 Source 385 (attributes only to a popular secondary book, with no letter, recipient or date) |
Abel's securely attested printed sentences on divergent series are in the 1826 binomial memoir Source 364 (Oeuvres 1881, vol. 1, pp. 66-67) |
Resolved. The letter is genuine and the received English wording is a translation of a translation. Abel to Holmboe, dated 16 January 1826, written from Berlin and not Paris, which he reached only in July 1826. Dano-Norwegian original, p. 16: “Divergente Rækker ere i det Hele noget Fandensskab, og det er en Skam at man vover at grunde nogen Demonstration derpaa.” French translation printed in the same 1902 volume by P. G. la Chesnais, p. 16: “Les séries divergentes sont en bloc une invention du diable, et c'est une honte que l'on ose fonder sur elles la moindre démonstration.” So four things follow. ‘Invention of the devil’ is la Chesnais's phrase and not Abel's, who wrote ‘noget Fandensskab’, ‘some devilry’. The English drops Abel's qualifier ‘i det Hele’ and ‘en bloc’, meaning on the whole, which turns a hedge into an absolute. The second half, ‘it is a shame that one dares found any demonstration on them’, is faithful. And the volume's editors argue the letter was written on 14 January and dated 16 January when it was sent. All of that is documented, so the sentence can appear here with the original beside the translation and with the caveat attached (S490). Method: Read both texts verbatim in the 1902 Memorial (archive.org item nielshenrikabelm00hols) through the item's own full-text index (fulltext/inside.php), which returns the surrounding paragraph and the scan leaf; printed page numbers taken from the item's nielshenrikabelm00hols_page_numbers.json (leaf 161 = p. 13 and leaf 164 = p. 16 of the French section; leaf 297 = p. 13 and leaf 300 = p. 16 of the parallel original-language section). Translator identified at leaf 16; the editors' dating note (“mais est certainement du 14”) at leaf 265; ‘lettre à Holmboe datée de Berlin’ at leaf 461. |
C-R004 |
Wording of the Hermite quotation | 'I turn away with fright and horror from this lamentable plague of functions with no derivatives' common English rendering, incl. the project brief |
French original: 'Je me detourne avec effroi et horreur de cette plaie lamentable des fonctions continues qui n'ont point de derivees' Source 365 (Correspondance vol. II, Lettre 374, 20 May 1893, p. 318) |
Primary settles it. 'effroi et horreur' = dread/fright and horror; and the functions are CONTINUOUS functions with no derivatives. English versions that drop 'continuous' destroy the point Method: read the primary French text |
C-R008 |
When Cauchy went into exile with Charles X | Cauchy followed Charles X into exile in 1830 project brief / common accounts |
Cauchy left Paris September 1830 for Switzerland, then Turin, and went to Prague to tutor Charles X's grandson only in 1833 Source 372 |
MacTutor's staged chronology is the accurate one. The 1830 departure and the 1833 Prague tutorship are different events. Method: biography read |
C-R009 |
Weierstrass's age on becoming professor | Professor at 39, after one paper project brief / common accounts |
Berlin professorship October 1856; born 31 October 1815, so 40 turning 41 Source 373 |
MacTutor's dating is the accurate one. The '39' probably comes from his age, 38, when the 1854 Abelian functions paper appeared. Method: biography read; arithmetic checked |
C-R010 |
Length of Weierstrass's schoolteaching | 14 years project brief |
Deutsch Krone 1842-1848, Braunsberg from 1848, university post October 1856: roughly 14-16 years depending on what is counted Source 373 |
'Roughly fourteen years' holds up for 1842 to 1856 in secondary schools. The count runs from 14 to 16 depending on what you include, so 'roughly' is the honest word and a precise number is not. Method: biography read |
C-R011 |
Kovalevskaya's Stockholm chair | The first professorship for a woman in northern Europe, 1889 project brief |
'the first woman since the physicist Laura Bassi and Maria Gaetana Agnesi to hold a chair at a European university', June 1889 (extraordinary professor from June 1884) Source 374 |
MacTutor's careful formulation is the accurate one: Kovalevskaya was 'the first woman since the physicist Laura Bassi and Maria Gaetana Agnesi to hold a chair at a European university', in June 1889. She had been an extraordinary professor since June 1884, which the bare '1889' hides. Method: biography read |
C-R014 |
Who first constructed the real numbers | Dedekind and Cantor, 1872 standard textbook accounts |
Meray published 'the earliest coherent and rigorous theory of the irrational numbers to appear in print' in 1869 Source 378 |
Meray has priority in print, with 'the earliest coherent and rigorous theory of the irrational numbers to appear in print' in 1869, three years before the 1872 work of Dedekind and Cantor. Textbooks routinely leave him out, which is the reason to name him. Method: biography read |
C-R017 |
When Bolzano's function was published | 'published in 1922' Source 386 abstract and section heading |
'The manuscript Functionenlehre was published in Prague in 1930 (in the Schriften I)' / MacTutor: first published 1930 by Rychlik Source 386 body; Source 384 |
Resolved: the PROOFS (Rychlik, Jarnik) were published in 1922; the MANUSCRIPT was published in 1930. S386 is internally inconsistent on this Method: internal comparison plus MacTutor |
C-R018 |
What Bolzano proved about his function | Bolzano exhibited a continuous nowhere-differentiable function Source 386 abstract |
MacTutor calls it a 'continuous but nowhere monotonic function'; S386's body says Bolzano proved only that the non-differentiability points are DENSE, and his continuity argument was 'not completely correct' Source 384;Source 386 body |
Resolved, and the precision matters: Bolzano constructed the function around 1830, and Rychlik and Jarnik proved the full theorem in 1922. The priority claim only holds in that form. Method: internal comparison plus MacTutor |
C-R019 |
First publication of the Weierstrass function | 'Weierstrass ... giving the first published example' in 1872 Source 389 |
Presented 18 July 1872; first PUBLISHED in 1875 by du Bois-Reymond in Borchardt's Journal Source 386 |
Resolved: presented 1872, published 1875 by someone else Method: cross-check of two sources |
C-E18003 |
The formula in the Euler-Diderot anecdote | (a + b^n)/n = x Source 313 |
Thiebault prints (a + b^n)/z = x, in italics; De Morgan miscopied the z as n and Cajori, Bell, Smith, Sanford and Hogben followed him Source 314 |
Resolved in favor of S314, which examined the printed text and states explicitly that the letter 'is however z clearly enough and not n'. The famous formula is therefore itself a transcription error inside a fabricated anecdote. Method: Gillings 1954 footnote 7 read in full; note that the underlying Thiebault volume was not independently checked |
C-E18004 |
Who is the mathematician in the Diderot anecdote | Euler, named Source 313 |
Thiebault does not name anyone; he writes 'a Russian philosopher, a learned mathematician and a distinguished member of the Academy'. De Morgan supplied the name Euler Source 314 |
Resolved. Both articles agree that the naming is De Morgan's addition. Gillings concedes Thiebault's phrase 'seems rather definitely to refer to' Euler, but a strong inference is not a source. Method: Both articles read in full |
C-E18008 |
Who first used the word 'integral' in its modern sense | Jacob Bernoulli, Acta Eruditorum, May 1690, p. 218 ('Ergo et horum Integralia aequantur'); the DSB calls this the first use in the present mathematical sense Source 324 |
Johann Bernoulli also claimed it, and D. E. Smith credits him with 'the use of the term integral in its technical sense in the calculus' Source 324 |
Resolved by separating two things. The first printed occurrence of the word is Jacob's, in 1690; the naming of the branch, calculus integralis, is Johann's proposal, which Leibniz accepted in 1696 over his own preferred calculus summatorius. Both belong in the story. Method: Read Miller's entries for INTEGRAL and INTEGRAL CALCULUS, including the Cajori and Smith citations, in full |
C-E18009 |
