In response to your second question, this is not precisely what you're looking for, but here is one quote by Yuri Manin along the same lines:

*All the other vehicles of mathematical rigor are secondary [to definitions], even that of rigorous proof.*

Manin makes this remark in an essay, entitled "*Interrelations between Mathematics and Physics*" that contains more memorable phrases, such as the final line of this extended quote:

All the other vehicles of mathematical rigor are secondary [to definitions], even that of rigorous proof. In fact, barring direct mistakes, the
most crucial difficulty with checking
a proof lies usually in the
insufficiency of definitions (or lack
thereof). In plain words, we are more
deeply troubled when we wonder what
the author wants to say than when we
do not quite see whether what he or
she is saying is correct. The flaws in
the argument in a strictly defined
environment are quite detectable. Good
mathematics might well be written down
at a stage when proofs are incomplete
or missing, but informed guesses can
already form a fascinating system:
outstanding instances are A. Weil’s
conjectures and Langlands’s program,
but there are many examples on a
lesser scale.

To the contrary, an inexperienced
reader of the most interesting
physical papers is often left in a
vacuum about the precise meaning of
the most common terms. Physicists are
undoubtedly constrained by their own
rules, but these rules are not ours.
What is a current algebra, a
supersymmetry transformation, a
topological field theory, a path
integral, finally? They are very open
concepts, and it is precisely their
openness that makes them so
interesting. Here is what the history
of our two metiers teaches: we cannot
live without each other. At least for
some of us, life becomes dull if it
goes on for too long without contacts
with good physics.
In this century romantics comes from
physics. Mathematics supplies hygienic
habits and headaches.

badcategory? – Mahdi Majidi-Zolbanin Jun 7 '13 at 2:25