Appendix K
What could not be verified, and what to request
K.1 Repeated everywhere, and unverified here
Each of these is repeated in popular writing and could not be verified in this research pass. None of them is stated as fact anywhere else in this book, and they are listed here so that nobody puts them back in by accident, including you.
- Euler's remark that blindness meant fewer distractions (Source 326, O'Connor).
- Hilbert's "this is a university, not a bath-house" (Source 418, OConnor and Robertson).
- Einstein's New York Times letter about Noether (Source 418, OConnor and Robertson).
- Sophie Germain's honorary degree from Gottingen (Source 410, OConnor and Robertson).
- Errett Bishop's 1977 review sentences on nonstandard analysis (Source 395, Bishop; Source 390, Katz). The review was blocked on five separate attempts, by a Project Euclid challenge page and by Cloudflare on the AMS PDF.
- Lebesgue's coin analogy, that Riemann counts coins in the order you pull them from your pocket while Lebesgue sorts them by denomination first. The idea is his and it circulates only in paraphrase; no wording here traces back to Lebesgue (Source 377, O'Connor).
- Nicolas Fatio de Duillier's exact words in the 1699 accusation that opened the priority fight. The event is documented and the tract was never obtained, so no source read here quotes a single line of it.
- Newton's "ashamed to tell you to how many figures" remark about π (Source 190, Whiteside).
- Voltaire's line that England buried Newton "like a king who had done well by his subjects" (Source 200, Westminster Abbey).
- The claim that Cardano ranked Richard Swineshead among the greatest intellects (Source 106, Gale).
- Anything at all from Goldberg, "Ideas and Eternity" (Source 74, Goldberg). Read in full and excluded. It is a homily in a journal of Orthodox Jewish thought, and its four sentences on calculus contain three errors: it has Newton corresponding with Leibniz during 1664 to 1666 (they corresponded in 1676, through Oldenburg), calls 1675 the year Leibniz published (1675 is the manuscript notation; publication was 1684), and says "two centuries later" where it is three. Logged so the exclusion is on the record.
- "The Helen of Geometers" as a phrase attributable to anyone. Whitman 1943, the leading candidate, was read in full and does not contain it (Source 64, Whitman).
- Chaucer's reference to Bradwardine on predestination (Source 103, O'Connor).
- The ∞ symbol as a corruption of the Roman numeral CIƆ (Source 451, Cajori).
- Thabit ibn Qurra having been a money-changer in Harran (Source 57, O'Connor).
- Liu Hui's 157/50 approximation and the 192-gon; the terms milü and yuelü; Zu Chongzhi's actual method (Source 21, O'Connor).
- The origin of the name "Gabriel's horn", which appears to be genuinely unknown (Source 157, Wijeratne).
- When English usage dropped "the calculus" in favor of "calculus" (Source 453, Miller and Aldrich).
- Whether Stigler's law was in fact first stated by Merton, which is Stigler's own joke and could not be verified because the 1980 paper is paywalled (Source 460, Stigler).
K.2 Open disputes that need a specific document
| Question | Why it is open | What would settle it |
|---|---|---|
| Did Newton discover the Principia results by calculus and translate them into geometry? | PARTLY NARROWED 17 Aug 2026. The only source for the claim is still Newton writing anonymously about himself, and Whiteside still disagrees. Guicciardini 2004 (Source 204, Guicciardini) now establishes that quadrature working was withheld and supplied privately to Gregory and Cotes, which is broader than Whiteside's one exception; but he describes the book's own mathematics as the geometric fluxional calculus of the Geometria curvilinea, using limits, which is Whiteside's picture and not Newton's | Cohen's Guide pp. 114-117, 122-127, 345-347, then Guicciardini, Reading the Principia (CUP 1999), pp. 179-186, which S204 n. 45 names as the place the detail lives. Archive.org holds the book print-disabled |
| Was Cauchy's 1821 sum theorem simply false, or coherent under an infinitesimal reading? | Both sides read in full and both have evidence. Live in refereed journals | Nothing. This one is genuinely unsettled and should be taught as such |
| Did Cauchy take his program from Bolzano without acknowledgment? | Grattan-Guinness charged it; Grabiner rejected it; her rebuttal was not obtained | Grabiner, "Cauchy and Bolzano" (1984), and Grattan-Guinness (1970) p. 54 |
| What exactly did Barrow give Newton? | Four distinguished scholars, four verdicts, same evidence | Probably nothing. A good classroom case study in how historians decide |
| Did Kerala mathematics reach Europe? | Motive, opportunity, and resemblance are documented. No transmitting document exists | A document. Nobody has one |