Whether the 'ghosts of departed quantities' passage is punctuated as a statement or a question | The Luce & Jessop editorial summary prints 'The velocities of evanescent increments.' with a full stop and encloses the last clause in quotation marks Source 310 |
Berkeley's body text at S.35 prints 'The velocities of evanescent increments?' with a question mark and no internal quotation marks Source 310 |
Resolved in favor of the body text, which prints a question mark where the editors' summary prints a full stop. The whole passage is a chain of rhetorical questions, which is the point: Berkeley is interrogating, not asserting. Method: Compared the editors' summary and the printed section within the same critical edition |
C-E18011 |
Frederick the Great's alleged 'cyclops' jibe at Euler | Frederick mocked the half-blind Euler behind his back as a 'limited cyclops' (widely repeated in popular biographies) - |
No such remark appears in MacTutor's biography of Euler, in Wikiquote's sourced Frederick II page, or in the Gutenberg text of the Voltaire-Frederick correspondence Source 326 |
Resolved, and the popular version is wrong in its framing. The jibe is real and locatable: Frederick II to Voltaire, 25 January 1778, writing about the failed Sanssouci fountain, calls him 'the Cyclop Euler' (Eckert's translation, S342): 'I wanted to make a fountain jet in my Garden; the Cyclop Euler calculated the effort of the wheels for raising the water to a basin ... My mill was constructed mathematically, and it could not raise one drop of water to a distance of fifty feet from the basin. Vanity of Vanities! Vanity of mathematics.' So it is one remark in one letter, written in 1778 about events of 1749, and not a standing nickname. It is also unjust: Eckert shows Euler was involved for about a month in autumn 1749, correctly diagnosed that the pump capacity was too large, warned Frederick, and was ignored. The sentence and Eckert's correction belong together. The French wording has not been checked against the Trier Oeuvres de Frederic le Grand, so the English translation is the safe one. Method: Located the letter through Eckert (Deutsches Museum), read in full text; supersedes the earlier negative search |
C-E18015 |
Whether L'Hopital concealed his debt to Johann Bernoulli | The 1696 preface names Bernoulli explicitly and invites the Bernoullis to reclaim whatever they please of the contents Source 316 |
There is not a single acknowledgment to Bernoulli in the body text, although half a dozen other people are credited by name Source 315 |
Resolved, and the resolution is the interesting part: both are true. L'Hopital made a general acknowledgment in the preface and then never credited Bernoulli for a single specific result. The contract required Bernoulli's silence, so the preface was the most L'Hopital could concede without breaching his own arrangement. It is a case study in how a technically honest statement can still mislead. Method: Read the 1716 preface in the original French and Truesdell's section IV in full |
C-N002 |
Who introduced the arrow in limits | Commonly credited to G. H. Hardy, A Course of Pure Mathematics (1908) (common textbook claim) |
J. G. Leathem introduced it in Volume and Surface Integrals Used in Physics (1905); Hardys own Preface credits "Mr J. G. Leathem and Mr T. J. IA. Bromwich"; Leathem stated in 1925 that it "has been erroneously attributed to another writer owing to its use, with inadvertent omission of acknowledgment, in an important book published three years later" Source 451;Source 452 |
Resolved for Leathem 1905. Hardy popularised it and said so. The "three years later" book is Hardys. Method: Cajori S 636 and Miller quote both Hardys Preface and Leathems 1925 Preface in full |
C-N003 |
Who introduced the partial-derivative symbol | Universally credited to Jacobi, 1841 (common textbook claim) |
Condorcet used a rounded d for a partial difference in 1770; Legendre published the modern form in 1786 and abandoned it in 1787; Jacobi reintroduced it in 1841 without any historical check Source 451;Source 452 |
Resolved as a three-stage story. Cajori S 611: "the mathematical public, uncritical on matters of priority, is crediting Jacobi with devices first proposed by Legendre and Hamilton." Jacobi is the reason we use it; Legendre is the reason it exists. Method: Read Cajori SS 596 and 611 in full, including Legendres and Jacobis own sentences |
C-N006 |
Date of the epsilon in Cauchy | Existing row T-R365 dates the epsilon of rigor to 1823 Source 360;Source 362 |
Cajori S 634 and Miller both cite Cauchy, Cours danalyse (1821), pp. 49, 50, 61, and Oeuvres II.3 p. 54, for epsilon used as an arbitrary small quantity in a limit argument Source 451;Source 452 |
Resolved in favor of 1821 for the symbol in use and 1823 for the first full epsilon-delta proof, in Calcul infinitesimal, Lecon 7. Both dates are right about different things. Method: Read Cajori S 634 and Millers Delta and epsilon entry, which quotes the 1821 passage |
C-N007 |
Whether the definite-integral limits are Fouriers 1822 or earlier | Fourier, Theorie analytique de la chaleur (1822), p. 252 Source 452 |
Cajori S 623: "Fourier had used this notation somewhat earlier in the Memoires of the French Academy for 1819-20, in an article of which the early part of his book of 1822 is a reprint" Source 451 |
Resolved: Fourier in both cases. The first appearance is a paper of 1819-20 and the famous one is the 1822 book, so the notation is Fourier's, 1822, and earlier in 1819-20. Method: Cajori S 623 read in full |
C-N012 |
What "continuous" means in an eighteenth-century text | Modern: a function with no jumps, defined by an epsilon-delta or limit condition Source 361;Source 363 |
Euler, Introductio vol. 2 (1748): "A continuous curve is one such that its nature can be expressed by a single function of x", and a curve needing different functions on different parts "we call discontinuous" Source 453 |
Resolved, and it is a trap worth knowing about: the two senses are not merely different, they can disagree outright. A function given by two formulas that agree at the join is discontinuous in Euler's sense and continuous in ours. Method: Millers CONTINUOUS entry read in full, quoting Euler via Katz p. 524 |
C-U411 |
Whether Whewell coined "scientist" and about whom | The word appears in the 1834 Quarterly Review article, attributed by the anonymous author to "some ingenious gentleman" at the British Association, and reported as "not generally palatable". The book under review is On the Connexion of the Physical Sciences (1834) Source 411 |
Popular accounts say Whewell coined "scientist" specifically to describe Mary Somerville, in a review of Mechanism of the Heavens (1831) popular accounts; the claim is absent from MacTutor Somerville (Source 414) and from Somerville's own memoir (Source 412) |
Resolved against the popular version, from the primary text. The review is of the wrong book, and the reviewer attributes the word to a third party rather than claiming it. What the evidence supports: the word scientist first appears in print in an anonymous 1834 review of Mary Somerville's On the Connexion of the Physical Sciences, written by William Whewell. The word appears nowhere in Somerville's Personal Recollections. Method: Read the 1834 article in full from a scan of the original, and searched the whole of Somerville's memoir for the word |
C-U412 |
Whether Mechanism of the Heavens was a required text at Cambridge | Peacock wrote on 14 February 1832 that he and Whewell "have already taken steps to introduce it into the course of our studies at Cambridge, and I have little doubt that it will immediately become an essential work to those of our students who aspire to the highest places in our examinations"; the whole 750-copy edition then sold chiefly at Cambridge Source 412 |
Commonly stated flatly as "it became a required textbook at Cambridge" popular accounts |
Resolved to the precise version. Peacock and Whewell took steps to bring the book into the course of study and expected it to be essential for the top Tripos candidates, which is not the same as requiring it of every undergraduate. Peacock's own sentence is sharper than any paraphrase of it. Method: Read the commissioning and adoption correspondence in Somerville's own memoir |
C-U416 |
