Click on the below to see a list of sources used in the writing of Math History: A Long-Form Mathematics Textbook. Clicking on the local link will pull up a flipbook-style reader. For books under copyright, a link is provided to purchase the book.
Chapter 1: Number Systems
- Strogatz, Steven. The Joy of x: A Guided Tour of Math, from One to Infinity. Houghton Mifflin Harcourt, 2012.
- Joseph, George Gheverghese. Indian Mathematics: Engaging with the World from Ancient to Modern Times. World Scientific, 2016.
- Babbage, Charles. On the Principles and Development of the Calculator and Other Seminal Writings.
- Joseph, George Gheverghese. The Crest of the Peacock: Non-European Roots of Mathematics. Princeton University Press, 2011.
- Clark, Kathleen M., and Clemency Montelle. Logarithms: The Early History of a Familiar Function. MAA article.
- Qiu, Jane. “Ancient Times Table Hidden in Chinese Bamboo Strips.” Nature, vol. 447, no. 7148, 2007, p. 123.
- Menninger, Karl. Number Words and Number Symbols: A Cultural History of Numbers. MIT Press, 1992.
- Ditz, Helen M., and Andreas Nieder. “Neurons selective to the number of visual items in the corvid songbird endbrain.” Proceedings of the National Academy of Sciences, vol. 112, no. 25 (2015): 7827-7832.
- Pines, Charles C. “The Story of Ink.” American Journal of Police Science, vol. 2, no. 3, 1931, pp. 290–294.
- Conner, Clifford D. A People’s History of Science: Miners, Midwives, and “Low Mechanicks”. Nation Books, 2005.
Chapter 2: Ancient Methods
- Dunham, William. Journey through Genius: The Great Theorems of Mathematics. Wiley, 1990.
- Powell, Christopher. The Shapes of Sacred Space: A Proposed System of Geometry Used to Lay Out and Design Maya Art and Architecture and Some Implications Concerning Maya Cosmology. University of Texas at Austin, 2010.
- Gillings, Richard J. Mathematics in the Time of the Pharaohs. Dover Publications, 1982.
- Joseph, George Gheverghese. The Crest of the Peacock: Non-European Roots of Mathematics. Princeton University Press, 2011.
- Hart, Roger. The Chinese Roots of Linear Algebra. Johns Hopkins University Press, 2010.
- Grcar, Joseph F. “Mathematicians of Gaussian Elimination.” Notices of the American Mathematical Society, vol. 58, no. 6, 2011, pp. 782–792.
- Liu, Hui. The Nine Chapters on the Mathematical Art. Translated by Dauben, Joseph W., 2007.
- Fowler, David, and Eleanor Robson. “Square Root Approximations in Old Babylonian Mathematics: YBC 7289 in Context.” Historia Mathematica, vol. 25, no. 4, 1998, pp. 366–378.
- Tibbetts, Gerald R. “The Beginnings of a Cartographic Tradition.” In Cartography in the Traditional Islamic and South Asian Societies, edited by J.B. Harley and David Woodward, University of Chicago Press, 1992.
Chapter 3: Transition to Proofs
- Blåsjö, Viktor. Intellectual Mathematics. “First Proofs: Thales and the Beginnings of Geometry.” Intellectual Mathematics, 16 May 2020.
- Joseph, George Gheverghese. Indian Mathematics: Engaging with the World from Ancient to Modern Times. World Scientific, 2016.
- Martínez, Alberto A. The Cult of Pythagoras: Math and Myths. University of Pittsburgh Press, 2012.
- Loomis, Elisha Scott. The Pythagorean Proposition: Its Proofs Analyzed and Classified. National Council of Teachers of Mathematics, 1968.
- Scriba, Christoph J. “The Autobiography of John Wallis, F.R.S.” Notes and Records of the Royal Society of London, vol. 25, no. 1, 1970, pp. 17–46.
- Dilke, O. A. W. “Illustrations from Roman Surveyors’ Manuals.” Imago Mundi, vol. 21, 1967, pp. 9–29.
Chapter 4: Euclidean Geometry
- Euclid. Elements.
- Joyce, David E. Euclid’s Elements. Clark University, 1996.
- Bendick, Jeanne. Archimedes and the Door of Science. Bethlehem Books, 1995.
- Grant, Hardy. “Geometry and Politics: Mathematics in the Thought of Thomas Hobbes.” Mathematics Magazine, vol. 63, no. 3, 1990, pp. 147–154.
