Before you start
How to read this book
This book is the story behind your calculus course: who found the ideas, who fought over them, and why the notation looks the way it does. Nothing in it is graded. Read what catches you.
Three promises before you start. Every fact traces to a source somebody read in full, and the little gray pointers like (Source 66, Sarasa) take you straight to it. When historians disagree, the book says so with a visible Disputed label instead of quietly picking a side. And when something could not be verified at all, the book tells you that too.
The honesty rule
This book distinguishes four things, and never blurs them:
- What a primary source says. Quoted, with a page or folio number.
- What historians conclude from it. Attributed to a named historian.
- What is disputed. Carries a visible Disputed label, with both sides given.
- What could not be verified. Listed in Appendix K.1, with the reason it could not be.
Appendix G is a list of beloved stories that fall apart when you check them. It is one of the more useful parts of this book, because several of them are in the textbooks you may have read before.
The reading tools
The top bar carries everything: Search finds any person, passage, or source; Listen reads the page aloud in your browser's own voice; Print makes a clean paper copy, including a large-print version; Night flips the lights. On a phone, the Contents button opens the full map of the book.
Every formatting choice in this book carries meaning. Nothing is decorative.
| Style | Meaning |
|---|---|
| A Disputed label, on a claim anywhere in the book | Sources disagree and the disagreement is not settled. Both readings are given, and the row is in Appendix F. The markup is <span class="disputed">, so the label survives a screen reader and a large-print printout. Never read a labeled claim as settled fact. |
| Italics | A work title, a word in another language, a mathematical variable, or plain emphasis. Those four jobs are the whole list. Italics on their own never mean disputed, so an italic phrase with no Disputed label beside it is settled like any other sentence. |
| Bold | A load-bearing fact: the thing to remember from the paragraph. |
Monospace |
A shelfmark, a manuscript reference, a file name, or a literal string (6accdae13eff7i3l9n4o4qrr4s8t12vx). |
| > Block quotation | A direct quotation from a source, with page or folio. Translator named when the original is not English. |
| (S183) | Source pointer. The bracketed code is the source ID in the bibliography, Appendix J. Every claim carries one. |
| Small text under a timeline entry | The nature of the dispute for that row. |
| Latin or Greek in italics | A term in its original language: summa, adaequalitas, tatkalika gati. |
One deliberate omission: there are no em dashes or en dashes anywhere in this book, including inside quotations, where the original punctuation is rendered with commas, colons, or parentheses. Ranges use "to" or a plain ASCII hyphen. A real minus sign on a real negative number is a minus sign.
One thing to know before you start. This book is easy to read, and easy reading feels like knowing. It is not the same thing. Robert Bjork's name for the gap is an illusion of competence, and it happens because fluent text feels like understood text. When a question appears, answer it in your head before you open the reveal, even when you are sure. Being sure is the part that fools you.
On spelling: the book's own voice uses US spelling throughout (rigor, catalog, center, analyze). Three things keep their original spelling on purpose, because changing them would falsify a source: direct quotations (Brewster prints "Bernouilli recognised"; Fourier's citation reads "generality and even rigour"), the exact rights wording recorded from a repository in Appendix H (many of which are British or Commonwealth institutions and write "licence"), and proper names such as the Open Government Licence. Everywhere else, if you see a British spelling, it is a bug.
On the tables: every large reference table is written as HTML inside the Markdown rather than as a pipe table. (A handful of short two- and three-column tables stay as pipe tables, where the alignment rules cost nothing.) Markdown ties header alignment to body alignment through a single separator row, so it cannot center a header over a left-aligned column, and it cannot wrap a header to keep a column narrow. HTML tables can do both, and they render in GitHub, VS Code, Obsidian, pandoc, and any browser. Headers are centered, text columns are left-aligned, numeric columns are right-aligned to a consistent number of decimal places, and any column that can go negative shows an explicit sign.
Abbreviations, expanded
| Short | Full |
|---|---|
| APA 7 | American Psychological Association citation style, 7th edition |
| BCE / CE | Before Common Era / Common Era |
| BnF | Bibliothèque nationale de France |
| CC BY / CC BY-NC / CC0 | Creative Commons Attribution / Attribution-NonCommercial / public domain dedication |
| CUL | Cambridge University Library |
| CUDL | Cambridge Digital Library |
| DSB | Dictionary of Scientific Biography |
| f. / ff. | folio / folios (a manuscript leaf, front and back) |
| FTC | Fundamental Theorem of Calculus |
| GWLB | Gottfried Wilhelm Leibniz Bibliothek, Hanover |
| IIIF | International Image Interoperability Framework |
| IVT | Intermediate Value Theorem |
| LH | Leibniz Handschriften, the manuscript series at Hanover |
| MP | D. T. Whiteside (ed.), The Mathematical Papers of Isaac Newton, 8 vols. |
| MS / MSS | manuscript / manuscripts |
| MVT | Mean Value Theorem |
| NS | New Style, the Gregorian calendar |
| OGL | Open Government Licence (UK) |
| OS | Old Style, the Julian calendar, used in England until 1752 |
| PD / PDM | public domain / Public Domain Mark |
| r / v | recto / verso (the front and back of a manuscript leaf) |
| RS | Royal Society, London |
| SEP | Stanford Encyclopedia of Philosophy |
| TNA | The National Archives, Kew |
A note on dates before 1752
England kept the Julian calendar until 1752 while Catholic Europe had moved to the Gregorian in 1582. Two consequences run through this whole document:
- The day count differs. Julian dates lag Gregorian by 10 days before 1700 and by 11 days from 1700 to 1752.
- The year started on 25 March in England, not 1 January. So an English document dated "20 March 1726" was written on a day we would call 31 March 1727.
Newton's tombstone reads MDCCXXVI. Your textbook says he died in 1727. Both are correct. Every Newton date in this book gives Old Style and New Style. That single fact is one of the cleanest cross-curricular lessons available: send students a photograph of the inscription and let them work out why it disagrees with Wikipedia (S200).
Curious how a book like this gets checked? The whole audit trail is in Provenance, and how this book was built.