mathematics

The issue, then, is not, What is the best way to teach? but, What is mathematics really all about?... Controversies about_teaching cannot be resolved without confronting problems about the nature of mathematics.

And, most important of all," added the Mathemagician, "here is your own magic staff. Use it well and there is nothing it cannot do for you."He placed in Milo's breast pocket a small gleaming pencil which, except for the size, was much like his own.

ZERO and Infinity both are very difficult to understand and explain but at the same time both are key assumption of Mathematics...

[I was advised] to read Jordan's 'Cours d'analyse'; and I shall never forget the astonishment with which I read that remarkable work, the first inspiration for so many mathematicians of my generation, and learnt for the first time as I read it what mathematics really meant.

Mathematics effectively began when a few Greek friends got together to talk about numbers and lines and angles.

Formal mathematics is nature's way of letting you know how sloppyyour mathematics is.

Mathematicians call it __he arithmetic of congruences._ You can think of it as clock arithmetic. Temporarily replace the 12 on a clock face with 0. The 12 hours of the clock now read 0, 1, 2, 3, _ up to 11. If the time is eight o__lock, and you add 9 hours, what do you get? Well, you get five o__lock. So in this arithmetic, 8 + 9 = 5; or, as mathematicians say, 8 + 9 _ 5 (mod 12), pronounced __ight plus nine is congruent to five, modulo twelve.

Teaching Ramanujan was like writing on a blackboard covered with excerpts from a more interesting lecture.

Children must be taught mathematics well in anywhere under every condition at every age and so we can have more rational, more logical societies!

Of course, reading novels was just another form of escape. As soon as he closed their pages he had to come back to the real world. But at some point Tengo noticed that returning to reality from the world of a novel was not as devastating a blow as returning from the world of mathematics. Why should that have been? After much deep thought, he reached a conclusion. No matter how clear the relationships of things might become in the forest of story, there was never a clear-cut solution. That was how it differed from math. The role of a story was, in the broadest terms, to transpose a single problem into another form. Depending on the nature and direction of the problem, a solution could be suggested in the narrative. Tengo would return to the real world with that suggestion in hand. It was like a piece of paper bearing the indecipherable text of a magic spell. At times it lacked coherence and served no immediate practical purpose. But it would contain a possibility. Someday he might be able to decipher the spell. That possibility would gently warm his heart from within.

The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.

How did Biot arrive at the partial differential equation? [the heat conduction equation] . . . Perhaps Laplace gave Biot the equation and left him to sink or swim for a few years in trying to derive it. That would have been merely an instance of the way great mathematicians since the very beginnings of mathematical research have effortlessly maintained their superiority over ordinary mortals.

This skipping is another important point. It should be done whenever a proof seems too hard or whenever a theorem or a whole paragraph does not appeal to the reader. In most cases he will be able to go on and later he may return to the parts which he skipped.

A brick can be used to represent the zero probability of this book being any good.

Mathematics, as much as music or any other art, is one of the means by which we rise to a complete self-consciousness. The significance of mathematics resides precisely in the fact that it is an art; by informing us of the nature of our own minds it informs us of much that depends on our minds.

Philosophers and psychiatrists should explain why it is that we mathematicians are in the habit of systematically erasing our footsteps. Scientists have always looked askance at this strange habit of mathematicians, which has changed little from Pythagoras to our day.

In the field of Egyptian mathematics Professor Karpinski of the University of Michigan has long insisted that surviving mathematical papyri clearly demonstrate the Egyptians' scientific interest in pure mathematics for its own sake. I have now no doubt that Professor Karpinski is right, for the evidence of interest in pure science, as such, is perfectly conclusive in the Edwin Smith Surgical Papyrus.

It appeared that way, Lawrence, but this raised the question of was mathematics really true or was it just a game played with symbols? In other words__re we discovering Truth, or just wanking?