a list compiled by Alex Kasman (College of Charleston)

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The Rule of Four (2004)
Ian Caldwell / Dustin Thomason

Contributed by Vijay Fafat

There is an enigmatic book from the late 15th century called Hypnerotomachia Poliphili, written by an Italian monk, Francesco Colonna (available at for download). The book chronicles the dream-within-a-dream love adventure of Poliphilo and his object of affection, Polia. The enigma of the book arises from the author's use of vocabulary from multiple languages and neologisms, which give it an inscrutable, labyrinth-like quality and a suspicion that it contains far more than just the richly illustrated love story.

“The Rule of Four” takes off on this premise that there is a hidden code in the text of Hypnerotomachia; in fact, the entire book is a cipher pointing to a very well-guarded secret. Set on the grounds of Princeton University, “The Rule of Four” shows how two students unlock the mystery. Naturally, the book is full of allusions to cryptography, mathematical patterns, breathless chases, historical and current murders, lost manuscripts, etc. For example,

  • an expert at the mathematical analysis of the Torah plays a role,
  • the sequence 3, 4, 6, 9 is found to unlock one part of the book since “it is the smallest sequence which produces all three harmonies (arithmetic, geometric and harmonic)” [I don't know what this means].
  • Eratosthenes and his measurement of Earth's circumference based on the geometry of shadows is discussed when one of the clues requires the students to calculate “the distance between you and the horizon” (the sub-puzzle at this point of the story is about art and perspective drawing).
  • Quote from book: “The most complicated concept he taught me was how to decode a book based on algorithms or ciphers from the text itself. In those cases, the key is built right on. You solve for the cipher, like an equation or a set of instructions, the you use the cipher to unlock the text. The book acually interprets itself.”
The novel is a lot of fun to read and savor.

More information about this work can be found at
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Works Similar to The Rule of Four
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. The Da Vinci Code by Dan Brown
  2. Bone Chase by Weston Ochse
  3. PopCo by Scarlett Thomas
  4. The Lost Books of the Odyssey by Zachary Mason
  5. The Eight by Katherine Neville
  6. Lord Byron's Novel: The Evening Land by John Crowley
  7. Tetraktys by Ari Juels
  8. Decoded by Mai Jia
  9. The Crimson Cipher by Susan Page Davis
  10. She Spies (Episode: Message from Kassar) by Vince Manze (script) / Joe Livecchi (script) / Steven Long Mitchell (script)
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Exciting News: The 1,600th entry was recently added to this database of mathematical fiction! Also, for those of you interested in non-fictional math books let me (shamelessly) plug the recent release of the second edition of my soliton theory textbook.

(Maintained by Alex Kasman, College of Charleston)