In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance.
--
"Mathematical Games", in Scientific American (October 1973); also quoted in Roger B. Nelson, Proofs Without Words: Exercises in Visual Thinking (1993), "Introduction", p. vMartin Gardner
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I do not have the courage to force myself to search out beautiful prayers in books. There are so many of them it really gives me a headache! and each prayer is more beautiful than the others. I cannot recite them all and not knowing which to choose, I do like children who do not know how to read, I say very simply to God what I wish to say, without composing beautiful sentences, and He always understands me. For me, prayer is an aspiration of the heart, it is a simple glance directed to heaven, it is a cry of gratitude and love in the midst of trial as well as joy; finally, it is something great, supernatural, which expands my soul and unites me to Jesus.
Therese of Lisieux
A mathematician, then, will be defined in what follows as someone who has published the proof of at least one non-trivial theorem.
Jean Dieudonne
The idea that theorems follow from the postulates does not correspond to simple observation. If the Pythagorean theorem were found to not follow from the postulates, we would again search for a way to alter the postulates until it was true. Euclid's postulates came from the Pythagorean theorem, not the other way around.
Richard Hamming
As a boy of six I could understand the proof of a mathematical theorem more readily than that meat had to be cut with one's knife, not one's fork.
Ferdinand Eisenstein
The geometric point is an invisible thing. Therefore, it must be defined as an incorporeal thing. Considered in terms of substance, it equals zero. […] Thus we look upon the geometric point as the ultimate and most singular union of silence and speech. The geometric point has, therefore, been given its material form, in the first instance, in writing. It belongs to language and signifies silence.
Wassily Kandinsky
Gardner, Martin
Garfield, James A.
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