constructive vs. classical (existential) mathematics..

[Subbarao Kambhampati <rao@asu.edu>]

Check out
 http://digitalphysics.org/Publications/Cal79/html/cmath.htm

for a nice discussion on the Constructive vs. Classical mathematics--and 
how during Hilbert's time there was a pretty big
controversy in mathematics--with mathematicians such as Brouer insisted 
that all math that depended on existential proofs be thrown out.
Papa Hilbert had to come to rescue--pretty heady stuff.

You might also look at

http://plato.stanford.edu/entries/mathematics-constructive/

which also talks about the "slick" irrational power irrational can be 
rational proof...

rao