What if angry
vectors veer
Round your
sleeping head, and
form.
There's
never need to
fear
Violence
of the poor world's
abstract storm.
Lullaby in Encounter, 1957.
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Loci: Convergence
Mathematical Quotations
Our library of quotations is organized alphabetically by surname of the author.
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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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