Attribution of the enri (circle principle) | Modern research leads most historians to attribute the enri to Takebe Katahiro Source 430 |
For many years it was believed to be Seki's, with only the writing due to Takebe; MacTutor's Seki page still credits Seki with "undocumented calculus discoveries" Source 429 |
Resolved in favor of Takebe, on the explicit statement of the more detailed page. The enri is not Seki's, and this is a reattribution from master to pupil, which runs the opposite way from the usual direction of these corrections. Method: Compared the two MacTutor pages, which disagree in emphasis |
C-U418 |
Marjorie Lee Browne's doctorate year | 1949 - all requirements completed, and the convention used in her own lifetime Source 428 |
1950 - the earliest graduation ceremony was February 1950, and from 1999 some references switched to this date Source 428 |
Resolved as a documented ambiguity with a known cause: she completed the requirements in 1949 and the earliest graduation ceremony was February 1950. The full form is completed 1949, conferred February 1950. Method: MacTutor states both facts and the reason for the discrepancy |
C-U419 |
Whether Rumelhart, Hinton and Williams invented backpropagation | No. It was "brought to fame" by them in 1986; the reverse mode was published by Linnainmaa in 1970, formalised by Werbos in 1974, and implemented automatically by Speelpenning in 1980 Source 436 |
A very common textbook and press claim that the 1986 paper introduced the algorithm popular accounts |
Resolved. Two independent peer-reviewed surveys say explicitly that 1986 was popularisation. Both note that the PDP group had not read Parker and that Parker had not read Werbos. Method: Read both surveys in full |
C-U422 |
Gladys West: computer model and Hall of Fame year | MacTutor text: "IBM Stretch 7073" and "inducted into the Space and Missiles Pioneers Hall of Fame in 2028" Source 426 |
The IBM Stretch was the model 7030; the Air Force induction is elsewhere dated 19 December 2018, consistent with the other 2018 honors listed in the same paragraph Source 426 (its own reference list, Colorado Springs Gazette, 19 December 2018) |
Resolved as typographical errors in the source. The machine is the IBM 7030 Stretch and not the 7073, and the Hall of Fame induction is 2018 and not 2028. Both errors are on the record here so that nobody reintroduces them from the same page. Method: Internal consistency check against the same page's own reference list |
C-LIB01 |
Who called the cycloid "the Helen of Geometers" | Whitman 1943 was the expected source for the phrase and for its coiner Source 64 |
Whitman 1943 does not contain the phrase anywhere in its eight pages; Martin 2010 (S161) uses "The Helen of Geometry" as a title with no citation Source 64;Source 161 |
Closed as unattributable from the sources available. Whitman's full text was read and searched on 2026-08-14, and the words Helen, Troy, Trojan and discord do not occur in it. The phrase has no owner here, so it carries no name. Method: Full-text read and keyword search of S064, 2026-08-14 |
C-LIB02 |
Whether Kerala mathematicians used ibn al-Haytham's summation identity | Katz 1995 states that in deriving the sine series the Indian mathematicians used ibn al-Haytham's equation for the case k=1, and sketched a proof of the general result themselves Source 61 |
Katz also states the Indian mathematicians did not refer to ibn al-Haytham or any other predecessor Source 61 |
Not a contradiction, and worth stating carefully. The identity is used and the attribution is absent. Katz treats independent rediscovery as likely and says separately that 'there seems a good chance that transmission to India did occur'. So the mathematical link is documented and the transmission is open, and they are two different questions. Method: Read S061 in full, 2026-08-14 |
C-LIB04 |
Status of du Chatelet's Principia translation | Described in this book as "still the standard French edition" Source 332 |
Allen 2007 states it is "to this day the only complete French translation of this great work" Source 69 |
Resolved to the stronger and more precise claim. Allen 2007 says du Chatelet's is 'to this day the only complete French translation of this great work', which is why it is still the standard one. Method: Read S069 in full, 2026-08-14 |
C-LIB05 |
Whether the Principia geometric style was a barrier to Continental readers | The standard story is that its classical geometry made it hard for Continental analysts to use - |
Fellmann 1988 shows Leibniz had 'not the slightest difficulty in mastering Newton's arguments in detail' (p. 20) and 'did not find it particularly difficult to convert the substance of Newton's text into his own mathematical form' (p. 24). The evidence of limited engagement is about attention, not intelligibility Source 70 |
The usual framing is wrong. The obstacle was not that Continental mathematicians could not read the Principia. Huygens, the leading Continental figure, preferred geometry himself, and Fellmann attributes his distance from the calculus to 'conservative adherence to a strictly geometrical conception' (p. 14). The analytical reworking has a dated chain: Johann Bernoulli teaching l'Hospital and Varignon in Paris from 1692, Varignon transposing the propositions into Leibnizian symbolism from 1700, then Hermann's Phoronomia in 1716, then Euler. Method: Read Fellmann 1988 in full text, 2026-08-14 |
C-LIB06 |
Page and date for the versiera passage and the "witch" mistranslation | Cupillari 2014 puts the passage at Instituzioni p. 380, spells the confused word "aversiera" with one v, does not mention Grandi, and derives "versiera" from a change of concavity or "verse" Source 75 |
Mazzotti 2001 n. 44 gives the passage at Vol. 1, p. 381; spells it "avversiera"; states the term "versiera" (Lat. "versoria") was coined by Guido Grandi in 1718; and dates the English "witch" to Colson's translation AS EDITED BY JOHN HELLINS AND PUBLISHED IN 1801, at p. 222, reading "which is vulgarly called the Witch" Source 77;Source 320 |
Resolved in favor of Mazzotti, who quotes the Italian and the English with page numbers and names the coiner. The passage is at Vol. 1 p. 381; Grandi coined versoria and versiera in 1718; and the English 'witch' comes from Colson's translation as edited by Hellins and published in 1801, at p. 222. Two refinements follow. Colson died in 1760, so he translated before then, and the printed book is 1801 with Hellins as editor, which is why both names belong on it. And Mazzotti hedges the mechanism with 'perhaps because of an interesting confusion with... avversiera', so 'probably' is as far as the evidence goes and 'because' goes further than she does. Method: Read Mazzotti 2001 and Cupillari 2014 in full text, 2026-08-14. SEPARATE NOTE: Cupillari 2014 p. 5 prints the versiera as y = 1/sqrt(1+x^2), which contradicts her own opening on the same page and her own algebra. It is a published typo. Do not propagate it. |
C-LIB07 |
The Bologna chair: appointed, offered, or neither | Cupillari 2014 says the Pope offered the position and "she never took the position", without dates Source 75 |
Mazzotti 2001 documents it: Benedict XIV's letter of 10 September 1750 informed her of appointment to a "lettura"; the university diploma is dated 5 October 1750 and names the post "Cattedra di Pubblico Lettore di Matematica"; "Agnesi never went to Bologna to take up this teaching post". Documents at Biblioteca Ambrosiana O.202.Sup Source 77 |
Resolved. The appointment was real, documented and dated: Benedict XIV's letter of 10 September 1750 told Agnesi of it, the university diploma is dated 5 October 1750, and the post is the 'Cattedra di Pubblico Lettore di Matematica'. She never went to Bologna to take it up. Method: Read Mazzotti 2001 in full text, 2026-08-14 |
C-LIB08 |
Agnesi's later life and death | This book previously said she "spent her remaining forty-seven years running a poorhouse for women in Milan, where she died destitute" Source 327;Source 343 |
Mazzotti 2001: she volunteered at the Ospedale Maggiore; in 1771 Archbishop Pozzobonelli asked her to direct the FEMALE DEPARTMENT of the newly opened Pio Albergo Trivulzio, which eventually housed about 450 patients; in 1783, having renounced her possessions, she MOVED IN; she died of pneumonia in January 1799 and was buried in a mass grave outside Porta Romana while war ravaged northern Italy Source 77 |
