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... mathematicians progress only by doubt, through humble and constant attempts to impinge on the immense domain of the unknown.
--
Leopold Infeld (1948). Whom the Gods Love: The Story of Évariste Galois. Whittlesey House. p. 9. 

 

Leopold Infeld

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These societies already begin to encroach everywhere on the functions of the State, and strive to substitute free action of volunteers for that of a centralized State. In England we see arise insurance companies against theft; societies for coast defense, volunteer societies for land defense, which the State endeavors to get under its thumb, thereby making them instruments of domination, although their original aim was to do without the State. Were it not for Church and State, free societies would have already conquered the whole of the immense domain of education. And, in spite of all difficulties, they begin to invade this domain as well, and make their influence already felt.
And when we mark the progress already accomplished in that direction, in spite of and against the State, which tries by all means to maintain its supremacy of recent origin; when we see how voluntary societies invade everything and are only impeded in their development by the State, we are forced to recognize a powerful tendency, a latent force in modern society.

 

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He liked the vast openness of sky and prairie, and found loneliness a pleasure with so immense a domain to be alone in.

 

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...it is rare that mathematicians are intuitive, and that men of intuition are mathematicians, because mathematicians wish to treat matters of intuition mathematically, and make themselves ridiculous, wishing to begin with definitions and then with axioms, which is not the way to proceed in this kind of reasoning. Not that the mind does not do so, but it does it tacitly, naturally, and without technical rules; for the expression of it is beyond all men, and only a few can feel it. 1

 

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Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians.

 

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