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.
Henri PoincaréRelated topics
aim certain education fill intuition mathematics mind precious principal pure real recourse should touch remainsRelated quotes
The Church is an enclosure, if you are within, the wolf cannot enter, but if you stray outside the wild beasts will get you...Do not wander from the Church; there is nothing more impregnable than the Church. She is your hope and your salvation. She is higher than the heavens, firmer than rock, wider than the world; she never grows old, but is forever renewing her youth.
John Chrysostom
For Christians above all men are forbidden to correct the stumblings of sinners by force...it is necessary to make a man better not by force but by persuasion. We neither have authority granted us by law to restrain sinners, nor, if it were, should we know how to use it, since God gives the crown to those who are kept from evil, not by force, but by choice.
John Chrysostom
When you are insulted by someone or humiliated, guard against angry thoughts, lest they arouse a feeling of irritation, and so cut you off from love and place you in the realm of hatred. You should know that you have been greatly benefited when you have suffered deeply because of some insult or indignity; for by means of the indignity self-esteem has been driven out of you.
Maximus the Confessor
Pure mathematics is a collection of hypothetical, deductive theories, each consisting of a definite system of primitive, undefined, concepts or symbols and primitive, unproved, but self-consistent assumptions (commonly called axioms) together with their logically deducible consequences following by rigidly deductive processes without appeal to intuition.
Joshua Girling Fitch
The bewildered novice in chess moves cautiously, recalling individual rules, whereas the experienced player absorbs a complicated situation at a glance and is unable to account rationally for his intuition. In like manner mathematical intuition grows with experience, and it is possible to develop a natural feeling for concepts such as four dimensional space.
William Feller