Appendix A — References
References
This is a practical references section, not a formal academic bibliography. It is meant for ordinary readers of this book.
The priorities here are:
- free online resources from reliable institutions
- public-domain primary texts when they exist
- books that are easy to buy, borrow, preview, or locate through libraries
If you want one rule of thumb, use free websites first for orientation, then move to books when you want depth.
Best Free Online Starting Points
MacTutor History of Mathematics Archive
The single best free starting point for this book. It is run by the University of St Andrews and is excellent for biographies, topic essays, and quick historical orientation.Stanford Encyclopedia of Philosophy
Best for the later chapters where mathematics meets philosophy and logic: infinity, set theory, foundations, and Gödel.Einstein Online
A clear, free, reliable relativity resource produced by the Max Planck Institute for Gravitational Physics and related institutions.Project Gutenberg
Best place to find free public-domain mathematical classics in readable formats.Open Library
Useful for checking whether a book is previewable, borrowable, or easy to locate in libraries and used-book markets.
Free Online References by Topic
Ancient Mathematics: Mesopotamia, Egypt, Greece
- Babylonian mathematics (MacTutor)
- Babylonian numerals (MacTutor)
- Egyptian mathematics (MacTutor)
- Ahmes and the Rhind Papyrus (MacTutor)
- Euclid, The First Six Books of the Elements (Project Gutenberg)
These are the best free starting points for Chapters 1-4. MacTutor is especially good on the ancient material because it combines biography, topic essays, and historical context in one place.
India, the Islamic World, and Kerala
- Aryabhata (MacTutor)
- Brahmagupta (MacTutor)
- al-Khwarizmi (MacTutor)
- Indian mathematics: “Redressing the balance” (MacTutor project)
- Kerala mathematics: introduction (MacTutor)
- Madhava of Sangamagrama (MacTutor)
For Chapters 5-7, this is the most realistic free route. It is not a substitute for serious books on Indian mathematics, but it is much more accessible than journal literature and far better than random web summaries.
Renaissance Europe, Calculus, and Early Modern Mathematics
Cardano’s Ars Magna on Open Library
If the exact edition page changes, searching Open Library for “Ars Magna Cardano” will usually find it quickly.Project Gutenberg: Euclid
Still useful in the Renaissance chapters because so much early modern mathematics is written in conversation with Euclid.MacTutor biographies and essays
Best free general source for Tartaglia, Cardano, Newton, Leibniz, Euler, Gauss, Riemann, Cantor, Hilbert, and Gödel.
Probability, Statistics, Infinity, and Foundations
- Infinity (Stanford Encyclopedia of Philosophy)
- Set Theory (Stanford Encyclopedia of Philosophy)
- Gödel’s Incompleteness Theorems (Stanford Encyclopedia of Philosophy)
- Kurt Gödel (Stanford Encyclopedia of Philosophy)
These are especially useful for Chapters 14 and 16, where ordinary popular summaries often become unreliable.
Relativity
- Einstein Online: Special relativity
- Einstein Online: overview site and glossary
- Einstein, Relativity: The Special and General Theory (Project Gutenberg)
- The Principle of Relativity (Project Gutenberg)
For Chapter 15, Einstein Online is the best free explanatory resource, and Project Gutenberg gives you the classic texts themselves.
If You Only Read a Few Books
If you want a realistic short shelf for this manuscript, start here:
Carl B. Boyer and Uta C. Merzbach, A History of Mathematics (Open Library)
Still one of the best one-volume overviews of the field.Victor J. Katz, A History of Mathematics: An Introduction (Open Library)
Broader and often more teachable than Boyer for modern readers.George Gheverghese Joseph, The Crest of the Peacock (Open Library)
Essential if you want a less Eurocentric history.Kim Plofker, Mathematics in India (Open Library)
The most important book for the Indian chapters.
If you read only those four, you will already be on much firmer ground than most readers of popular histories of mathematics.
Good Books for Particular Parts of This Book
For Zero, Negative Numbers, and the Expansion of Number
- Charles Seife, Zero: The Biography of a Dangerous Idea (Open Library)
Popular rather than scholarly, but lively and very readable.
For Probability and Statistics
Peter L. Bernstein, Against the Gods (Open Library)
Excellent for the human story behind risk, probability, and finance.Stephen M. Stigler, The History of Statistics (Open Library)
More serious, but still readable and extremely useful.
For Calculus and the Early Modern Period
- Amir Alexander, Infinitesimal (Open Library)
A vivid and accessible book on the seventeenth-century struggle around infinitesimals.
For Symmetry, the Quintic, and Galois
- Mario Livio, The Equation That Couldn’t Be Solved (Open Library)
Probably the best popular book for Chapter 13 territory.
For Gödel and the Foundations Crisis
- Ernest Nagel and James Newman, Gödel’s Proof (Open Library)
Old, short, still useful, and much more approachable than most logic textbooks.
Free Primary Texts Worth Reading
These are not always easy, but they are real sources rather than second-hand summaries:
- Euclid, The First Six Books of the Elements (Project Gutenberg)
- Albert Einstein, Relativity: The Special and General Theory (Project Gutenberg)
- Albert Einstein and others, The Principle of Relativity (Project Gutenberg)
For most earlier material in India, the Islamic world, and Kerala, good free primary texts are harder to find in reader-friendly editions. In those cases, the most realistic path is: MacTutor first, then Open Library, then specialist books if you want to go deeper.
A Practical Reading Path
If you want to follow up this book without disappearing into academic papers, this is the best order:
- Read the free MacTutor essays and biographies for the people or periods that interested you most.
- Use Project Gutenberg for Euclid and Einstein if you want to see original voices.
- Use Open Library to locate or borrow the broader books listed above.
- Use the Stanford Encyclopedia only for the later conceptual chapters: infinity, set theory, foundations, and Gödel.
That is enough for most readers. It keeps the references section genuinely usable while still pointing toward serious material.