Todhunter, Isaac (1820-1910)
[Asked whether he
would like to see an
I have been teaching
it all my life, and
I do not want to
have my ideas upset.
Tolstoy, [Count] Lev Nikolgevich (1828-1920)
A modern branch of mathematics, having achieved the art of dealing with the infinitely small, can now yield solutions in other more complex problems of motion, which used to appear insoluble. This modern branch of mathematics, unknown to the ancients, when dealing with problems of motion, admits the conception of the infinitely small, and so conforms to the chief condition of motion (absolute continuity) and thereby corrects the inevitable error which the human mind cannot avoid when dealing with separate elements of motion instead of examining continuous motion. In seeking the laws of historical movement just the same thing happens. The movement of humanity, arising as it does from innumerable human wills, is continuous. To understand the laws of this continuous movement is the aim of history. Only by taking an infinitesimally small unit for observation (the differential of history, that is, the individual tendencies of man) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history.
Tolstoy, Count Lev Nikolgevich (1828-1920)
A man is like a fraction whose numerator is what he is and whose denominator is what he thinks of himself. The larger the denominator the smaller the fraction.
In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1989.
Turgenev, Ivan Sergeievich (1818-1883)
Whatever a man prays for, he prays for a miracle. Every prayer reduces itself to this: "Great God, grant that twice two be not four."
Attaching significance to invariants is an effort to recognize what, because of its form or colour or meaning or otherwise, is important or significant in what is only trivial or ephemeral. A simple instance of failing in this is provided by the poll-man at Cambridge, who learned perfectly how to factorize \(a^2 - b^2\) but was floored because the examiner unkindly asked for the factors of \(p^2 - q^2.\)
In J. R. Newman (ed.), The World of Mathematics, New York: Simon and Schuster, 1956.
I have resumed the
study of mathematics
with great avidity.
It was ever my
favourite one ...
on the mind; all is
James J. Tattersall,
Theory in Nine