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Math Quotes

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Math Quotes

“These long chains of perfectly simple and easy reasonings by means of which geometers are accustomed to carry out their most difficult demonstrations had led me to fancy that everything that can fall under human knowledge forms a similar sequence; and that so long as we avoid accepting as true what is not so, and always preserve the right order of deduction of one thing from another, there can be nothing too remote to be reached in the end, or to well hidden to be discovered.”

“Educators, long disturbed by schoolchildren's lagging scores in math and reading, are realizing there is a different and more alarming deficiency: emotional literacy. And while laudable efforts are being made to raise academic standards, this new and troubling deficiency is not being addressed in the standard school curriculum. As one Brooklyn teacher put it, the present emphasis in schools suggests that "we care more about how well schoolchildren can read and write than whether they'll be alive next week."”

“Games are among the most interesting creations of the human mind, and the analysis of their structure is full of adventure and surprises. Unfortunately there is never a lack of mathematicians for the job of transforming delectable ingredients into a dish that tastes like a damp blanket.”

“Geometry enlightens the intellect and sets one's mind right. All of its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence.”

“I am encouraged as I look at some of those who have listened to their "different drum": Einstein was hopeless at school math and commented wryly on his inadequacy in human relations. Winston Churchill was an abysmal failure in his early school years. Byron, that revolutionary student, had to compensate for a club foot; Demosthenes for a stutter; and Homer was blind. Socrates couldn't manage his wife, and infuriated his countrymen. And what about Jesus, if we need an ultimate example of failure with one's peers? Or an ultimate example of love?”

“What is necessary for 'the very existence of science,' and what the characteristics of nature are, are not to be determined by pompous preconditions, they are determined always by the material with which we work, by nature herself. We look, and we see what we find, and we cannot say ahead of time successfully what it is going to look like. ... It is necessary for the very existence of science that minds exist which do not allow that nature must satisfy some preconceived conditions.”

“The principle of science, the definition, almost, is the following: The test of all knowledge is experiment. Experiment is the sole judge of scientific "truth." But what is the source of knowledge? Where do the laws that are to be tested come from? Experiment, itself, helps to produce these laws, in the sense that it gives us hints. But also needed is imagination to create from these hints the great generalizations--to guess at the wonderful, simple, but very strange patterns beneath them all, and then to experiment to check again whether we have made the right guess.”

“One may ask the question as to the extent to which the quest for beauty is an aim in the pursuit of science. . . . It is, indeed, an incredible fact that what the human mind, at its deepest and most profound, perceives as beautiful finds its realization in external nature. What is intelligible is also beautiful.”

“Why should there be the method of science? There is not just one way to build a house, or even to grow tomatoes. We should not expect something as motley as the growth of knowledge to be strapped to one methodology.”

“Next you'd see a raft sliding by, away off yonder, and maybe a galoot on it chopping. . . you'd see the ax flash and come down-you don't hear nothing; you see the ax go up again, and by the time it's above the man's head then you hear the k'chunk!-it had took all that time to come over the water.”

“To the pure geometer the radius of curvature is an incidental characteristic - like the grin of the Cheshire cat. To the physicist it is an indispensable characteristic. It would be going too far to say that to the physicist the cat is merely incidental to the grin. Physics is concerned with interrelatedness such as the interrelatedness of cats and grins. In this case the "cat without a grin" and the "grin without a cat" are equally set aside as purely mathematical phantasies.”

“A number of aspects of mathematics are not much talked about in contemporary histories of mathematics. We have in mind business and commerce, war, number mysticism, astrology, and religion. In some instances, writers, hoping to assert for mathematics a noble parentage and a pure scientific experience, have turned away their eyes. Histories have been eager to put the case for science, but the Handmaiden of the Sciences has lived a far more raffish and interesting life than her historians allow.”