Loci: Convergence
Mathematical Quotations
Our library of quotations is organized alphabetically by surname of the author.
Page: 1 of 9 | Next
Hadamard, Jacques
Practical
application is found
by not looking for
it, and one can say
that the whole
progress of
civilization rests
on that principle.
Hadamard, Jacques
The shortest path between two truths in the real domain passes through the complex domain.
Jacques Hadamard
The shortest path
between two truths
in the real domain
passes through the
complex domain.
Haldane, John Burdon Sanderson (1892-1964)
A time will however come (as I believe) when physiology will invade and destroy mathematical physics, as the latter has destroyed geometry.
Haldane, John Burdon Sanderson (1892-1964)
In scientific thought we adopt the simplest theory which will explain all the facts under consideration and enable us to predict new facts of the same kind. The catch in this criterion lies in the world "simplest." It is really an aesthetic canon such as we find implicit in our criticisms of poetry or painting. The layman finds such a law as dx/dt = K(d^2x/dy^2) much less simple than "it oozes," of which it is the mathematical statement. The physicist reverses this judgment, and his statement is certainly the more fruitful of the two, so far as prediction is concerned. It is, however, a statement about something very unfamiliar to the plainman, namely, the rate of change of a rate of change.
Halmos, Paul R.
To be a scholar of
mathematics you must
be born with talent,
insight,
concentration,
taste, luck, drive
and the ability to
visualize and guess.
Halmos, Paul R.
Don't just read it;
fight it! Ask your
own questions, look
for your own
examples, discover
your own proofs. Is
the hypothesis
necessary? Is the
converse true? What
happens in the
classical special
case? What about the
degenerate cases?
Where does the proof
use the hypothesis?
Halmos, Paul R.
The joy of suddenly
learning a former
secret and the joy
of suddenly
discovering a
hitherto unknown
truth are the same
to me -- both have
the flash of
enlightenment, the
almost incredibly
enhanced vision, and
the ecstasy and
euphoria of released
tension.
Halmos, Paul R.
[T]he source of all
great mathematics is
the special case,
the concrete
example. It is
frequent in
mathematics that
every instance of a
concept of seemingly
great generality is
in essence the same
as a small and
concrete special
case.
Halmos, Paul R.
I remember one
occasion when I
tried to add a
little seasoning to
a review, but I
wasn't allowed to.
The paper was by
Dorothy Maharam, and
it was a perfectly
sound contribution
to abstract measure
theory. The domains
of the underlying
measures were not
sets but elements of
more general Boolean
algebras, and their
range consisted not
of positive numbers
but of certain
abstract equivalence
classes. My proposed
first sentence was:
"The author
discusses valueless
measures in
pointless spaces."
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