Russell, Bertrand (1872-1970)
It can be shown that a mathematical web of some kind can be woven about any universe containing several objects. The fact that our universe lends itself to mathematical treatment is not a fact of any great philosophical significance.
W. H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms, New York: Viking Press, 1966.
Rutherford, Ernest (1871-1937)
If your experiment needs statistics, you ought to have done a better experiment.
In N. T. J. Bailey the Mathematical Approach to Biology and Medicine, New York: Wiley, 1967.
Richard Courant
Calculus is the
culmination of a
dramatic
intellectual
struggle which has
lasted for over 2500
years and has proved
itself to be the
greatest achievement
of western
civilization.
Richard Courant
The interplay
between generality
and individuality,
deduction and
construction, logic
and imagination -
this is the profound
essence of live
mathematics. Any
one or another of
these aspects of
mathematics can be
at the center of a
given achievement.
In a far reaching
development all of
them will be
involved. Generally
speaking, such a
development will
start from the
"concrete" ground,
then discard ballast
by abstraction
and rise to the
lofty layers of thin
air where navigation
and observation are
easy; after this
flight comes the
crucial test of
landing and reaching
specific goals in
the newly surveyed
low plains of
individual
"reality." In
brief, the flight
into abstract
generality must
start from and
return again to the
concrete and
specific.
Ralph Waldo Emerson
We do not listen
with the best regard
to the verses of a
man who is only a
poet, nor to his
problems if he is
only an algebraist;
but if a man is at
once acquainted with
the geometric
foundation of things
and with their
festal splendor, his
poetry is exact and
his arithmetic
musical.
Rota, Gian-Carlo (1932-1999)
There is, thus, a hidden circularity in formal mathematical exposition. The theorems are proved starting with definitions; but the definitions themselves are motivated by the theorems that we have previously decided ought to be correct.
Indiscrete Thoughts (Birkhauser Boston, 1997), p. 97
Rota, Gian-Carlo (1932-1999)
There is nothing more deadly for a non-professional mathematician than being assaulted by a rigorous version of facts which have always been obvious.
Indiscrete Thoughts (Birkhauser Boston, 1997), p. 245