Resolved to Mazzotti, who is precise where the earlier sources were loose. Agnesi directed the female department of the Pio Albergo Trivulzio and not the institution; the directorship began in 1771 and not in 1752; and she was buried in a mass grave outside Porta Romana, which the earlier accounts leave out. Method: Read Mazzotti 2001 in full text, 2026-08-14 |
C-LIB09 |
Whether Newton had a proof of Principia Lemma 12 and withheld it | Newton prints only "Patet ex Conicis" (it is clear from the Conics) in De motu and "Constat utrumque ex Conicis" in 1687, proving nothing Source 76 |
Del Centina and Fiocca found a three-line proof in Newton's own hand, written as an unpublished "Corollary 6" in his copy of De Witt/van Schooten, a volume from BARROW'S library, using Euclid III.36. Lemma 12 as printed in 1687 is defective (the conjugate-diameter condition is missing) and the marginal corollary carries the identical defect, which is their evidence the two were written together Source 76 |
Resolved, and it refutes a specific legend. William Whiston claimed in 1749 that Newton 'saw it by intuition' and 'used it before it had ever been demonstrated by any one'. Apollonius, Saint Vincent and La Hire had all demonstrated it, and so had Newton himself in private. The limit matters: this is one lemma. Del Centina and Fiocca say nothing about calculus versus geometry in general, and the words calculus, fluxions and analysis do not appear in their paper. Method: Read Del Centina and Fiocca 2020 in full text, 2026-08-14 |
Partly resolved
| ID | Topic | One source says | Another says | Resolution |
|---|---|---|---|---|
C-A003 |
Whether Archimedes handled actual infinity | The Method demonstrates 'Archimedes' concept of absolute infinity' (Walters) / shows an understanding of infinity 'scholars believed ancient Greeks couldn't grasp' (Smithsonian) Source 4;Source 6 |
The specialists who produced the reading say the key application of Lemma 11 is left implicit: 'we did not have anything explicit in Archimedes' text to support this statement'; the text may be 'the produce of a collaboration' with later interpolation; and the argument 'does remain strange' Source 3 |
Open in principle, and the specialists who produced the reading are more careful than the press accounts of it. In Method Prop. 14 Archimedes sets up a one-to-one correspondence between two infinite collections, calls them 'equal in multitude', and then uses a proportion between infinite aggregates. The decisive inferential step is not stated by him and nobody knows who supplied it, so 'Archimedes understood infinity' claims more than the palimpsest shows. Method: Compared the institutional/press accounts with the underlying SCIAMVS paper, read in full |
C-A010 |
Death date of Ibn al-Haytham | 1040 Source 58 |
possibly 1039 (the same source allows both) ; Katz 1995 (S061) gives 965-1039 Source 58;Source 61 |
Leaning to 1039. Katz (S061), the standard English-language citation for ibn al-Haytham's calculus-adjacent work, gives 965 to 1039 without qualification, and the 1040 variant survives in other reference works. The dates read c. 965 to 1039, and the death year stays unsettled between 1039 and 1040. Method: Read Katz 1995 in full text 2026-08-14 |
C-S008 |
How much did Barrow have, and did Newton take it from him | Child: 'ISAAC BARROW was the first inventor of the Infinitesimal Calculus; Newton got the main idea of it from Barrow by personal communication'; Toeplitz: Barrow was 'the real discoverer' Source 158;Source 138 |
Whiteside: Barrow was merely 'a thoroughly competent university don' whose importance lay in 'coordinating of available knowledge'; Mahoney: 'competent and well informed, but not particularly original'; Mahnke and Hofmann concluded Leibniz was independent ; Feingold 1993 (S073) takes a third position: he explicitly declines Child's thesis, but argues the revisionist dismissal was an overcorrection produced by the priority dispute itself Source 138;Source 73 |
Explained rather than settled, which is the useful outcome. Feingold shows why the verdicts diverge: both camps had a propaganda use for Barrow. De Morgan saw it in 1835 and called Barrow 'a sort of retrenched position, on which to fall back in case of defeat'. Feingold sets his own limits and states them himself: 'Due recognition of Barrow shifts no credit for the invention of the calculus away from Newton and Leibniz' (p. 338). The dispute and its explanation belong together, and so do Feingold's argument and his disclaimer. Method: Read Feingold 1993 in full text, 2026-08-14 |
CN-01 |
Date Newton was admitted to Trinity College | Conduitt's draft memoir states Newton was admitted to Trinity 'the 5th of Iune in 1660' Source 181 (Keynes Ms. 129.02, f. 1v) |
Standard scholarship (and the college admission book) gives 5 June 1661 Source 190 (Whiteside MP 1, which works from the college records) |
Almost certainly a slip by Conduitt. The admission date is 5 June 1661, and Conduitt's draft memoir, an early manuscript, says 1660. Method: Compared Conduitt's draft against Whiteside's use of the Trinity admission and commons records; did not inspect the admission book itself |
C-L015 |
Charta volans | Conventionally: a single anonymous sheet dated 29 July 1713, circulated for Leibniz, quoting an unnamed "eminent mathematician" (Johann Bernoulli) from a letter of 7 June 1713 common secondary accounts |
No full text of the sheet, and no scholarly edition of it, was obtained , |
Partly resolved from a primary source. Newton's own draft reply (CUL MS Add. 9597/2/18/94, Newton Project NATP00290 = S289) establishes three things: the sheet was printed in Germany and circulated from August 1713 'without the name of the Author Publisher Printer or place'; it quoted the judgment of an unnamed eminent ('primary') mathematician from a letter dated 7 June 1713, and Newton quotes the Latin 'literis 7 Junij 1713 datis'; and Newton's charge is that 'it was set on foot by Mr Leibnitz himself'. On the date, the Newton Project titles the sheet 29 July 1713 and the Cambridge Correspondence of Isaac Newton prints it as no. 1009 dated 18 July 1713, an eleven-day gap, which is Old Style against New Style and almost certainly the same day. Still open: nobody obtained the text of the sheet itself, and the identification of the unnamed mathematician as Johann Bernoulli is an editorial inference rather than something the sheet or Newton's draft says, so 'Johann Bernoulli wrote it' goes past the documents until somebody reads Correspondence VI no. 1008-1009. Method: Read Newton's draft response in full (Newton Project normalized and diplomatic texts); Correspondence VI not obtained |
C-R005 |
Whose integral do students learn? | The Riemann integral standard textbooks |
What is taught (upper and lower sums, upper and lower integrals) is Darboux's 1875 reformulation; Riemann's own definition uses tagged sums over arbitrary partitions Source 391 (Werke, pp. 239-240) |
Riemann's own definition is the one recorded in S391, and what students learn is Darboux's 1875 reformulation. That attribution is standard, and nobody working on this book read Darboux 1875, so it stays second hand. Method: primary read for Riemann; Darboux not obtained |
C-R006 |
Publication year of Riemann's Habilitationsschrift | 1867, in Goettingen Abhandlungen vol. 13 Source 391 (header of the Werke printing) |
MacTutor gives no year for the dissertation and 1868 for the geometry lecture Source 375 |
Likely 1867 for the trigonometric-series paper and 1868 for the geometry lecture; volume 13 spans 1866-67 Method: header of the Werke reprint; needs the original Abhandlungen title page |
C-R007 |
Date of Bolzano's dismissal | Suspended December 1819 after Austrian government pressure Source 371 |
Removed from his professorship by Emperor Franz in January 1820 Source 370 |
Probably two acts rather than one: an administrative suspension in December 1819 and a formal imperial removal in January 1820. A single date says nothing here unless it also says which act it means. Method: two tier-3 sources compared; primary decree not consulted |
C-R016 |
Did Cauchy lose Galois' memoir? | Cauchy lost or suppressed Galois' memoir widespread legend, incl. the framing in the project brief |
