The following is an incomplete list of (primarily mathematics-related) books that I find interesting or
useful, or that I've used as references when writing this site's
material. For online resources, please see my
For a list of physics-related books, please see my
- Hofstadter, Douglas R. Gödel, Escher, Bach: An Eternal Golden Braid. Basic Books, 1979.
A Pulitzer Prize winner, this book is a true classic.
Those who are interested in computability theory,
philosophy of mind, and many other fields will find something of interest
here. The dialogues between Achilles and the Tortoise (of
fame) keep the 700+ page book
- Maor, Eli. To Infinity and Beyond: A Cultural History of The Infinite. Boston: Birkhäuser, 1987.
- Butterworth, Brian. What Counts: How Every Brain Is Hardwired for Math. New York: The Free Press, 1999.
- Galotti, Dr. Kathleen M. Cognitive Psychology In and Out of the Laboratory. 4th ed. Thomson Wadsworth, 2008.
This textbook is written well in an informal, almost chatty, tone. I enjoyed reading this book. The sections on problem solving
were of use in creating this site. The one disadvantage about this book is that, being a current textbook, it's incredibly expensive.
- Falletta, Nicholas. The Paradoxicon. New York: John Wiley & Sons, 1990.
- Aristotle. On Sophistical Refutations. On Coming-to-be and Passing-away. On the Cosmos. Trans. E. S. Forster and D. J. Furley. Cambridge: Harvard University Press, 1955. Loeb Classical Library.
My On Sophistical Refutations page
is a copy of this translation. Nice-looking book; I believe that Martha Stewart used these books as decoration on her bookshelves.
- Davis, Philip J. and William G. Chinn. 3.1416 and All That. Boston: Birkhäuser, 1985.
An interesting and worthwhile book. Contains 25 short essays on topics relating to popular and recreational mathematics. The essays date from the 1960s and are starting to show their age in parts, but for the most part this is still a relevant book.
- Polya, G. How to Solve It: A New Aspect of Mathematical Method. Second ed. Princeton: Princeton University Press, 1957.
The classic book on problem solving
. I feel that this book is a "must-read" for anyone who is a student of mathematics, and it's still a worthwhile read if you're not.
- Davis, Philip J. and Reuben Hersh. The Mathematical Experience. Boston: Birkhaüser, 1981.
An interesting book that mediates well between being too technical
and being too simplistic. In some ways (specifically its discussion of
philosophical issues), I found it somewhat reminiscent of
Gödel, Escher, Bach; in other ways it's quite different.
- Pickover, Clifford. Keys to Infinity. John Wiley & Sons, 1995.
A very interesting book which is of the same (high) calibre as all of the
author's other works. Lots of food for thought here.
- Noller, Ruth B., Ruth E. Heintz, and David A. Blauer. Creative Problem Solving in Mathematics. Buffalo: State University College at Buffalo, 1978.
A small, cute book dealing with the fundamentals of problem solving
and containing some nice examples.
- Taplan, Margaret. "Mathematics Through Problem Solving." Math Goodies. Web. 21 Feb. 2011. <http://www.mathgoodies.com/articles/problem_solving.html>.
- Dudley, Underwood. Mathematical Cranks. Washington: The Mathematical Association of America, 1992.
This book is hilarious! This book contains discusses mathematical cranks (people who hold eccentric mathematical beliefs, believe they're right and the rest of the mathematical establishment is wrong, and write profusely. The book is divided into about fifty topics, which intersperse crank writing with Dudley's insightful and humourous comments. Dudley also includes a discussion of the actual mathematics, which aids in understanding the topics from a mainstream mathematical perspective. Now that we're in the Internet age, you can find crank writings all over the Internet, but they're just not as funny without Dudley's commentary.
- Richardson, William F. Numbering and Measuring in the Classical World. Revised Ed. Bristol: Bristol Phoenix Press, 2004.
- Gibilisco, Stan. Puzzles, Paradoxes and Brain Teasers. Blue Ridge Summit: Tab Books, 1988.
A very interesting book, containing short discussions on a wide
variety of topics, from infinity
, some physics topics, and more.
The format of the book (each chapter of the book is divided into
small articles of about half a page or so) is quite interesting.
I found parts of the book to be
somewhat speculative in nature and a few little mathematical errors can
be found in the text, but it's still an interesting work.
- Euclid. The Thirteen Books of The Elements. Trans. Sir Thomas L. Heath. Second ed. Vol. 1. New York: Dover Publications, 1956.
A few of the proofs in the book can be found at Elements
- Falconer, Kenneth. Fractal Geometry: Mathematical Foundations and Applications. Chichester: John Wiley & Sons, 1990.
- Richardson, A. Stephen. "Logical Fallacies in Scientific Writing." Department of Computer Science - The University of Auckland. Web. 04 Mar. 2011. <http://www.cs.auckland.ac.nz/~cristian/i2rcs/i2rcs_docs/logic.htm>.
- Hamblin, C. L. Fallacies. London: Methuen & Co., 1970.
- Dudley, Underwood. Elementary Number Theory. New York: Dover, 1978.
This is an excellent introductory textbook to number theory
. Textbooks are often expensive; however, Dover now has a reprint edition of this that is very inexpensively priced.
- Dodgson, Charles L., M.A. Pillow-Problems: Thought Out During Wakeful Hours. New York: Dover, 1958.
- Gardner, Martin. The Universe in a Handkerchief: Lewis Carroll's Mathematical Recreations, Games, Puzzles, and Word Plays. New York: Copernicus, 1996.
- Collins, A. Frederick. Rapid Math Without a Calculator. Secaucus: Citadel Press, 1987.
