„The principal aim of mathematical education is to develop certain faculties of the mind, and among these intuition is not the least precious.“

—  Henri Poincaré, libro Science and Method, Science and Method (1908), Context: The principal aim of mathematical education is to develop certain faculties of the mind, and among these intuition is not the least precious. It is through it that the mathematical world remains in touch with the real world, and even if pure mathematics could do without it, we should still have to have recourse to it to fill up the gulf that separates the symbol from reality. Part II. Ch. 2 : Mathematical Definitions and Education, p. 128 Variant translation: The chief aim of mathematics teaching is to develop certain faculties of the mind, and among these intuition is by no means the least valuable.
Texto original

Le but principal de l'enseignement mathématique est de développer certaines facultés de l'esprit et parmi elles l'intuition n'est pas la moins précieuse. C'est par elle que le monde mathématique reste en contact avec le monde réel et quand les mathématiques pures pourraient s'en passer, il faudrait toujours y avoir recours pour combler l'abîme qui sépare le symbole de la réalité.

Science and Method (1908)

Henri Poincaré Foto
Henri Poincaré11
científico y filósofo francés 1854 - 1912

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„Education doesn’t have aims. It is the aim of other things.“

—  Andrew Abbott American sociologist and Professor of Sociology at the University of Chicago. 1948
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„The assumptions and definitions of mathematics and science come from our intuition“

—  Richard Hamming American mathematician and information theorist 1915 - 1998
Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985), Context: The assumptions and definitions of mathematics and science come from our intuition, which is based ultimately on experience. They then get shaped by further experience in using them and are occasionally revised. They are not fixed for all eternity.

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—  Paul Cohen American mathematician 1934 - 2007
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„One of the goals of education should be to teach that life is precious.“

—  Abraham Maslow, libro Motivation and Personality
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„I propose that the aim of education is exactly the opposite, namely, the widening and deepening of consciousness. To the extent that education can help the student develop sensitivity, depth of perception, and above all the capacity to perceive significant forms in what he is studying, it will be developing at the same time the student's capacity to deal with anxiety constructively.“

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Wholeness and the Implicate Order (1980), Context: My suggestion is that at each state the proper order of operation of the mind requires an overall grasp of what is generally known, not only in formal logical, mathematical terms, but also intuitively, in images, feelings, poetic usage of language, etc. (Perhaps we could say that this is what is involved in harmony between the 'left brain' and the 'right brain'). This kind of overall way of thinking is not only a fertile source of new theoretical ideas: it is needed for the human mind to function in a generally harmonious way, which could in turn help to make possible an orderly and stable society. <!-- p. xi

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„Physics is essentially an intuitive and concrete science. Mathematics is only a means for expressing the laws that govern phenomena.“

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„Numbers instill a feeling for the lie of the land, and furnish grist for the mathematical mill that is the physicist's principal tool.“

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„Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam egestas wisi a erat. Morbi imperdiet, mauris ac auctor dictum.“

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