"It is fair to claim that it is a students understanding of mathematics, above all other subjects, which suffers most from unenlightened teaching methods. ...the troubles may well stem mainly from the first year or two of the childs encounter with numbers... if children come to fear them or to be bored with them, they will eventually join the ranks of the present majority for whom the word mathematics is guaranteed to bring social conversation to an immediate halt. If, on the other hand, numbers are made a genuine source of adventure and exploration from the beginning, there is a good chance that the level of numeracy in society can be raised significantly. There is a real role here for the history of mathematics—and the history of number in particular—for history emphasizes the diversity of approaches and methods which are possible and frees us from the straightjacket of contemporary fashions in mathematics education. It is, at the same time, both interesting and stimulating in its own right."
A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers: 1, 2, 3, 4, 5, and so forth. Individual numbers can be represented in spoken or written language with number words, or with dedicated symbols called numerals; for example, "eleven" is a number word and "11" is the corresponding numeral. As only a limited list of symbols can be memo
"Bourgeois society is ruled by equivalence. It makes dissimilar things comparable by reducing them to abstract quantities. For the Enlightenment, anything which cannot be resolved into numbers, and ultimately into one, is illusion; modern positivism consigns it to poetry."
Number"Number is the ruler of forms and ideas, and the cause of gods and daemons."
Number"By the ancients [Greeks], arithmetic was studied through geometry. If a number was regarded as simple, it was a line. If as composite, it was a rectangular figure. To multiply was to construct a rectangle, to divide was to find one of its sides. Traces of this still remain in such terms as square, cube, common measure, but the method itself is obsolete. Hence, it requires an effort to conceive of the square root, not as that which multiplied into itself produces a given number, but as the side of a square, which [square area] either is the number, or is equal to the rectangle which is the number."
Number"Philosopher of science Keith Devlin is wrong to aver that numbers "arise from the recognition of patterns in the world around us." They arise because they are necessary for running a certain kind of society; number has only an imposed relationship to what is found in the world. Math historian Graham Flegg makes a similar error when he asserts, "Numbers reveal the unity which underlies all of life as we experience it." The "unity" in question did not exist before it was produced, with the invaluable assistance of number."
Number"Cest de lInde que nous vient lingénieuse méthode dexprimer tous les nombres avec dix caractères, en leur donnant à la fois, une valeur absolue et une valeur de position; idée fine et importante, qui nous paraît maîntenant si simple, que nous en sentons à peine, le mérite. Mais cette simplicité même, et lextrême facilité qui en résulte pour tous les calculs, placent notre système darithmétique au premier rang des inventions utiles; et lon appréciera la difficulté dy parvenir, si lon considère quil a échappé au génie dArchimède et dApollonius, deux des plus grands hommes dont lantiquité shonore."
Number"I esteem myself happy to have as great an ally as you in my search for truth. I will read your work … all the more willingly because I have for many years been a partisan of the Copernican view because it reveals to me the causes of many natural phenomena that are entirely incomprehensible in the light of the generally accepted hypothesis. To refute the latter I have collected many proofs, but I do not publish them, because I am deterred by the fate of our teacher Copernicus who, although he had won immortal fame with a few, was ridiculed and condemned by countless people (for very great is the number of the stupid)."
Number