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Battle of the Frog and the Mouse (1984)
John Barrow
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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
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  1. Gauß, Eisenstein, and the ``third'' proof of the Quadratic Reciprocity Theorem: Ein kleines Schauspiel by Reinhard C. Laubenbacher / David J. Pengelley
  2. Infinities by John Barrow
  3. Lucy and David and the God Equation by Alan McKenzie
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  5. Ultima lezione a Gottinga [Last lecture at Göttingen] by Davide Osenda
  6. Pythagorean Crimes by Tefcros Michaelides
  7. Intoxicating Heights (Höhenrausch. Die Mathematik des XX. Jahrhunderts in zwanzig Gehirnen) by Dietmar Dath
  8. Ramanujan’s Miracles – A Drama To Demystify Mathematics by R.N. Kapur
  9. The Extraordinary Hotel or the Thousand and First Journey of Ion the Quiet by Naum Ya. Vilenkin
  10. Turing (A Novel About Computation) by Christos Papadimitriou
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MotifReal Mathematicians, Gödel,
TopicReal Mathematics, Logic/Set Theory,
MediumShort Stories,

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(Maintained by Alex Kasman, College of Charleston)