A mathematician of the first rank, Laplace quickly revealed himself as
only a mediocre administrator; from his first work we saw that we had
been deceived. Laplace saw no question from its true point of view; he
sought subtleties everywhere; had only doubtful ideas, and finally carried
the spirit of the infinitely small into administration.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
Teach to the the problems, not to the text.
In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.
To state a theorem and then to show examples of it is literally to teach
backwards.
In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.
A good preparation takes longer than the delivery.
In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.
The greatest reward lies in making the discovery; recognition can add little or nothing to that.
In mathematics you don't understand things. You just get used to them.
In G. Zukav The Dancing Wu Li Masters.
The most painful thing about mathematics is how far away you are from
being able to use it after you have learned it.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
The discovery in 1846 of the planet Neptune was a dramatic and spectacular
achievement of mathematical astronomy. The very existence of this new
member of the solar system, and its exact location, were demonstrated
with pencil and paper; there was left to observers only the routine task
of pointing their telescopes at the spot the mathematicians had marked.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
It is hard to know what you are talking about in mathematics, yet no one
questions the validity of what you say. There is no other realm of discourse
half so queer.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
Mathematical economics is old enough to be respectable, but not all economists
respect it. It has powerful supporters and impressive testimonials, yet
many capable economists deny that mathematics, except as a shorthand or
expository device, can be applied to economic reasoning. There have even
been rumors that mathematics is used in economics (and in other social
sciences) either for the deliberate purpose of mystification or to confer
dignity upon commonplacesas French was once used in diplomatic communications.
....
To be sure, mathematics can be extended to any branch of knowledge, including
economics, provided the concepts are so clearly defined as to permit accurate
symbolic representation. That is only another way of saying that in some
branches of discourse it is desirable to know what you are talking about.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
The Theory of Groups is a branch of mathematics in which one does something
to something and then compares the result with the result obtained from
doing the same thing to something else, or something else to the same
thing.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
Games are among the most interesting creations of the human mind, and
the analysis of their structure is full of adventure and surprises. Unfortunately
there is never a lack of mathematicians for the job of transforming delectable
ingredients into a dish that tastes like a damp blanket.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
...from the same principles, I now demonstrate the frame of the System of
the World.
Principia Mathematica.
Hypotheses non fingo.
I feign no hypotheses.
Principia Mathematica.
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.
The description of right lines and circles, upon which geometry is founded,
belongs to mechanics. Geometry does not teach us to draw these lines,
but requires them to be drawn.
Principia Mathematica.
The latest authors, like the most ancient, strove to subordinate the phenomena of nature to the laws of mathematics.
[His epitaph:]
Who, by vigor of mind almost divine, the motions and figures
of the planets, the paths of comets, and the tides of the seas first demonstrated.
[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.