| Who called the cycloid "the Helen of Geometers"? | CLOSED as unattributable. Whitman 1943 was the leading candidate and does not contain the phrase; full text read and searched 14 Aug 2026 | Nothing further. Stop looking, and stop attributing it |
| Who wrote the Charta volans (1713)? | Newton's own draft reply describes an anonymous libel quoting an unnamed mathematician's letter of 7 June 1713. The Johann Bernoulli attribution is an editorial inference, not in any document read | The Charta volans itself, and the Bernoulli correspondence |
| Was John Craig's Cambridge transcription visit in 1684 or 1685? | Guicciardini gives 1684 at pp. 460 and 462 and 1685 at p. 465, in one article, with neither passage acknowledging the other. The 1685 passage carries the fuller narrative | Whiteside, Mathematical Papers vol. 7, pp. 3 to 4, which both of Guicciardini's statements cite |
| Was Newton's 1675 royal dispensation from holy orders exactly as the biographies describe it? | Snobelen (Source 194, Snobelen) reports it and builds an argument on it, and nobody here read the dispensation itself or a source that quotes it. The claim is standard and very likely right, and it is carried at second hand | Richard Westfall, Never at Rest (Cambridge, 1980), which narrates the dispensation in detail, and behind that the instrument itself in the royal records |
| Exact day-level dates for the 1712 Royal Society committee | De Morgan names all eleven members and gives March 1712 for appointment and April 1712 for the report, but the names were never officially published | The Royal Society Journal Books |
K.3 Library requests, in priority order
These need institutional access. Everything else in this book was obtained.
- I. Bernard Cohen, A Guide to Newton's Principia, pages 114 to 117, 122 to 127, and 345 to 347. This displaces Guicciardini at the top of the list. Cohen's section 5.8 is 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". The PDF obtained holds the Guide's table of contents, not its body. Five pages would probably settle a question this book has carried as open from the beginning. The Guide is bound with the Cohen and Whitman translation (University of California Press, 1999), so any library copy of that translation has it.
1b. Guicciardini, Reading the Principia (Cambridge, 1999), pages 179 to 186 first, and Isaac Newton on Mathematical Certainty and Method (MIT, 2009). Still second in line behind five pages of Cohen, but the request is now much sharper than it was.
The Guicciardini gap is partly closed. His article "Isaac Newton and the publication of his mathematical manuscripts", Studies in History and Philosophy of Science 35(3), 2004, pp. 455 to 470, was obtained and read in full on 17 August 2026 (Source 204, Guicciardini). Be precise about what that did and did not do.
What S204 settles. Why Newton withheld: he judged the "new analysis" unfit to print after a methodological shift toward ancient geometry that begins in the 1670s. How the manuscripts moved instead: scribal publication, a named inner circle of acolytes, an outer circle of philomaths fed mutilated copies, transcripts made from transcripts, and hired scribes selling double copies by 1720. What ended it: priority, first against David Gregory in 1688 and then against Leibniz, plus journals changing what publication meant. And that Newton rewrote his own early texts to remove infinitesimals as he printed them. It also settles one Principia point: integration technique was used and withheld, and Newton supplied the missing steps privately to David Gregory and to Roger Cotes, his own editor.
What S204 does not settle, and does not claim to. It is not a line-by-line reading of the Principia. Guicciardini's own footnotes 44 and 45 hand that job to Reading the Principia, and footnote 45 gives the page range: pp. 179 to 186. He describes the Principia's mathematics as the geometric fluxional calculus of the Geometria curvilinea, built on limits, so he does not endorse the "worked it in calculus, then translated it" story, so this book does not cite him as if he did. He also calls the extent of the hidden calculus an open research front and names Nauenberg (2001), C. Wilson (2001) and Brackenridge (2003) as where the evidence is surfacing. Logged as CN-15.
What S204 opened. Six sources behind it that this project does not hold: Harold Love, Scribal Publication in Seventeenth-Century England (Clarendon, 1993), which is where the central concept comes from; P. Beal, In Praise of Scribes (Clarendon, 1998); H. Pycior, Symbols, Impossible Numbers, and Geometric Entanglements (Cambridge, 1997), the source of "geometric backlash"; W. G. Hiscock, David Gregory, Isaac Newton and Their Circle (1937), for Gregory's memoranda; R. Iliffe, "Butter for parsnips" (Routledge, 2003), on Principia authorship; and Whiteside's Mathematical Papers vol. 7, pp. 3 to 4, which would settle whether Craig's Cambridge visit was 1684 or 1685 (CN-14).
