FOM: Mathematical Intuition

[F. Xavier Noria]

On Fri, 05 Jan 2001 14:13:36 -0500, you wrote:

; A very good observation.  There's a lot going on in mathematicians'
; brains which may not be so easy to reduce to a completely rigorous proof
; in written form, but which is in its own way reliable.  This is probably
; because the mathematician has formal structures in his brain which he
; does not explicitly understand but which represent reliable intuition
; because of the way they have developed over the course of the
; mathematician's life of studying proofs -- they arose via a gradual
; pushing of mathematical reasoning-steps below the level of consciousness
; as more mathematics was learned and the same types of arguments were
; seen over and over.

Just for the record, last year was published an IMHO very interesting book
that talks about maths from a cognitive science perspective:

   G. Lakoff, Rafael E. Nu~nez, "Where Mathematics Comes From:
   How the Embodied Mind Brings Mathematics into Being".
   Basic Books, 2000. ISBN 0465037704.
   http://www.amazon.com/exec/obidos/ASIN/0465037704/o/qid=978731943/sr=8-1/ref=aps_sr_b_1_1/105-4734841-3568734

(Not too recommendable for platonists :-)

-- fxn