Pure mathematics is on the whole distinctly more useful
than applied. For what is useful above all is technique,
and mathematical technique is taught mainly through
pure mathematics.
Young Men should prove theorems, old men should write books.
Quoted by Freeman Dyson in Freeman Dyson: Mathematician, Physicist,
and Writer. Interview with Donald J. Albers, The College Mathematics Journal,
vol. 25, No. 1, January 1994.
A science is said to be useful of its development tends to
accentuate the existing inequalities in the distribution of
wealth, or more directly promotes the destruction of
human life.
A Mathematician's Apology, London,
Cambridge University Press, 1941.
I believe that mathematical reality lies outside us,
that our function is to discover or observe it,
and that the theorems which we prove,
and which we describe grandiloquently
as our "creations,"
are simply the notes of
our observations.
A Mathematician's Apology, London,
Cambridge University Press, 1941.
It is now quite lawful for a Catholic woman to avoid pregnancy
by a resort to mathematics, though she is still forbidden to
resort to physics and chemistry.
Newton, Isaac
(1642-1727) To explain all nature is too difficult a task for any one man
or even for any one age. `Tis much better to do a little with certainty,
and leave the rest for others hat come after you,
than to explain all things.
In G. Simmons Calculus Gems,
New York: McGraw Hill Inc., 1992.
[Of her:] Her statistics were more than a study, they were indeed her religion. For her Quetelet was the hero as scientist, and the presentation copy of his Physique sociale is annotated by her on every page. Florence Nightingale believed -- and in all the actions of her life acted upon that belief -- that the administrator could only be successful if he were guided by statistical knowledge. The legislator -- to say nothing of the politician -- too often failed for want of this knowledge. Nay, she went further; she held that the universe -- including human communities -- was evolving in accordance with a divine plan; that it was man's business to endeavor to understand this plan and guide his actions in sympathy with it. But to understand God's thoughts, she held we must study statistics, for these are the measure of His purpose. Thus the study of statistics was for her a religious duty.
K. Pearson The Life, Letters and Labours for Francis Galton, vol. 2, 1924.
Today, it is not only that our kings do not know mathematics,
but our philosophers do not know mathematics and -- to go a step further --
our mathematicians do not know mathematics.
Our federal income tax law defines the tax y to be paid in terms of the income x; it does so in a clumsy enough way by pasting several linear functions together, each valid in another interval or bracket of income. An archeologist who, five thousand years from now, shall unearth some of our income tax returns together with relics of engineering works and mathematical books, will probably date them a couple of centuries earlier, certainly before Galileo and Vieta.
The Mathematical Way of Thinking, an address given at the Bicentennial Conference at the University of Pennsylvania, 1940.
Without the concepts, methods and results found and developed by
previous generations right down to Greek antiquity one cannot understand
either the aims or achievements of mathematics in the last 50 years.
[Said in 1950] The American Mathematical Monthly, v. 100. p. 93.
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