- Kucharski, Adam. “Euclid as Founding Father.” Nautilus, 7 Oct. 2016.
- Ramana, D. Surya. “Carl Friedrich Gauss.” Resonance: Journal of Science Education, vol. 2, no. 6, 1997, pp. 60–67.
- Joseph, George Gheverghese. Indian Mathematics: Engaging with the World from Ancient to Modern Times. World Scientific, 2016.
- Blåsjö, Viktor. Intellectual Mathematics Blog.
- Rothman, Tony, and Hidetoshi Fukagawa. “Japanese Temple Geometry.” Scientific American, vol. 278, no. 5, 1998, pp. 84–91.
- Bezuszka, Stanley J., and Margaret J. Kenney. “Even Perfect Numbers: (Update) 2.” The Mathematics Teacher, vol. 90, no. 8, 1997, pp. 628–633.
Chapter 5: Number Theory
- Euclid. Elements.
- Bendick, Jeanne. Archimedes and the Door of Science. Bethlehem Books, 1995.
- Joseph, George Gheverghese. Indian Mathematics: Engaging with the World from Ancient to Modern Times. World Scientific, 2016.
- Blåsjö, Viktor. Intellectual Mathematics Blog.
- Wichelt, Lexi. “Amicable Pairs.” Mathematics in the Middle School, University of Nebraska-Lincoln, 2008.
- Shen, Kangsheng. “Historical Development of the Chinese Remainder Theorem.” Archive for History of Exact Sciences, vol. 38, no. 4, 1988, pp. 285–305.
- A History of Chinese Mathematics by Jean-Claude Martzloff.
- Lloyd, G. E. R. Adversaries and Authorities: Investigations into Ancient Greek and Chinese Science. Cambridge University Press, 1996.
Chapter 6: Algebra
- Edwards, Harold M. “Galois for 21st-Century Readers.” Notices of the American Mathematical Society, vol. 59, no. 7, 2012, pp. 912–923.
- Hong, Sung Sa, Hong Young Hee, and Kim Chang Il. “Zengcheng Kaifangfa and Zeros of Polynomials.” Journal for History of Mathematics, vol. 33, no. 6, 2020, pp. 303–314.
- Katz, Victor J. A History of Mathematics: An Introduction. 3rd ed., Pearson, 2008.
- Neumann, Peter M. The Mathematical Writings of Évariste Galois. European Mathematical Society, 2011.
- Strogatz, Steven. The Joy of x: A Guided Tour of Math, from One to Infinity. Houghton Mifflin Harcourt, 2012.
- Cajori, Florian. A History of Mathematical Notations. Open Court Publishing, 1928.
- Livio, Mario. The Equation That Couldn’t Be Solved: How Mathematical Genius Discovered the Language of Symmetry. Simon & Schuster, 2005.
- Noel, Linda Hand. “The Fundamental Theorem of Algebra: A Survey of History and Proofs.” PhD dissertation, Oklahoma State University, 1991.
- Cain, Harel. “C. F. Gauss’s Proofs of the Fundamental Theorem of Algebra.” 2004.
- Au Yong, Ke-Xin. “Qin Jiushao and His Mathematical Treatise in Nine Sections in Thirteenth-Century China.” MA thesis, University of Alberta, 2011.
- Rowe, David E., and Mechthild Koreuber. Proving It Her Way: Emmy Noether, a Life in Mathematics. Springer, 2020.
- McMillan, Robert D. “Babylonian Quadratics.” The Mathematics Teacher, vol. 77, no. 1, 1984, pp. 63–65.
- Nordgaard, Martin A. “Sidelights on the Cardan-Tartaglia Controversy.” National Mathematics Magazine, vol. 12, no. 7, 1938, pp. 327–346.
- Gamwell, Lynn. Mathematics and Art: A Cultural History. Princeton University Press, 2015.
- Grünbaum, Branko. “What Symmetry Groups Are Present in the Alhambra?” Notices of the American Mathematical Society, vol. 53, no. 6, 2006, pp. 670–673.
- Lu, Peter J., and Paul J. Steinhardt. “Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture.” Science, vol. 315, no. 5815, 2007, pp. 1106–1110.
Chapter 7: Early Calculus
- Richeson, David. “Circular Reasoning: Who First Proved That C/d Is a Constant?” The College Mathematics Journal, vol. 46, no. 3, 2015, pp. 162–171.
