André Weil - Collected Quotes

"Finally, students must learn to realize that mathematics is a science with a long history behind it, and that no true insight into the mathematics of the present day can be obtained without some acquaintance with its historical background. In the first-place time gives an additional dimension to one's mental picture both of mathematics as a whole, and of each individual branch." (André Weil, "The Mathematical Curriculum", 1954)

"Rigor is to the mathematician what morality is to man. It does not consist in proving everything, but in maintaining a sharp distinction between what is assumed and what is proved, and in endeavoring to assume as little as possible at every stage." (André Weil, Mathematical Teaching in Universities", The American Mathematical Monthly Vol. 61 (1), 1954)

"As every mathematician knows, nothing is more fruitful than these obscure analogies, these indistinct reflections of one theory into another, these furtive caresses, these inexplicable disagreements; also nothing gives the researcher greater pleasure." (André Weil, "De la Métaphysique aux Mathématiques", 1960)

"Nothing is more fruitful - all mathematicians know it - than those obscure analogies, those disturbing reflections of one theory on another; those furtive caresses, those inexplicable discords; nothing also gives more pleasure to the researcher. The day comes when this illusion dissolves: the presentiment turns into certainty; the yoked theories reveal their common source before disappearing. As the Gita teaches, one achieves knowledge and indifference at the same time. Metaphysics has become Mathematics, ready to form the material of some treatise whose cold beauty has lost the power to move us." (André Weil, "De la métaphysique aux mathématiques", 1960)

"Alternative models are neither right nor wrong, just more or less useful in allowing us to operate in the world and discover more and better options for solving problems." (Andrew Weil," The Natural Mind: A Revolutionary Approach to the Drug Problem", 2004)

"A tediously laborious proof may be a sign that the writer has been less than felicitous in expressing himself; but more often than not, as we know, it indicates that he has been laboring under limitations which prevented him from translating directly into words or formulas some very simple ideas." (André Weil)

"In the future, as in the past, the great ideas [of mathematics] must be simplifying ideas, the creator must always be one who clarifies, for himself, and for others, the most complicated issues of formulas and concepts." (André Weil)

"Strategy means the art of recognizing the main problems, attacking them at their weak points, setting up future lines of advance. Mathematical strategy is concerned with long-range objectives; it requires a deep understanding of broad trends and of the evolution of ideas over long periods." (André Weil)