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Battle of the Frog and the Mouse (1984)
John Hays

Contributed by Vijay Fafat

This succinct, well-writtten fable captures the polemics between Hilbert and Brouwer related to Hilbert's Formalist position and Brouwer's Constructivist position vis a vis the foundations of mathematics (in particular, the use of devices like the law of excluded middle applied to infinite sets and reductio ad absurdum). The fabular setting is in a forest where animals are mathematicians, philosophers and scientists, Hilbert playing the role of a mouse and Brouwer a frog. The title and the characterization goes back to Einstein, who, upon hearing about the acrimonious exchange between the two mathematicians, asked: "What is this frog and mouse battle?". The fable ends with the annnouncement of Godel's result and a mathematical poem.

For people not familiar with the issues, a good background start would be in Hal Hellman's book, "Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever" which delves into the blow-by-blow between Hilbert and Brouwer, as well as the related Wikipedia articles.

Appeared in Mathematical Intelligencer, VOL. 6, NO. 2, 1984, reprinted 1992 in Pi in the Sky.

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Works Similar to Battle of the Frog and the Mouse
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Gauß, Eisenstein, and the ``third'' proof of the Quadratic Reciprocity Theorem: Ein kleines Schauspiel by Reinhard C. Laubenbacher / David J. Pengelley
  2. Cantor’s Dragon by Craig DeLancy
  3. Infinities by John Barrow
  4. Puzzles from Other Worlds by Martin Gardner
  5. Science Fiction Puzzle Tales by Martin Gardner
  6. Lucy and David and the God Equation by Alan McKenzie
  7. Ultima lezione a Gottinga [Last lecture at Göttingen] by Davide Osenda
  8. Murder on the Einstein Express by Harun Šiljak
  9. Pythagorean Crimes by Tefcros Michaelides
  10. What the Tortoise Said to Achilles by Lewis Carroll
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MotifReal Mathematicians, Kurt Gödel,
TopicReal Mathematics, Logic/Set Theory,
MediumShort Stories,

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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)