Contributed by
Vijay Fafat
This succinct, wellwrittten 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 blowbyblow between Hilbert and Brouwer, as well as the related Wikipedia articles.