A reprint of an older book from 1916 originally entitled Short Cuts in Figures
, republished in 1956 as Magic with Figures
. Quite a useful book; contains lots of methods for improving your mental calculation speed
. There are some inaccuracies in the book, so it is best read critically
- Gardner, Martin. The Second Scientific American Book of Mathematical Puzzles and Diversions. Chicago: University of Chicago Press, 1987.
A collection of Gardner's Scientific American columns from
parts of 1958 through 1960, there are some gems here, such as the section
on "Probability and Ambiguity" and "Phi: The Golden Ratio".
- Bell, Eric Temple. The Search For Truth. New York: Reynal & Hitchcock, 1934.
- Walton, Douglas. Fallacies Arising from Ambiguity. Dordrecht: Kluwer Academic, 1996. Applied Logic Ser. 1.
- Walton, Douglas. A Pragmatic Theory of Fallacy. Tuscaloosa: The University of Alabama Press, 1995.
- Benson, William H. and Oswald Jacoby. New Recreations With Magic Squares. New York: Dover Publications, 1976.
- Foundation for Critical Thinking, "Defining Critical Thinking", http://www.criticalthinking.org/aboutCT/define_critical_thinking.cfm (Retrieved August 7, 2011).
- Ball, W. W. Rouse. A Short Account of the History of Mathematics. London: MacMillan & Co., 1912. Find this book online.
- Smullyan, Raymond. The Lady or the Tiger?: and Other Logic Puzzles. New York: Alfred A. Knopf, 1982.
- Burns, Marilyn. Math for Smarty Pants. New York: Little Brown, 1982.
- Pappas, Theoni. The Magic of Mathematics: Discovering the Spell of Mathematics. San Carlos, CA: Wide World Publishing/Tetra, 1994.
- Ball, W. W. Rouse. Mathematical Recreations & Essays. Eleventh Edition. London: MacMillan, 1939.
- Groza, Vivian Shaw. A Survey of Mathematics: Elementary Concepts and Their Historical Development. New York: Holt, Rinehart and Winston, 1968.
- Chace, Arnold Buffum. The Rhind Mathematical Papyrus. Reston, VA: The National Council of Teachers of Mathematics, 1979.
- Datta, Bibhutibhushan and Avadhesh Narayan Singh. History of Hindu Mathematics: A Source Book. (Bombay: Asia Publishing House, 1962).
- Boyer, Carl B. and Uta C. Merzbach. A History of Mathematics, second edition (New York: John Wiley & Sons, 1991). View book review for this book.
- Posamentier, Alfred S. Math Charmers: Tantalizing Tidbits for the Mind. (Amherst: Prometheus Books, 2003).
- Robison, Gerson B. An Introduction to Mathematical Logic. (Englewood Cliffs: Prentice-Hall, 1969).
- Larson, Loren C. Problem-Solving Through Problems. (New York: Springer-Verlag, 1983).
- Gardner, Martin. aha! Insight. (San Francisco: W. H. Freeman and Company, 1978).
- Gardner, Martin. Entertaining Mathematical Puzzles. (New York: Dover Publications, 1986).
- Gibilisco, Stan. More Puzzles, Paradoxes and Brain Teasers. (Blue Ridge Summit: Tab Books, 1990).
- Pickover, Clifford. Mazes for the Mind. (New York: St. Martin's Press, 1992). View book review for this book.
- Sharp, Evelyn. A Parent's Guide to the New Mathematics. (New York: E. P. Dutton & Co., 1964). You can read a book review of this book.
- Crilly, Tony. The Big Questions: Mathematics. (London: Quercus Publishing, 2011).
- Kasner, Edward and James R. Newman. Mathematics and the Imagination. (New York: Simon and Schuster, 1940).
- Dudeney, H. E. The Canterbury Puzzles. (New York: Dover Publications, 2002).
- Posamentier, Alfred S. and Ingmar Lehmann. Mathematical Amazements and Surprises. (Amherst: Prometheus Books, 2009).
- Berlinghoff, William P. Mathematics: The Art of Reason. (Boston: D. C. Heath and Company, 1967).
- Orkin, Mike. Can you Win? (New York: W. H. Freeman and Company, 1991).
- Rapoport, Anatol. Strategy and Conscience (New York: Harper & Row, 1964).
- Pickover, Clifford. The Math Book (New York: Sterling Publishing Co., 2009).
- Boaler, Jo. What's Math Got to Do With it? (New York: Viking, 2008).
- Gardner, Martin. aha! Gotcha (San Francisco: W. H. Freeman and Company, 1982).
- Pickover, Clifford. Computers and the Imagination (New York: St. Martin's Press, 1991).
- Brecht, George and Patrick Hughes. Vicious Circles and Infinity: A Panoply of Paradoxes. London: Jonathan Cape, 1975.
- Salmon, Wesley (ed.) Zeno's Paradoxes. Indianapolis: The Bobbs-Merrill Company, 1970.
- Frochlichstein, Jack. Mathematical Fun, Games and Puzzles. New York: Dover Publications, 1962.
- Phillips, Hubert, S. T. Shovelton and G. Struan Marshall. Caliban's Problem Book. New York: Dover Publications, 1961.
- MacNeal, Edward. Mathsemantics: Making Numbers Talk Sense. New York: Penguin Books, 1994.
- Kline, Morris. Mathematics in the Modern World. San Francisco: W. H. Freeman, 1968.
- Bolt, Brian. The Amazing Mathematical Amusement Arcade. Cambridge: Cambridge University Press, 1984.
- Keynes, John Neville. Studies and Exercises in Formal Logic. London: MacMillan, 1906.
- Geach, Peter Thomas. Reference and Generality. Ithaca: Cornell University Press, 1962.
- Donner, Michael. Calculator Games. New York: Golden, 1977.
For a list of books I used in 1999–2002 when first working on the site, see the old bibliography page.