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A. Rupert Hall, Philosophers at War (Cambridge, 1980) and Domenico Bertoloni Meli, Equivalence and Priority (Oxford, 1993). The archive.org copy of Hall is print-disabled, so it cannot be read there; the record is
philosophersatwa0000hall, ISBN 0521227321, 338 pages. It does have a full-text search index, so "Search inside" will answer a targeted question even though the book cannot be read through. One sentence of Hall is already in hand at second remove: Feingold quotes him at p. 8 on Barrow's reputation "descending toward the status of an elegant codifier" (Source 73, Feingold). Interlibrary loan remains the route for the whole book. -
~~Victor J. Katz, "Ideas of Calculus in Islam and India"~~ OBTAINED 14 August 2026 via Boston Public Library and read in full (Source 61, Katz). It closed the ibn al-Haytham material, supplied the paraboloid result, and documented the summation-identity link from Baghdad to Kerala.
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~~R. P. Burn, "Alphonse Antonio de Sarasa and logarithms"~~ NO LONGER NEEDED. The primary sources were obtained instead, on 14 August 2026, which is a better outcome than the article. Sarasa 1649 (Source 66, Sarasa) was read in full, including the scholium that identifies hyperbolic areas with logarithms, and its marginal citations to Saint-Vincent. The Opus geometricum (Source 67, Gregorius a Sancto Vincentio) was obtained as the volume holding the front matter, the complete contents, and Books I to V. One residual gap: Book VI's body is not in that volume, so the exact Latin of propositions 125 to 130 has not been read. If you ever want to print that text verbatim, the second volume is the thing to find. Everything else this request existed for is now closed.
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~~E. A. Whitman, "Some historical notes on the cycloid"~~ OBTAINED 14 August 2026 and read in full (Source 64, Whitman). Outcome: it does not contain "the Helen of Geometers", which closes that question as unattributable. It did supply Galileo's 1599 weighing, Wren's rectification, and the mechanism behind Roberval's secrecy.
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Taton (1971) on Cauchy and Galois, Revue d'histoire des sciences. Persée robots-blocks it.
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~~Massimo Mazzotti, The World of Maria Gaetana Agnesi~~ CLOSED 14 August 2026. The article version was obtained and read in full: "Maria Gaetana Agnesi: Mathematics and the Making of the Catholic Enlightenment", Isis 92(4), 2001, pp. 657 to 683 (Source 77, Mazzotti). It settled the versiera page and date, the Bologna chair to the day, and her later life and burial, and it supplied the argument for why she wrote a geometrical calculus textbook. Antonella Cupillari's survey of her other curves (Source 75, Cupillari) came with it. The Agnesi gap is closed; the monograph would now only add depth.
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Edith Sylla, The Oxford Calculators in Context, and Bressoud, A Radical Approach to Real Analysis, and Bottazzini, The Higher Calculus.
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Stigler (1980), "Stigler's Law of Eponymy". Paywalled; Appendix D's framing device is currently unsourced at the primary level.
K.4 Images that need a license or a request
Full detail and the exact rights wording found for each repository is in Appendix H and in registers/IMAGE-RIGHTS-REPORT.md. The four actions:
- Cambridge University Library Imaging Services (imagingservices.lib.cam.ac.uk), for the six Newton manuscript images. CUDL licenses its downloads CC BY-NC 4.0, which rules out a sold textbook, and there is no free workaround. The license appears only inside the IIIF manifest; CUDL has no public terms page.
- Royal Society Picture Library (picturelibrary@royalsociety.org), for De analysi (MS/81/4). Rights-managed and priced by how commercial the project is. Note: they offer free download for classroom resources and unpublished theses, so this image is usable in class today and needs a license only for the published book.
- Gottfried Wilhelm Leibniz Bibliothek, Hanover, for LH 35, the 29 October 1675 manuscript carrying the first integral sign. No public-domain reproduction of it exists anywhere. This is the single most important missing image.
- King's College, Cambridge (Keynes MS 8) and The National Archives (the Chaloner letter, MINT 15/17/205). TNA images of out-of-copyright records are normally released under the Open Government Licence, which does permit commercial reuse, so this one is probably free. Worth confirming.
A note on Cupillari. Her 2014 article is valuable and is cited here, but page 5 prints the versiera as y = 1 / sqrt(1 + x squared), which contradicts her own opening sentence on the same page and her own algebra. It is a published typo. Do not propagate it.
One trap to remember. Two archive.org items in the early-european-books collection carry a ProQuest copyright notice burned into the pixels, invisible in the metadata: Kepler's Nova stereometria (© 2010) and Cavalieri 1635 (© 2011). They were found only by cropping and enhancing the image footer, and both were deleted. Kepler was replaced with a clean EPFL scan under Public Domain Mark 1.0. Cavalieri 1635 still needs a non-ProQuest scan. Check the pixels, not just the license page.