( George Pólya, “ How to Solve It“)Īn education isn’t how much you have committed to memory, or even how much you know. We have a natural opportunity to investigate the connections of a problem when looking back at its solution. One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. … A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted. Doing so, they miss an important and instructive phase of the work. ( John Hope Franklin)Įven fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. We must get beyond textbooks, go out into the bypaths… and tell the world the glories of our journey. ( Susan Ertz, “Anger in the Sky”)Įvery composer knows the anguish and despair occasioned by forgetting ideas which one had no time to write down. Millions long for immortality who do not know what to do with themselves on a rainy Sunday afternoon. The best teacher is the one who suggests rather than dogmatizes, and inspires his listener with the wish to teach himself.
( Oliver Wendell Holmes, “The Poet at the Breakfast Table”) It is the province of knowledge to speak and it is the privilege of wisdom to listen. Know how to listen, and you will profit even from those who talk badly. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis? ( Paul Halmos, “I want to be a mathematician”) ( Helen Keller)ĭon’t just read it fight it! Ask your own questions, look for your own examples, discover your own proofs. Worse than being blind, is to see and have no vision. ( William Shakespeare, “ The Taming of the Shrew“) In brief, sir, study what you most affect. No profit grows where is no pleasure ta’en Integrity without knowledge is weak and useless, and knowledge without integrity is dangerous and dreadful.
Once you have experienced it, you are eager to repeat it but unable to do it at will, unless perhaps by dogged work… ( André Weil, “The Apprenticeship of a Mathematician”) ( José Ortega y Gasset, “Notes on the novel”)Įvery mathematician worthy of the name has experienced … the state of lucid exaltation in which one thought succeeds another as if miraculously… this feeling may last for hours at a time, even for days. ( Welsh triad later attributed to Benjamin Disraeli)īetter beware of notions like genius and inspiration they are a sort of magic wand and should be used sparingly by anybody who wants to see things clearly. The three pillars of learning seeing much, suffering much, and studying much. For instance, the first phase is characterized by the question ‘How can we eat?’, the second by the question ‘Why do we eat?’ and the third by the question, ‘Where shall we have lunch?’ ( Douglas Adams, “ The Hitchhiker’s Guide to the Galaxy“) The history of every major galactic civilization tends to pass through three distinct and recognizable phases, those of Survival, Inquiry and Sophistication, otherwise known as the How, Why, and Where phases. When you have mastered numbers, you will in fact no longer be reading numbers, any more than you read words when reading books. ( René Descartes, “ Discours de la Méthode“) ( Edward Malloy)Ĭhaque vérité que je trouvois étant une règle qui me servoit après à en trouver d’autres. ( George Will)Ī college degree is not a sign that one is a finished product but an indication a person is prepared for life. Sports serve society by providing vivid examples of excellence. If you can give your son or daughter only one gift, let it be enthusiasm. © Career advice - What’s new - By Terence TaoĪdvice is what we ask for when we already know the answer but wish we didn’t.
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