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I saw exactly how it happened Mathematics is the language of nature. Everything around us can be represented and understood through numbers. If you graph these numbers, patterns emerge.

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Therefore: There are patterns everywhere in nature. For me, mathematics is a collection of examples; a theorem is a statement about a collection of examples and the purpose of proving theorems is to classify and explain the examples In speaking about their work, mathematicians use the words 'elegance', 'truth', and 'beauty' more than everyone else combined. Darwin "Je serais reconnaissant a toute personne ayant compris cette demonstration de me l'expliquer.

The idea is to be able to paint a landscape in which the proof is obvious. But what is an 'educational result?

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It goes with creativity. The inductive step tells us that they are close enough for each domino to knock over the next one, the base case tells us that the first domino falls over, the conclusion is that they all fall over. The fault in this analogy is that it takes time for each domino to fall and so a domino which is a long way along the line won't fall over for a long time. Mathematical implication is outside time.

Eccles An Introduction to Mathematical Reasoning , p.

Guide N Mathematical Quotations (Where n ~ )

I've just found 10, ways that won't work. It is the source of true art and science. It's just that I spent more time on problems. Monthly , p. There is no other way to do it. Feynman "Education's purpose is to replace an empty mind with an open one. Forster "Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them. I only think about how to solve the problem. But when I have finished, if the solution is not beautiful, I know it is wrong. For example, there are no solids in the universe.

There's not even a suggestion of a solid. There are no absolute continuums.

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There are no surfaces. There are no straight lines. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it.

Why don't you saw Martin in half? Magician: Oh, I'm not the kind of magician who does tricks. I'm a mathemagician!

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Magician: Uh, this is a magic 7. The last digit is one! Homer: Mmmm, pie. Ned: Nope, you will. Homer: 'Fraid not. Ned: 'Fraid so! Homer: 'Fraid not infinity! Ned: 'Fraid so infinity plus one! Homer: D'oh! Bart: But I have 52 million shares! What's 52 million times zero?! And don't tell me it's zero! Lisa: Well, where's my dad?

Frink: Well, it should be obvious to even the most dimwitted individual who holds an advanced degree in hyperbolic topology, n'gee, that Homer Simpson has stumbled into Lisa: [flips the light switch back] Sorry. Frink: [drawing on a blackboard] Here is an ordinary square Wiggum: Whoa, whoa--slow down, egghead! Everyone: [gasps] Frink: This forms a three-dimensional object known as a "cube," or a "Frinkahedron" in honor of its discoverer, n'hey, n'hey.

Homer's voice: Help me! Are you helping me, or are you going on and on? Frink: Oh, right. And, of course, within, we find the doomed individual. Hamerton "The purpose of computation is insight, not numbers. It's up to us to develop the sensitivity to pick up on it. Pedantry can be the enemy of insight. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers.

And if one could get hold of the book, one would have everything settled. That's so unlike the true nature of mathematics. Experience comes from bad judgement. The details are available from the author on request. The author does hope someone will check the calculations, because he does not have a great deal of faith in his ability to carry through the details in a fault-free manner.

He hopes however that the answers are qualitatively correct as stated. Indian Acad. Every time we count pairs, we learn something from it. I'd used email since about , and it seems to me that 15 years of email is plenty for one lifetime. It is the willingness of his teacher to listen to him. Wir Sind Dichter.

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I will admit, however, that one key ingredient is caffeine. I get a couple cups of coffee into me and weird things just start to happen. Nowadays when a number-theorist applies for a grant, he says that it is good for security, but in those days, way before America, he would say that it's good for music. I will not comment whether we have progressed Es ist fast mit der Mathematik wie mit der Theologie.

It is every bit as mind blowing as cosmology or physics mathematicians conceived of black holes long before astronomers actually found any , and allows more freedom of expression than poetry, art, or music which depends heavily on properties of the physical universe. Mathematics is the purest of the arts, as well as the most misunderstood. Mencken "The [ Last night, I concluded my talk with a quote from Dover, PA creationist school board member William Buckingham, who declared, 'Two thousand years ago someone died on a cross.

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Can't someone take a stand for him? We take a stand for him. Whymper made several efforts before he climbed the Matterhorn in the 's and even then it cost the life of four of his party. Now, however, any tourist can be hauled up for a small cost, and perhaps does not appreciate the difficulty of the original ascent. So in mathematics, it may be found hard to realise the great initial difficulty of making a little step which now seems so natural and obvious, and it may not be surprising if such a step has been found and lost again.

Good teaching will come from a mind well made rather than well filled.