We can... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics.
Hans Reichenbach
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A few rules include all that is necessary for the perfection of the definitions, the axioms, and the demonstrations, and consequently of the entire method of the geometrical proofs of the art of persuading.
Blaise Pascal
Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning... The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.
Alan Turing
The real problem in speech is not precise language. The problem is clear language. The desire is to have the idea clearly communicated to the other person. It is only necessary to be precise when there is some doubt as to the meaning of a phrase, and then the precision should be put in the place where the doubt exists. It is really quite impossible to say anything with absolute precision, unless that thing is so abstracted from the real world as to not represent any real thing. Pure mathematics is just an abstraction from the real world, and pure mathematics does have a special precise language for dealing with its own special and technical subjects. But this precise language is not precise in any sense if you deal with real objects of the world, and it is only pedantic and quite confusing to use it unless there are some special subtleties which have to be carefully distinguished.
Richard Feynman
There is still a difference between something and nothing, but it is purely geometrical and there is nothing behind the geometry.
Martin Gardner
Beauty cannot be defined by abscissas and ordinates; neither are circles and ellipses created by their geometrical formulas.
Carl von Clausewitz
Reichenbach, Hans
Reinfeldt, Fredrik
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