In numbers warmly pure and sweetly strong.

 

In numbers warmly pure and sweetly strong.
--
Ode to Simplicity.

 

William Collins

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If the heart of a man is depressed with cares,
The mist is dispell'd when a woman appears;
Like the notes of a fiddle, she sweetly, sweetly
Raises the spirits, and charms our ears.

 

John Gay

 

Pythagoras, as everyone knows, said that "all things are numbers." This statement, interpreted in a modern way, is logical nonsense, but what he meant was not exactly nonsense. He discovered the importance of numbers in music and the connection which he established between music and arithmetic survives in the mathematical terms "harmonic mean" and "harmonic progression." He thought of numbers as shapes, as they appear on dice or playing cards. We still speak of squares or cubes of numbers, which are terms that we owe to him. He also spoke of oblong numbers, triangular numbers, pyramidal numbers, and so on. These were the numbers of pebbles (or as we would more naturally say, shot) required to make the shapes in question.

 

Pythagoras

 

For me Greece is Maria Farantouri. This is how I imagined Goddess Hera to be: strong, pure and vigilant. I have never encountered any other artist able to give me such a strong sense of the divine.

 

Francois Mitterrand

 

The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational numbers is wholly dissimilar to, and I might even say in principle the same as, my method described above of introducing transfinite numbers. One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite.

 

Georg Cantor

 

That from the outset they expect or even impose all the properties of finite numbers upon the numbers in question, while on the other hand the infinite numbers, if they are to be considered in any form at all, must (in their contrast to the finite numbers) constitute an entirely new kind of number, whose nature is entirely dependent upon the nature of things and is an object of research, but not of our arbitrariness or prejudices.

 

Georg Cantor