The memoir that vanished was the February 1830 Grand Prize submission, held by Fourier, who died in April 1830. Cauchy's documented role in 1829 was to referee and advise Galois to resubmit Source 380;Source 372 |
The legend is not supported and the documents correct it. Taton 1971, the decisive study, could not be obtained (S394), so nothing here goes further than S380 does. Method: Biography read; Taton inaccessible. GAP-CLOSING PASS 2026-08-14: Persee blocks automated retrieval by robots.txt on both the document page and the docAsPDF address. Definitively unreachable by this route. |
C-E18001 |
Wording and language of Johann Bernoulli's 'lion' remark about Newton's anonymous brachistochrone solution | Bernoulli said, in Latin, 'tanquam ex ungue leonem' - 'as the lion is known by his claw' Source 321 |
Bernoulli wrote in FRENCH in the June 1697 Histoire des ouvrages des scavans, p. 455: 'par cet echantillon, comme ex ungue Leonem'; the Latin 'tanquam' is Brewster's 1831 substitution Source 337 |
Partly resolved. Brewster 1831 p. 194 was read directly and does print 'tanquam ... ex ungue leonem' as a quotation. The 1697 original could not be retrieved, so the French reading rests on a citation trail rather than on the page. Until somebody sees the 1697 text, what stands is that Bernoulli recognized Newton and said so in print, and that the Latin wording belongs to Brewster and not to Bernoulli. Method: Read Brewster 1831 in full text; searched archive.org, Google Books and Gallica for Histoire des ouvrages des scavans 1697 without success |
C-N001 |
Date of Newton's dot (fluxion) notation, and what the dots printed in the 1736 Method of Fluxions are | Two early datings. Cajori S 567: "Newtons earliest use of dots, pricked letters, to indicate velocities or fluxions is found on a leaf dated May 20, 1665", citing S. P. Rigaud, Historical Essay on ... Newtons Principia (1838), Appendix p. 23, and adding "no facsimile reproduction of it has ever been made". Separately, the 1736 printed Method of Fluxions uses dotted letters throughout for a treatise written in 1671, and popular accounts put the notation in the anni mirabiles on the strength of it Source 185 (Colson 1736, p. 20);Source 451 |
Whiteside, MP 3: 73 n.86: "Newton himself did not introduce this standard Newtonian dot-notation till late 1691." In the October 1666 tract the rates are p, q, r; in the 1671 autograph they are l, m, n, r. William Jones's 1710 transcript substituted dots and Colson translated Jones's copy, which is where the 1736 dots come from (existing register row T-NEW-05) Source 183;Source 185;Source 192 |
Half settled and half open, and the two halves come apart cleanly. Settled: the dots printed in the 1736 Method of Fluxions are William Jones's 1710 substitution and not Newton's own hand, so any image captioned 'Newton's 1666 notation' that shows dots is showing Jones's tidying-up. The October 1666 tract uses p, q, r and the 1671 autograph uses l, m, n, r. Open: Cajori's 20 May 1665 leaf of pricked letters, reported at second hand from Rigaud 1838 with no facsimile ever made, and argued over by Enestrom and Witting in Bibliotheca mathematica 1910-12. Whiteside's dating rests on the surviving manuscripts and carries the weight for what Newton habitually wrote; Cajori's leaf, if it exists, would be an isolated early instance and not a practice. So Newton's dot is first securely attested in the 1690s, reached print in 1693, and the dots you see in the 1736 book are Jones's. Method: Read Whiteside's editorial note at MP 3: 73 n.86 and checked the 1666 tract transcription independently; read Cajori S 567 in full including its footnote and compared it against the Newton-block register rows. Merged 17 August 2026 from CN-10 (resolved = yes) and C-N001 (resolved = no): one fact, two rows, opposite verdicts, because each row had answered a different half of the question. |
C-LIB03 |
The proposition numbers in Saint-Vincent that carry the hyperbola-logarithm result | Sarasa 1649 cites them directly. His marginal references read, in the Google OCR of the long-s type, "Demonstrationem vide l. 6 de Hyperb. Prop. 129" and "Demonstrationem habes l. 6 de Hyperb. Prop. 130" Source 66 |
The Elenchus (table of contents) of the Opus geometricum lists, under Liber Sextus De Hyperbola, Pars Tertia, "Proprietates admirandae de superficiebus inter hyperbolam, asymptoton unam, et duas parallelas alteri asymptoto interiacentibus" at propositions 125 to 129, and the continued-proportionals result immediately after Source 67 |
Consistent. Both witnesses point to Book VI (De Hyperbola), Part III, propositions in the 125 to 130 range. The individual digits are not legible with confidence in a 1649 long-s scan, and the two independent witnesses agree on the book and the part but not on a number, so the reference is a range rather than a single proposition. One caveat: the copy of the Opus geometricum obtained is the volume holding the front matter, the full Elenchus, and Books I to V. Book VI is not in it, so nobody has read the proposition texts. Method: Read Sarasa 1649 in full and the Opus geometricum Elenchus, 2026-08-14 |
CN-15 |
How much of the Principia's mathematics is withheld calculus | Whiteside, from the working manuscripts: the Principia is built natively from limit-ratios of infinitesimal increments, with one clear case of suppressed analysis, the solid of least resistance Source 191;Source 70 |
Guicciardini: there are 'obvious traces of the use of integration techniques in many demonstrations of the Principia' and Newton 'did not give the reader any detail on these highly algorithmic techniques'; when Gregory and Cotes asked how to finish proofs depending on the quadrature of curves, Newton told them privately how to apply his integral tables Source 204 (pp. 465-466, and n. 45 pointing to Guicciardini 1999, pp. 179-186) |
Partly resolved, and the resolution narrows CN-03 rather than settling it. Withheld quadrature working in the Principia is now established beyond Whiteside's single exception: Newton supplied the missing integrations privately to his own editor. But Guicciardini also states that the mathematics Newton put on the page is the geometric fluxional calculus of the Geometria curvilinea, using limits and not infinitesimals, which is Whiteside's picture and not Newton's 1715 one. So S204 supports 'Newton hid quadrature technique' and does not support 'Newton worked the book out in the new analysis and translated it'. Guicciardini himself calls the extent an open research front, naming Nauenberg (2001), C. Wilson (2001) and Brackenridge (2003) Method: Read S204 in full and compared it against the CN-03 record; separated the two distinct claims that CN-03 had been carrying as one |
Open
| ID | Topic | One source says | Another says | What would settle it |
|---|---|---|---|---|
C-A001 |
Date of the Archimedes Palimpsest colophon | Scribe Johannes Myronas completed the prayer book on 14 April 1229 Source 4 |
The colophon recovered by X-ray fluorescence reads 'Ioannes Myronas, on April 29, 1229' Source 6 |
Compared the two accounts; no primary transcription of the colophon obtained |
C-A004 |
Dates of Madhava of Sangamagrama | c. 1340-1420 Source 50 |
1350-1425 (MacTutor); 1340-1425 (Almeida & Joseph) Source 55;Source 51 |
Compared three secondary sources; no primary dating evidence exists, as Madhava's own works are lost |
C-A005 |
Whether Sharaf al-Din al-Tusi used the derivative | Rashed: al-Tusi's implicit use of the derivative 'arises from algebraic proofs based on analytical procedures' Source 53 |
Hogendijk: 'a rather different approach, not one analogous to the modern derivative, lay behind Al-Tusi's method' Source 53 |
Not adjudicated; primary papers not obtained (Rashed's is paywalled in Arabic Sciences and Philosophy) |
C-A006 |
Publication year of Charles Whish's paper on the Kerala series | 1835, Transactions of the Royal Asiatic Society of Great Britain and Ireland, vol. 3 Source 51 |
Commonly cited as 1834 (the year the paper was read); MacTutor project chapter does not resolve it Source 52 |
Compared secondary citations; primary volume not consulted |
C-A007 |