- Archimedes. The Works of Archimedes. Translated by Sir Thomas Heath, Cambridge University Press, 1897.
- Joseph, George Gheverghese. A Passage to Infinity: Medieval Indian Mathematics from Kerala and Its Impact. SAGE Publications, 2009.
- Laubenbacher, Reinhard, and David Pengelley. Mathematical Expeditions: Chronicles by the Explorers. Springer, 1999.
- Stewart, Ian. Significant Figures: The Lives and Work of Great Mathematicians. Basic Books, 2017.
- Rabinovitch, Nachum L. “Rabbi Levi Ben Gershon and the Origins of Mathematical Induction.” Archive for History of Exact Sciences, vol. 6, no. 3, 1970, pp. 237–248.
- Acerbi, F. “Plato: Parmenides 149a7-c3. A Proof by Complete Induction?” Phronesis, vol. 55, no. 1, 2010, pp. 1–22.
- Gauss, Carl Friedrich. Carl Friedrich Gauß → [Johanna Gauß], 1809 Okt. Göttingen Digital Library, Akademie der Wissenschaften zu Göttingen.
- Krantz, Steven G. Mathematical Apocrypha: Stories and Anecdotes of Mathematicians and the Mathematical. Mathematical Association of America, 2002.
- Krantz, Steven G. Mathematical Apocrypha Redux: More Stories and Anecdotes of Mathematicians and the Mathematical. Mathematical Association of America, 2005.
Chapter 8: Modern Analysis
- Berlinghoff, William P., and Fernando Q. Gouvêa. Math Through the Ages: A Gentle History for Teachers and Others. Expanded Second Edition, American Mathematical Society, 2020.
- Grabiner, Judith V. “Who Gave You the Epsilon? The Origins of Cauchy’s Rigorous Calculus.” The American Mathematical Monthly, vol. 90, no. 3, 1983, pp. 185–194.
- Felscher, Walter. “Bolzano, Cauchy, epsilon, delta.” The American Mathematical Monthly 107.9 (2000): 844-862.
- Dunham, William. Euler: The Master of Us All. Mathematical Association of America, 1999.
- Kanigel, Robert. The Man Who Knew Infinity: A Life of the Genius Ramanujan. Scribner, 1991.
- Gleick, James. Isaac Newton. Vintage Books, 2003.
- Dunham, William. Euler: The Master of Us All. Mathematical Association of America, 1999.
- Baruah, Nayandeep Deka, Bruce C. Berndt, and Heng Huat Chan. “Ramanujan’s Series for 1/𝝅: A Survey.” The American Mathematical Monthly, vol. 116, no. 7, 2009, pp. 567–587.
- Gouvêa, Fernando Q. “Was Cantor Surprised?” The American Mathematical Monthly, vol. 118, no. 3, 2011, pp. 198–209.
Chapter 9: Topology
- Richeson, David S. Euler’s Gem: The Polyhedron Formula and the Birth of Topology. Princeton University Press, 2008.
- Poincaré, Henri. Papers on Topology: Analysis Situs and Its Five Supplements. Translated by John Stillwell, American Mathematical Society, 2010.
- James, I. M., editor. History of Topology. Elsevier Science, 1999.
- O’Shea, Donal. The Poincaré Conjecture: In Search of the Shape of the Universe. Walker & Company, 2007.
- Klarreich, Erica. “Getting into Shapes: From Hyperbolic Geometry to Cube Complexes.” Quanta Magazine, 2 Oct. 2012.
- Scoville, Nicholas A. “Georg Cantor at the Dawn of Point-Set Topology.” MAA Convergence, Mathematical Association of America, July 2011.
- Moore, Gregory H. “The Emergence of Open Sets, Closed Sets, and Limit Points in Analysis and Topology.” Historia Mathematica, vol. 35, no. 3, 2008, pp. 220–241.
- Lakatos, Imre. Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge University Press, 1976.
Chapter 10: Combinatorics
- Wilson, Robin, and John J. Watkins, editors. Combinatorics: Ancient & Modern. Oxford University Press, 2013.
- Kalai, Gil. “DESIGNS EXIST! [after Peter Keevash].” Combinatorics and More, 16 Jan. 2014.
- Soifer, Alexander. Ramsey Theory: Yesterday, Today, and Tomorrow. Birkhäuser, 2011.
- Soifer, Alexander. The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of Its Creators. Springer, 2009.
