[FOM] Quotation of Brouwer on Cantor

Martin Davis martin at eipye.com
Thu Sep 8 14:15:55 EDT 2005

Patrick Caldon wrote:

 >I dimly recall a statement of Brouwer's, something vaguely along the 
lines of
 >"Cantorian mathematics was a sickness which is best forgotten"

For years I heard something similar attributed to Poincaré: "Some day set 
theory will be regarded as a disease from which one has recovered." Wanting 
to quote this in a book I was writing I researched the matter and came up 
empty-handed. Remarks about Cantor's transfinite I could find in Poincaré's 
writings were much more equivocal.

Stories about sayings of mathematicians float around the profession, but 
must be regarded as mere rumors without a firm attribution. Another 
example: Rebecca Goldstein's recent book on Goedel quotes Hilbert, almost 
certainly incorrectly,  on his foundational views. But she could cite  an 
actual book of mathematical sayings for the quote. Of course that book of 
sayings gave no source, merely repeating hearsay. This instance seems to 
have gone back to E.T. Bell's rather crude expalantion of Hilbertian 
formalism that later writers turned into an alleged quote from Hilbert.

The supposed quotation from Brouwer doesn't ring true to my ear, but of 
course I may be mistaken about that.


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