Whether Kerala mathematics was transmitted to Europe | Almeida & Joseph argue transmission via Jesuit missionaries is established by motivation, opportunity, communication routes, methodological similarity and evidence of Jesuit transmission activity (ARSI Goa 38/46/58) Source 51 |
Pearce: 'There is no evidence of direct transmission by way of relevant manuscripts'; the Jesuit resemblances may be 'mere coincidence'. Almeida & Joseph themselves concede there is no direct evidence and that the route to the manuscripts is conjecture. Source 52;Source 51 |
Read both arguments in full; the disagreement is about evidentiary standards, not about the facts |
C-A008 |
Date of Jyeshthadeva's Yuktibhasa | c. 1530 Source 50 |
c. 1550 Source 55 |
Compared two secondary sources |
C-A009 |
Death date of Nilakantha Somayaji | c. 1550 (implying he lived to about 106) Source 50 |
'died after 1501'; born 14 June 1444 ; Katz 1995 (S061) gives a third set, 1445-1545 Source 56;Source 61 |
Three independent date sets now on file (S050, S056, S061). No primary record of his death located. Print the birth date, which is settled, and treat the death year as disputed. |
C-A011 |
Birthplace of Aryabhata I | Kusumapura, near Pataliputra (modern Patna), in the north Source 59 |
Kerala, Tamil Nadu, Andhra Pradesh or Bengal have each been proposed Source 59 |
Noted the range of scholarly proposals reported in the source |
C-A012 |
Auction date of the Archimedes Palimpsest | 28 October 1998 Source 4 |
29 October 1998 Source 5 |
Compared two institutional sources |
C-M001 |
Bradwardine's birth year and birthplace | Born 1290 in Sussex Source 104 |
Born circa 1295 in Chichester, England Source 103 |
source_comparison |
C-S002 |
Publication year of Harmonices/Harmonice Mundi | 1618, Book V ch. 3 Source 152 |
1619 Source 154 |
source_comparison |
C-S003 |
Publication year of Arithmetica Infinitorum | 1656 Source 145 |
1655 Source 151;Source 139 |
source_comparison |
C-S004 |
Why the Jesuits suppressed indivisibles | Because the method undermined efforts to establish a perfect rational and hierarchical order modelled on Euclidean geometry Source 133 |
Because indivisibles, being non-quantitative parts, conflict with the doctrine of the Eucharist; Alexander conflates indivisibles with infinitesimals Source 132 |
expert_disagreement |
C-S005 |
Whether the indivisible/infinitesimal distinction explains the 17th-century fight | The distinction is essential; indivisibles but not infinitesimals conflict with the Eucharist Source 132 |
The Jesuits objected to all forms of the method, so the distinction cannot explain the fight Source 133 |
expert_disagreement |
C-S006 |
What Fermat meant by adequality | Approximate equality, with e best read as an infinitesimal (Weil, Mahoney, Katz-Schaps-Shnider) Source 130 |
Breger: adaequare means simply 'to set equal', a formal algebraic procedure with no element of approximation Source 130 |
expert_disagreement |
C-S007 |
Who first established that differentiation and integration are inverse operations | Gregory proved it in Geometriae pars universalis (1668) Source 136 |
Barrow 'was the first to recognize that integration and differentiation are inverse operations' (Lectiones Geometricae, 1670) Source 140 |
date_comparison |
C-S009 |
Fermat's birth year | 17 August 1601, Beaumont-de-Lomagne Source 144 |
A rival tradition gives 1607/1608 (arising from a baptismal record); MacTutor notes 'some dispute exists about this date' Source 144;Source 130 |
internal_flag |
C-S013 |
Publication year of Sluse's tangent rule | 1672, Philosophical Transactions Source 146 |
1673 is also widely cited (no source read confirms 1673) |
single_source |
CN-03 |
Did Newton find the Principia's results by calculus and then recast them geometrically? | Newton, anonymously, 1715: 'By the help of the new Analysis Mr. Newton found out most of the Propositions in his Principia Philosophiae: but because the Ancients ... admitted nothing into Geometry before it was demonstrated synthetically, he demonstrated the Propositions synthetically ... And this makes it now difficult for unskilful Men to see the Analysis by which those Propositions were found out' Source 189 (Phil. Trans. 29 no. 342, p. 206) |
Whiteside, from the working manuscripts: the Principia's 'underlying mathematical edifice is in the main built up from demonstrations ... appealing in a wholly non-classical manner ... to the limit-ratios of infinitesimal ... increments'; 'there is no evidence that Newton sought deliberately to be any more esoteric therein than he needed be'; and Newton's 1715 claim 'was very much in the current fashion' (Johann Bernoulli said the same of his own work). Whiteside identifies exactly ONE clear case of suppressed analysis: the solid of least resistance, Bk II Prop. XXXV (1687) ; Fellmann 1988 (S070) does not state the received claim at all, and independently corroborates only Whiteside's single exception, the solid of least resistance Source 191 (Whiteside MP 6: 24-26, incl. note 74);Source 70;Source 72;Source 204 |
Still open. NEW AND ACTIONABLE: Cohen's Guide to the Principia addresses this directly at section 5.8, titled 'Methods of Proof versus Method of Discovery; The New Analysis and Newton's Allegations about How the Principia Was Produced; The Use of Fluxions in the Principia', at Guide p. 122, with related material at 5.4 (p. 114), 6.2 (p. 129), 10.7 (p. 316) and 10.13 (p. 345). Cohen's word 'Allegations' shows he treats Newton's 1715 account as a claim to be assessed. The PDF obtained contains the Guide's table of contents only, not its body. Guide pp. 114-117, 122-127, 316-317 and 345-347 are now the highest-value unobtained pages in the whole Newton block, ahead of Guicciardini. PARTLY NARROWED 17 Aug 2026 by Guicciardini 2004 (S204), logged separately as CN-15. S204 establishes that quadrature working was withheld from the Principia and supplied privately to Gregory and Cotes, which goes beyond Whiteside's single exception; it does NOT endorse the 'worked in calculus, then translated' story, because it describes the book's own mathematics as the geometric fluxional calculus of the Geometria curvilinea, built on limits rather than infinitesimals. S204 n. 44 and n. 45 point to Reading the Principia (1999), pp. 179-186, for the detailed reading. Cohen's Guide remains the top request. |
CN-05 |
When the gravity insight happened | Conduitt: 'in the year 1665 when he was retired to his own estate on account of the Plague, he discovered his system of gravity' Source 181 (f. 2v) |
Newton's own memorandum (CUL Add. 3968.41, f. 85r): November 1665 direct method of fluxions, January 1666 theory of colours, May 1666 inverse method, 'And the same year I began to think of gravity extending to the orb of the moon ... All this was in the two plague years of 1665 and 1666' Source 190 (Whiteside MP 1: 152 n.25, giving the shelfmark and the printing history) |
Compared two retrospective testimonies against each other and against Whiteside's editorial assessment |
CN-07 |
Newton's decimal-place showing-off: pi, or logarithms? | Widely repeated: Newton computed pi to 15 (or 16) decimal places in 1666 using the binomial series, and said 'I am ashamed to tell you to how many figures I carried these computations, having no other business at the time' Tier-4 web sources only (Wikipedia-derived). I could NOT trace this quotation to any manuscript, critical edition or scholarly citation |
VERIFIED ALTERNATIVE: Newton's own note (CUL Add. 4000, f. 14v): 'in summer 1665 being forced from Cambridge by the Plague I computed y[e] area of y[e] Hyperbola at Boothby in Lincolnshire to two & fifty figures by the same method.' Whiteside: that is 51 decimal places, correctly rounded to 50D. The working sheets are CUL Add. 3958, ff. 78r-80v, which Cambridge's own catalog describes as 'logarithms up to more than 50 decimal places' Source 190 (MP 1: 8); Source 199 (CUDL MS Add. 3958) |
Searched Whiteside MP 1 full text for 'ashamed' (no hits) and for the pi digits; traced the quotation only to tertiary sources |
CN-08 |
How many words of alchemy Newton wrote | Frequently attributed to Keynes: 'about a million words' Common secondary usage |
Keynes 1946, actual wording: 'I have glanced through a great quantity of this at least 100,000 words, I should say.' That is Keynes's estimate of what HE read, not a total for the corpus Source 193 |