- Rankin, Joy Lisi. A People’s History of Computing in the United States. Harvard University Press, 2018.
Appendix A: Topics in Applied Math
- Setzeus. “Differential Equations: History Overview.” Setzeus Community Blog, 2023.
- Krishnachandran, V. N. “Differential Equations: A Historical Refresher.” arXiv preprint, 2020.
- Stillwell, John. Mathematics and Its History. 3rd ed., Springer, 2010.
- David, F. N. Games, Gods and Gambling: The Origins and History of Probability and Statistical Ideas from the Earliest Times to the Newtonian Era. Hafner Publishing Company, 1962.
- Chatterjee, Shoutir Kishore. Statistical Thought: A Perspective and History. Oxford University Press, 2003.
- “Pierre de Fermat.” Encyclopædia Britannica.
- Fermat, Pierre de. “De Linearum Curvarum cum Lineis Rectis Comparatione.” 1659.
- Fermat and Pascal letters
- Devlin, Keith. The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern. Basic Books, 2008.
- Harkness, Timandra. “John Graunt at 400: Fighting Disease with Numbers.” Significance, vol. 17, no. 4, 2020, pp. 22–25.
Appendix B: Mathematician Pronunciation Guide
- Boyadzhiev, Khristo. “Non-English Names of Prominent Mathematicians.” ResearchGate Publication, 2016.
- How to Say Mathematics. “Guide to Pronouncing Mathematical Terms and Names.” How to Say Mathematics Blog.
- Pronounce Names. “Pronounce Names – Dictionary of Name Pronunciations.” PronounceNames.com.
- Dictionary.com. “The Dictionary of Pronunciations.” Dictionary.com.
- Voice of America. “VOA Pronunciation Guide.” Pronounce VOA.
- OpenAI. “ChatGPT: AI Language Model.” ChatGPT.com.
Appendix C: Mathematical Quotes
I did not save my sources for these quotes, but they came from all over. My colleague Scott Farrand provided many. The Twitter account Fermat’s Library often posted a good one that I saved. Many books have epigraphs at the start of each chapter, so I spent a fun day flipping through dozens of books reading nice quotes and jotting down my favorites. Of course, the ultimate source for each is the person who said them, which is included in the text itself.
I tried my best to check their accuracy. ChatGPT was particularly helpful with this.
Appendix D: History of Math Words
- Lo Bello, Anthony. Origins of Mathematical Words: A Comprehensive Dictionary of Latin, Greek, and Arabic Roots. Johns Hopkins University Press, 2013.
- Schwartzman, Steven. The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English. Mathematical Association of America, 1994.
- Etymonline. “Online Etymology Dictionary.” Etymonline.com.
Appendix E: History of Math Symbols
- Stallings, L. Lynn. “A Brief History of Algebraic Notation.” School Science and Mathematics, vol. 100, no. 5, 2000, pp. 225–269.
- Cajori, Florian. A History of Mathematical Notations. Mineola, New York: Dover Publications, 1993.
- Boyer, Carl B. A History of Mathematics. 2nd ed., John Wiley & Sons, Inc., 1991.
- “Earliest Uses of Symbols for Matrices and Vectors.” Jeff Miller’s Math History Website.
Appendix F: Biographical Sketches
- Stewart, Ian. Significant Figures: The Lives and Work of Great Mathematicians. Basic Books, 2017.
- Ada Lovelace’s biography on MacTutor.
- Stephen Wolfram’s article “Untangling the Tale of Ada Lovelace.”
- Ada Lovelace: A Life from Beginning to End by Hourly History.
- Fuegi, John, and Jo Francis. “Lovelace & Babbage and the Creation of the 1843 ‘Notes’.” IEEE Annals of the History of Computing, vol. 25, no. 4, 2003, pp. 16–26.
- Alan Turing: The Enigma by Andrew Hodges.
- Alan Turing’s biography on MacTutor.
- Fibonacci’s biography on MacTutor.
- K. Vogel’s biography of Fibonacci in Dictionary of Scientific Biography (New York, 1970–1990).
- Liu Hui’s biography on MacTutor.
- A History of Chinese Mathematics by Jean-Claude Martzloff.
- Euclid’s biography on MacTutor.
- Holt, Jim. When Einstein Walked with Gödel: Excursions to the Edge of Thought. Farrar, Straus and Giroux, 2018.
- Kurt Gödel’s biography on MacTutor.
