Math Quotes - Page 36

In American math classes, we teach a lot of concepts poorly over many years. In the Asian systems they teach you very few concepts very well over a few years.

The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself.

Projective geometry is all geometry.

Everything of importance has been said before by somebody who did not discover it.

... preliminary accounting, banking and surveying (known as arithmetic, algebra and geometry).

A mathematician's reputation rests on the number of bad proofs he has given.

But Piglet is so small that he slips into a pocket, where it is very comfortable to feel him when you are not quite sure whether twice seven is twelve or twenty-two.

By the end of the first month of the 1995 session, each senator will have made more money than any person who works 40 hours a week at minimum wage for the entire year.

Do I contradict myself? Very well then, I can bear it.

Mathematics has not a foot to stand upon which is not purely metaphysical.

... the notions category and functor were not formulated or put in print until the idea of a natural transformation was also at hand.

If I am given a formula, and I am ignorant of its meaning, it cannot teach me anything, but if I already know it what does the formula teach me?

Someone has remarked that 'An ideal math talk should have one proof and one joke and they should not be the same'.

Natural selection is a mechanism for generating an exceedingly high degree of improbability.

From somewhere, back in my youth, heard Prof say, 'Manuel, when faced with a problem you do not understand, do any part of it you do understand, then look at it again.' He had been teaching me something he himself did not understand very well—something in math—but had taught me something far more important, a basic principle.

No wonder that Churchill described this effort [the British codebreakers working at Bletchley Park] as "Britian"s secret weapon," a weapon far more effective than the buzz bombs and the rockets that Werner von Braun designed for a German victory, a weapon absolutely decisive, in the judgement of many, in winning the war for the Allies.

It is the merest truism, evident at once to unsophisticated observation, that mathematics is a human invention.

Why don't we want our children to learn to do mathematics? Is it that we don't trust them, that we think it's too hard? We seem to feel that they are capable of making arguments and coming to their own conclusions about Napoleon. Why not about triangles?

No mathematician in the world would bother making these senseless distinctions: 2 1/2 is a "mixed number " while 5/2 is an "improper fraction." They're EQUAL for crying out loud. They are the exact same numbers and have the exact same properties. Who uses such words outside of fourth grade?

Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.

Mathematical Reasoning is not only exact; it has its own criteria of reality.

Mathematics is universal. It's discovered by human beings, but the rules of mathematics are the same throughout the universe and the laws of the universe.

The origins of graph theory are humble, even frivolous.

Nixon's motto was, if two wrongs don't make a right, try three.

Am I really a good mathematician?