Quotes

$$ \Large e^{i\pi} + 1 = 0 \qquad i = \sqrt{ -1 } \qquad e = \sum \limits _{n=0}^{\infty}{\frac{1}{n!}} = \lim _{n\to \infty} \left( 1 + {\frac{1}{n}} \right)^{n} $$

$$ \Large \pi = 2 \int_{-1 }^{+1}(\sqrt{1 - x^2})dx \qquad \int_{ -\infty }^{ + \infty } e^{-x^2 }dx = \sqrt{\pi} \qquad n! = \Gamma \left( n + 1 \right) = \int_{ 0 }^{ + \infty } x^{n}e^{-x}dx $$

There are only two kinds of math books: those you can’t read past the first sentence, and those you can’t read past the first page

Chen Ning Yang, Nobel Laureate in Physics (1957)

A book on mathematics without any difficulty would be useless. Geoffrey Hardy, Nature 150, 673-674,1942 (review in Courant-Robbins, What is Mathematics, 1941)

It is almost impossible for me to read contemporary mathematicians who, instead of saying “Petya washed his hands,” simply write: There is a $ t_{1} < 0 $ such that the $ t_{1} $ image under the natural application $ t_{1} \mapsto{\rm {Petya}}(t_{1}) $ belongs to the set of dirty hands $ S $, and there exists a $ t_{2} $ satisfying the condition $ t_{1} < t_{2} \leq 0 $ and such that the image of $ t_{2} $ under the above mapping $ t_{2} \mapsto{\rm {Petya}}(t_{2}) $ belongs to the complement of the set $ S $ defined in the previous sentence.

Vladimir Arnold, in Conversation with Vladimir Igorevich Arnol’d, The Mathematical Intelligencer, December 1987, Volume 9, Issue 4, pp 28-32. http://link.springer.com/article/10.1007/BF03023727

A mathematician who does not have some of the poet cannot be a perfect mathematician

Karl Weierstrass, letter to Sof’ja Kovalevskaya, August 27, 1883

The mathematician, like the painter and the poet, is a creator of forms. if the forms he creates are more enduring than theirs, it is because his are made of ideas …

The forms created by the mathematician, like those created by the painter or the poet, must be beautiful; ideas, like colors or words, must bind harmoniously.

Beauty is the basic requirement: there is no perennial place in the world for ugly math.

Archimedes will be remembered when Aeschylus is forgotten, because languages die but mathematical ideas do not.

Pure mathematics is on the whole definitely more useful than applied mathematics.

I am interested in mathematics only as a creative art.

Godfrey H. Hardy,Apology of a Mathematician (1940)

No mathematician can afford to forget that mathematics, more than any other art or any other science, it is an activity for young people. I don’t know of a single example of a major mathematical advance undertaken by a man over the age of fifty. Godfrey H. Hardy,Apology of a Mathematician (1940)