- Holt, Jim. When Einstein Walked with Gödel: Excursions to the Edge of Thought. Farrar, Straus and Giroux, 2018.
- Pierre de Fermat’s biography on MacTutor.
- Sophie Germain’s biography on MacTutor.
- Sophie Germain’s biography on Biographies of Women Mathematicians by Agnes Scott College.
- Grosholz, Emily. “Candles in the Dark: Émilie du Châtelet and Mary Somerville.” The Hudson Review, vol. 65, no. 4, 2013, pp. 669–676.
- Reid, Constance. Hilbert. Springer, 1996.
- David Hilbert’s biography on MacTutor.
- Muhammad ibn Musa al-Khwarizmi’s biography on MacTutor.
- Toomer, G. J. “Al-Khwarizmi.” Dictionary of Scientific Biography, New York, 1970–1990.
- Livio, Mario. The Equation That Couldn’t Be Solved: How Mathematical Genius Discovered the Language of Symmetry. Simon & Schuster, 2005.
- Niels Abel’s biography on MacTutor.
- Évariste Galois’s biography on MacTutor.
- Waltershausen, Wolfgang Sartorius von. Gauss. Leipzig: S. Hirzel, 1856.
- Collected works of Carl Friedrich Gauss on the Göttingen Digital Library.
- MathPages entry “Charles Henry Gauss and His Letters.”
- E.T. Bell. Men of Mathematics. Simon & Schuster, 1937.
- Carl Friedrich Gauss’s biography on MacTutor.
- Rowe, David E., and Mechthild Koreuber. Proving It Her Way: Emmy Noether, a Life in Mathematics. Springer, 2020.
- Emmy Noether’s biography on MacTutor.
- Boria, Vittorio. Marin Mersenne: Educator of Scientists. PhD dissertation, American University, 1989.
- Marin Mersenne’s biography on MacTutor.
- Archimedes’s biography on MacTutor.
- Archimedes. The Works of Archimedes. Edited by T.L. Heath, Dover Publications, 2002.
- Joseph, George Gheverghese. The Crest of the Peacock: Non-European Roots of Mathematics. Princeton University Press, 1991.
- Joseph, George Gheverghese. A Passage to Infinity: Medieval Indian Mathematics from Kerala and Its Impact. Sage Publications, 2009.
- Madhava of Sangamagrama’s biography on MacTutor.
- Brahmagupta’s biography on MacTutor.
- Bhaskara II’s biography on MacTutor.
- Antognazza, Maria Rosa. Leibniz: A Very Short Introduction. Oxford University Press, 2016.
- Gottfried Wilhelm Leibniz’s biography on MacTutor.
- Gleick, James. Isaac Newton. Vintage Books, 2003.
- Isaac Newton’s biography on MacTutor.
- Augustin-Louis Cauchy’s biography on MacTutor.
- Dunham, William. Euler: The Master of Us All. Mathematical Association of America, 1999.
- Leonhard Euler’s biography on MacTutor.
- Musielak, Dora E. “Euler and the German Princess.” 2014.
- The Bernoullis: Mathematical Genius by Elephant Learning.
- The Bernoullis: Mathematical Genius and Serious Family Drama by Anagrath on Medium.
- Johann Bernoulli’s biography on MacTutor.
- Jacob Bernoulli’s biography on MacTutor.
- Daniel Bernoulli’s biography on MacTutor.
- Kanigel, Robert. The Man Who Knew Infinity: A Life of the Genius Ramanujan. Washington Square Press, 1991.
- Srinivasa Ramanujan’s biography on MacTutor.
- Georg Cantor’s biography on MacTutor.
- Bernhard Riemann’s biography on MacTutor.
- Henri Poincaré’s biography on MacTutor.
- Krantz, Steven G. Mathematical Apocrypha: Stories and Anecdotes of Mathematicians and the Mathematical. Mathematical Association of America, 2002.
- Grigori Perelman’s biography on MacTutor.
- Gessen, Masha. Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century. Houghton Mifflin Harcourt, 2009.
- Maryam Mirzakhani’s biography on MacTutor.
- Bertrand Russell’s biography on MacTutor.
- Audin, Michèle. Remembering Sofya Kovalevskaya. Springer, 2011.
- Sofia Kovalevskaya’s biography on MacTutor.
- Hoffman, Paul. The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth. Hyperion, 1998.
- Paul Erdős’s biography on MacTutor.
- Ron Graham’s biography on MacTutor.
- Terence Tao’s biography on MacTutor.