“But in our opinion truths of this kind should be drawn from notions rather than from notations.”

— Carl Friedrich Gauss, book Disquisitiones Arithmeticae

About the proof of Wilson's theorem. Disquisitiones Arithmeticae (1801) Article 76

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Carl Friedrich Gauss50

German mathematician and physical scientist 1777–1855

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“The problem in our society and in our schools is to inclulcate, without overdoing it, the notion of education, as in the Latin educere--to lead, to bring out what is in someone rather than merely to indoctrinate him/her from the outside. (89)”

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“Somewhere we taught ourselves that our opinions are more significant than the facts. And somehow we get our egos and our opinions and Truth all mixed up in a single package, so that when something does challenge one of the notions to which we subscribe, we react as if it challenges us.”

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“It would be better, I think, for the man who really seeks the truth not to ask what the poets say; rather, he should first learn the method of finding the scientific premises that I discussed in the second book; then he should train and exercise himself in this method; and when his training is sufficiently advanced, then, as he approaches each particular problem, he should enquire into the premise needed for proving it, which premise he should take from simple sense-perception, which from experience, whether drawn from life or from the arts, which from the truths clearly apprehended by the mind, in order to draw out from them the desired conclusion.”

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“There are different kinds of truths for different kinds of people. There are truths appropriate for children; truths that are appropriate for students; truths that are appropriate for educated adults; and truths that are appropriate for highly educated adults, and the notion that there should be one set of truths available to everyone is a modern democratic fallacy. It doesn't work.”

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“The moment we begin to fear the opinions of others and hesitate to tell the truth that is in us, and from motives of policy are silent when we should speak, the divine floods of light and life no longer flow into our souls.”

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“It seems to me that this last piece, The Poet Speaks, which is the title Schumann gave to this immortal work, should be a transition into a kind of intimate reverie. It is not just about making a beautiful sound and expressive phrasing. You also need to create a sense of dreaming. The truth is, you need to dream this piece, rather than play it.
Will you allow me to take your place? These two phrases are not connected. They are two different elements… of the same musical state. Here, like a question… And here again, another, tenderly asking the way. And from this moment, you should convey the music not just through the notes but through some kind of inspiration drawn from its immortal spirit. Now the sonorities should fade away…grow fainter and dimmer…and you are left simply in the presence of a reminiscent dream.”

Alfred Cortot (1877–1962) Franco-Swiss pianist and conductor

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“So it is more useful to watch a man in times of peril, and in adversity to discern what kind of man he is; for then at last words of truth are drawn from the depths of his heart, and the mask is torn off, reality remains.”
Quo magis in dubiis hominem spectare periclis convenit adversisque in rebus noscere qui sit; nam verae voces tum demum pectore ab imo eliciuntur et eripitur persona, manet res.

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“A work, however, should be judged by its design and its execution, and not by any preconceived notion of what it ought to be according to the critic, rather than the author.”

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“But in our opinion truths of this kind should be drawn from notions rather than from notations.”

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Carl Friedrich Gauss50

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