> In conversationally questioning the mathematical interest of the
> Dedekind-Peano axioms [and formal logical systems generally],
> Gian-Carlo Rota once remarked that number theorists he knew consider
> using mathematical induction in a proof to be "tasteless" [I think
> that was his term -- it may well have been "childish"].
> ...
My favorite sniffy quote on induction is from the preface to a book on
combinatorics by Daniel Cohen (probably Basic techniques of combinatorial
theory / Daniel I. A. Cohen
Wiley, c1978, but I don't have it hand to check):
As another matter of taste, I must confess to feeling that, of
all proof techniques, mathematical induction is the least
satisfying. It is usually non-constructive, inelegant, hard to
generalize, and does not shed the light of understanding on the
origins of the formula that it merely verifies.
-- Duncan J. Melville Dept of Mathematics St. Lawrence University Canton, NY 13617