The older I get, the more I believe that at the bottom of most deep mathematical problems there is a combinatorial problem.
One of the principal objects of theoretical research in my department of knowledge is to find the point of view from which the subject appears in its greatest simplicity.
Mathematics is a language
It doesn't matter how fast your modem is if you're being shelled by ethnic separatists.
Merely corroborative detail, intended to give artistic verisimilitude to an otherwise bald and unconvincing narrative.
The mathematician requires tact and good taste at every step of his work, and he has to learn to trust to his own instinct to distinguish between what is really worthy of his efforts and what is not...
The subtleties of mathematics defecate the grossness of our apprehension, and supply the elements of a sounder and severer logic.
Nature has neither kernel Nor shell
It has been said that figures rule the world. Maybe. But I am sure that figures show us whether it is being ruled well or badly.
She goes in with a prejudice and comes out with a statistic.
If arithmetic overflow is a fatal error, some fascist pig with a read-only mind is trying to enforce machine independence.
GUIs normally make it simple to accomplish simple actions and impossible to accomplish complex actions.
The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there was never any other object for it.
A definition is death. A definition is the answer to which you must look up the question in the back of your book.
He is trying to decide which of two daydreams he will inhabit.
Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane.
Isolated, so-called "pretty theorems" have even less value in the eyes of a modern mathematician than the discovery of a new "pretty flower" has to the scientific botanist, though the layman finds in these the chief charm of the respective sciences.
Without going out of my door I can know all things on Earth.
Why does the universe go to all the bother of existing?
To me, the main weakness of EDA is its failure to enquire why the data were collected in the first place and its consequent tendency to apply ingenious methods largely because they are so attractively ingenious.
Hungry Joe collected lists of fatal diseases and arranged them in alphabetical order so that he could put his finger without delay on any one he wanted to worry about.
The propositions of mathematics have, therefore, the same unquestionable certainty which is typical of such propositions as "All bachelors are unmarried," but they also share the complete lack of empirical content which is associated with that certainty: The propositions of mathematics are devoid of all factual content; they convey no information whatever on any empirical subject matter.
Under the bludgeonings of chance My head is bloody, but unbowed.
Religions often partake of the myth of progress that shields us from the terrors of an uncertain future.
I do not think that the radio waves I have discovered will have any practical application.
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