Read Keynes's exact sentence; could not reach the Chymistry project's own word-count statement (robots-blocked) |
CN-09 |
Was 'standing on the shoulders of giants' a jab at Hooke? | Popular reading (associated with Robert K. Merton and with the claim that Hooke was short and stooped): the line was a sneer Secondary/tertiary |
Against: the metaphor is a medieval commonplace attributed to Bernard of Chartres by John of Salisbury; the immediately preceding sentences credit Descartes and then Hooke generously; and the February 1675/6 letter belongs to a conciliatory phase of the relationship Source 197 (catalog record and quoted text; FULL TEXT NOT YET VERIFIED) |
Located the manuscript (HSP item 9792) and the critical-edition reference but could not obtain a verified full transcription |
CN-11 |
Newton's only speech in Parliament | Widely repeated: Newton spoke once in the Commons, to ask that a window be closed (or opened) No source found. Circulates only in tier-4 material |
The History of Parliament's scholarly register records no speech by Newton at all, and describes him as not 'a particularly active Member' whose main business was the coinage bill Source 201 |
Read the History of Parliament entry in full; searched for an early printed source and found none |
CN-12 |
Is Newton's proof of Principia Book I Prop. I (Kepler's area law) mathematically adequate? | Whiteside (MP 6, note 19) and E. J. Aiton (1989): the continuum limit is inadequate; it applies only to infinitesimal arcs Source 191 (Whiteside MP 6) as reported in Source 202 |
Nauenberg: 'the critics of Prop. 1 have misunderstood Newton's fundamental limit argument by neglecting to consider the justification for this limit which he gave in Lemma 3'; neither Whiteside nor Aiton commented on Lemma 3 Source 202 |
Read Nauenberg's paper in full; did not read Aiton 1989 |
CN-13 |
The date of William Chaloner's execution | 22 March 1699, at Tyburn Tertiary sources only |
The Newton Project dates Chaloner's last surviving letter to Newton to early March 1698/9, which is consistent Source 196 |
Checked the Newton Project MINT catalog dating; did not reach a primary execution record |
C-L003 |
Date Leibniz was elected FRS | 9 April 1673 Source 235 |
19 April 1673 (widely printed elsewhere) - |
Neither date verified against a primary record. |
C-L005 |
Page references printed in the 1686 subtitle of De geometria recondita | The OCR of the 1686 Acta reads "in Actis a. 1684, Maji p. 233; Octob. p. 264; Decemb. p. 586" Source 233 |
Walker's 1929 translation prints "Maji, p. 233; Octob. p. 467; Decem. p. 585" and footnotes: "The errors in the pages to which reference is made have been corrected by the translator." Source 232 |
Compared the Latin scan OCR with the translator's corrected text; page image not yet inspected. |
C-L013 |
Leibniz's funeral | MacTutor: "his only mourner was his secretary"; and quotes "He was buried more like a robber than what he really was, the ornament of his century" Source 235 |
The Stanford Encyclopedia entry on Leibniz contains no statement about the funeral at all Source 236 |
Checked both reference works; no primary source obtained. |
C-R012 |
When Kovalevskaya reached Berlin | 1870 Source 373 (MacTutor Weierstrass) |
1871 Source 374 (MacTutor Kovalevskaya) |
two pages of the same source compared |
C-R013 |
Year of Kovalevskaya's Prix Bordin | 1888 Source 374 (main text); project brief and standard accounts |
The retrieved MacTutor text renders it as 1886 in one rendering of the same page; 1889 is also printed in some accounts Source 374;Source 417 |
Noted the discrepancy in retrieval and the internal inconsistency in the existing register entry |
C-R015 |
Date of Dirichlet's Fourier-series convergence paper | 1828, in Crelle's Journal Source 379 |
Standard bibliographies give 1829 for 'Sur la convergence des series trigonometriques', Crelle vol. 4 standard bibliography (not retrieved in full this session) |
noted only |
C-R020 |
Was Cauchy's 1821 sum theorem wrong? | The theorem is false as stated; the missing hypothesis is uniform convergence; Cauchy's use of infinitesimals is 'precisely' what stopped him seeing it (Bottazzini); the epsilon-delta reading is the right frame (Grabiner) Source 360;Source 367 quoting Bottazzini 1986, pp. 115-116 |
Cauchy's procedures find better modern proxies in infinitesimal frameworks; his 1853 condition is stated with infinitely large n and infinitesimal remainder, not with alternating quantifiers, so the received account is internally inconsistent (Laugwitz, Katz et al.) Source 367;Source 368 |
both sides read in full; primaries read in full |
C-R021 |
Did Cauchy take his program from Bolzano? | Cauchy took his rigorization program, definition of continuity, convergence criterion and IVT proof from Bolzano's 1817 paper without acknowledgment Grattan-Guinness, Development of the Foundations of Mathematical Analysis from Euler to Riemann (1970), p. 54, as reported in Source 360 n.30 |
'not, in my opinion, valid; the similarities are better explained by common prior influences, especially that of Lagrange' Source 360 n.30 (Grabiner) |
One side read in full; Grattan-Guinness not obtained. GAP-CLOSING PASS 2026-08-14: re-verified Grabiner's exact sentence in the full text of 'Who Gave You the Epsilon?' (S360): the contention 'that Cauchy took his program of rigorizing analysis, definition of continuity, Cauchy criterion, and proof of the intermediate-value theorem, from Bolzano's paper without acknowledgment is not, in my opinion, valid', the similarities being better explained by 'common prior influences, especially that of Lagrange'. Grabiner's documented rebuttal (her 1984 'Cauchy and Bolzano' paper) and Grattan-Guinness 1970 p. 54 were both still unobtainable. Present as a dispute, naming Grattan-Guinness and Grabiner. |
C-E18002 |
Edition of Thiebault's Mes souvenirs, the sole source of the Euler-Diderot anecdote | Paris, 1801, 5 vols Source 313 |
Paris, 1804, 3 vols; the passage is on p. 141 of vol. 3 Source 314 |
Compared the bibliographies of two peer-reviewed articles both read in full; no copy of Thiebault obtained |
C-E18005 |
Whether Johann Bernoulli backdated the Hydraulica to claim priority over his son | Hydraulica appeared in print in 1743, backdated to 1732; Johann did not mention it to Euler until October 1738, after Daniel's Hydrodynamica appeared in April/May 1738 Source 333 |
The printed title is 'Hydraulica nunc primum detecta ac demonstrata directe ex fundamentis pure mechanicis. Anno 1732', in Opera omnia 4: 387-493 (Bousquet, Lausanne and Geneva, 1742) Source 336 |
Read Tou's timeline in full; Craik's reference list only (paywalled). Truesdell's Opera Omnia II.12 introduction and Darrigol ch. 1 not obtained |
C-E18006 |
Publication year of Johann Bernoulli's Opera omnia (containing the Hydraulica) | 1743 Source 333 |
1742 Source 336 |
Compared a conference timeline with a journal reference list |
C-E18007 |
Publication year of vol. 2 of Agnesi's Instituzioni analitiche | Vol. 1 in 1748, vol. 2 'the following year' (1749) Source 327 |
The Biblioteca de la Universidad de Sevilla copy of Tomo II carries the imprint MDCCXLVIII (1748) Source 319 |
Inspected the title-page transcription in the OCR of two separate scans |
C-E18010 |
Length of the brachistochrone extension granted at Leibniz's request | Extended from six months to twelve months Source 321 |
Extended so that French and Italian mathematicians would have time; MacTutor does not give a length; other accounts say to Easter 1697 Source 330 |
Read both accounts; no primary Acta Eruditorum announcement obtained |
C-E18012 |
Whether James Gregory had the Taylor series before Taylor | Widely repeated: Gregory had the general series in a 1671 letter to John Collins - |
Gibson's forensic study of the priority question does not mention Gregory at all; MacTutor's page on Taylor's dispute with Continental mathematicians does not mention him either Source 312;Source 331 |
Read Gibson 1921 in full and MacTutor's Taylor pages; neither supports the Gregory claim |
C-E18013 |
Chronology of Euler's blindness | Eyesight trouble from 1738 through overstrain on cartographic work; one eye lost by 1740 Source 326 |
Calinger argues the problems started earlier, and that a 1753 portrait shows the left eye still good and the right poor but not blind Source 326 |
MacTutor reports Calinger's revision alongside the traditional account; Calinger's book not obtained |
C-E18014 |
Whether Newton solved the brachistochrone 'in twelve hours' after returning from the Mint | MacTutor: solved it in an evening after returning from the Royal Mint, working until 4 a.m. Source 330 |
Brewster's 'received this problem about five o'clock in the afternoon, as he was returning from the Mint' is attached to LEIBNIZ'S 1716 orthogonal-trajectories problem, not to the 1697 brachistochrone Source 321 |
Read Brewster p. 194-195 in full and MacTutor's brachistochrone page; Whiteside vol. 8 not obtained |
C-N004 |
Who made the jiba/jaib mistranslation that produced "sine" | Existing register row T-A003 credits Gherardo (Gerard) of Cremona, c. 1150 Source 60 |
Miller: "Accounts differ on who was responsible for the subsequent confusion with jaib and who first translated this word into Latin." Robert of Chester (1145) is the other candidate commonly named Source 453 |
Compared the existing register row against Millers SINE entry read in full |
C-N005 |
First use of the word "integral" | Existing row T-E18001: Jacob Bernoulli, Acta Eruditorum May 1690, p. 218 Source 324 |
Cajori S 620 reports Johann Bernoulli as the one "who used the term integral (first employed by Jacob Bernoulli, see S 539)" and dates the Leibniz-Bernoulli naming negotiation to their correspondence of 1696; Smith dates Johann Bernoullis proposal of calculus integralis to 1690 Source 451;Source 453 |
Cajori S 620 read in full and compared with Millers INTEGRAL CALCULUS entry and existing row T-E18002 |
C-N008 |
Stirlings approximation: De Moivre or Stirling | Named for James Stirling, whose Methodus Differentialis (1730) Prop. 28 Ex. 2 p. 136 contains the formula Source 453 |
De Moivre had the asymptotic form n! ~ C n^(n+1/2) e^(-n) without the constant; Stirling supplied C = sqrt(2 pi) (secondary, unverified at primary level) |
Millers STIRLINGS FORMULA entry read in full; De Moivres text not obtained |
C-N009 |
Whether Stigler credited his own law to Merton | Widely repeated: Stigler proposed the law in a self-exemplifying way and named Robert K. Merton as its true discoverer (tertiary sources only) |
Not verified. The 1980 paper is behind a paywall (HTTP 403) and no authorised full text was reachable from this environment Source 460 |
Attempted publisher fetch; no open-access copy found |
C-N010 |
IPA for Zu Chongzhi | Existing row P-A021 gives /tsu ʈʂʊŋ ʈʂɻ̩/ (register row P-A021) |
Standard Mandarin Chong is aspirated: [ʈʂʰʊŋ]. Suggested correction /tsù ʈʂʰʊ́ŋ ʈʂɻ̩́/, respelling unchanged (dzoo choong-JRR) Source 463 |
Applied the pronunciation convention set out in S463 |
C-N011 |
Respelling for Descartes | Existing row P-S134 gives "ruh-NAY day-KART" (register row P-Source 134) |
French [ʁəne dekaʁt]: the first syllable of Descartes is closer to "deh" than "day". Suggested "ruh-NAY deh-KART" Source 463 |
Applied the pronunciation convention set out in S463 |
C-U410 |
Year of Sophie Germain's Institut de France elasticity prize | The prize-winning third attempt was in the re-opened contest of 1815 Source 410 |
The prize is very widely printed, in popular and semi-scholarly accounts, as having been awarded in 1816 (the brief for this research block gave 1816) popular accounts (no admissible source read) |
Compared MacTutor full text against the framing in the research brief; the Institut's Proces-verbaux were not consulted |
C-U413 |
Whether Katherine Johnson used Euler's method for the Friendship 7 check | No NASA source read here names any numerical method. NASA's own biography (by Shetterly) says only that she ran "the same numbers through the same equations that had been programmed into the computer, but by hand". The 1960 technical report she co-authored contains no occurrence of the words Euler, Runge, Kutta or numerical integration; its method is an iterative correction of closed-form orbital equations with partial-derivative sensitivity analysis Source 422;Source 423;Source 424 |
The claim that she used Euler's method is extremely widespread in teaching materials, blogs and lesson plans popular accounts and Shetterly's trade book Hidden Figures (not read) |
Full-text search of NASA TN D-233 and full reading of two biographies |
C-U414 |
Number of research reports Katherine Johnson authored or co-authored | 26 Source 422 |
21 Source 424 |
Compared the two biographies |
C-U417 |
Whether Takebe performed differentiation in Tetsujutsu Sankei chapter 6 | He "stated a result in Chapter 6 which is equivalent to the statement that if a cubic polynomial takes an extreme value at a point the derivative vanishes at that point" Source 430 |
Ogawa: "It has been said that he had first done a calculation of a derivation for finding the maximum in Chapter 6 of the treatise, but that is not strictly true. A close look at the chapter will reveal that his method has nothing to do with the theory of differential." Source 430 (quoting Ogawa) |
Both positions are recorded in the same source; the primary text was not read |
C-U420 |
First calculus textbook in English | Charles Hayes, A Treatise of Fluxions, 1704 Source 439 |
Humphry Ditton, An Institution of Fluxions, 1706, is sometimes given this honor archive.org catalog record for the Ditton volume (not read) |
Compared imprint dates on archive.org; only the Hayes text was read |
C-U421 |
Errett Bishop's exact words about Keisler's textbook | The review exists: Bull. Amer. Math. Soc. 83(2) (1977), 205-208 Source 441 (MacTutor reference list) |
Widely circulated sentences ("obfuscation and devitalization of those wonderful ideas", "mathematics is common sense", "debasement of meaning") reach us only through unattributed web content tier 4, inadmissible |
Five retrieval attempts across two agents; all blocked |
C-U423 |
Authorship of the joint Young papers | William Young to Grace Chisholm Young: "our papers ought to be published under our joint names, but if this were done neither of us get the benefit of it. No. Mine the laurels now and the knowledge. Yours the knowledge only." Source 419 |
The 220 papers are cataloged under William Young's name Source 419 |
The primary letter is quoted in the source; the fuller correspondence (Grattan-Guinness) was not obtained |
C-U424 |
Whether Note G is "the first computer program" and how much is Lovelace's | The published Notes are signed A. A. L., are three times the length of Menabrea's article, and contain a loop-structured recurrence for the Bernoulli numbers with a trace table; Lovelace states in the text that she chose the harder formula deliberately to show off the engine Source 415 |
Babbage later claimed he supplied the mathematics of Note G; Menabrea's own article, which Lovelace translated, already names the Bernoulli numbers as candidates for hard-wired constants and already contains operation tables Source 415 |
Read the whole 1843 article including all seven Notes |
CN-14 |
Year of John Craig's Cambridge visit and his transcription of De methodis | Craig made copies of parts of the De methodis in 1684; Craig and David Gregory transcribed manuscripts after their visits to Cambridge in 1684 and 1694 respectively Source 204 (pp. 460, 462, citing Whiteside, Mathematical Papers vol. 7, pp. 3-4) |
Craig, having heard that Wallis was about to publish a summary of Newton's method for squaring curves in the Proposal of 1683, wrote to Newton and met him in Cambridge in 1685, and during that encounter was allowed to transcribe part of the De methodis and of the Epistola posterior; Newton had communicated the prime theorem to Craig in 1685 Source 204 (p. 465, citing Whiteside, Mathematical Papers vol. 7, pp. 3 ff.) |
Read S204 in full; compared pp. 460, 462 and 465; neither passage acknowledges the other |
CN-16 |
First-use year of the word fluxion | Merged row T-NEW-02, from Newton's own works: 1671 Source 185;Source 187;Source 192 |
Retired duplicate T-L010, from the priority-dispute sources: 1676 concealed in the anagram, 1693 in print. Retired duplicate T-U422: 1704, Charles Hayes, in the first English calculus book Source 280;Source 281;Source 286;Source 439 |
Compared the three duplicate fluxion rows (T-NEW-02, T-L010, T-U422) while merging them; no new source read |