Math Quotes - Page 33

The best defense against logic is ignorance.

Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.

My special pleasure in mathematics rested particularly on its purely speculative part.

Mathematicians care no more for logic than logicians for mathematics.

There is nothing strange in the circle being the origin of any and every marvel.

Yes, we now have to divide up our time like that, between politics and our equations. But to me our equations are far more important, for politics are only a matter of present concern. A mathematical equation stands forever.

Dealing with failure is easy: Work hard to improve. Success is also easy to handle: You've solved the wrong problem. Work hard to improve.

Without mathematics, we are blind.

Logic is a poor guide compared with custom.

Just as the introduction of the irrational numbers ... is a convenient myth [which] simplifies the laws of arithmetic ... so physical objects are postulated entities which round out and simplify our account of the flux of existence... The conceptional scheme of physical objects is [likewise] a convenient myth, simpler than the literal truth and yet containing that literal truth as a scattered part.

Logic leaves us no choice. In that sense, math always involves both invention and discovery: we invent the concepts but discover their consequences. … in mathematics our freedom lies in the questions we ask – and in how we pursue them – but not in the answers awaiting us.

It was not so much that I was doing mathematics, but rather that mathematics had taken possession of me.

A problem that we're seeing now in the aromatherapy world is that the market has got so huge that in some cases there are not enough plants to supply the demand.

I was born into a working class Irish Catholic family at the brutal bottom of the Great Depression. I suppose this early imprinting and conditioning made me a life-long radical. My education was mostly scientific, majoring in electrical engineering and applied math. Those imprints made me a life-long rationalist. I have become increasingly skeptical about, or detached from, the assumption that radicalism and rationalism are the only correct perspectives with which to view life, but they remain my favorite perspectives.

Mathematics was born and nurtured in a cultural environment. Without the perspective which the cultural background affords, a proper appreciation of the content and state of present-day mathematics is hardly possible.

My specific goal is to revolutionize the future of the species. Mathematics is just another way of predicting the future.

I know too well that these arguments from probabilities are imposters, and unless great caution is observed in the use of them, they are apt to be deceptive.

Mathematics is like draughts in being suitable for the young, not too difficult, amusing, and without peril to the state.

Mathematics is the language in which the gods talk to people.

He who can properly define and divide is to be considered a god.

One began to hear it said that World War I was the chemists' war, World War II was the physicists' war, World War III (may it never come) will be the mathematicians' war.

Mathematics is about problems, and problems must be made the focus of a student's mathematical life. Painful and creatively frustrating as it may be, students and their teachers should at all times be engaged in the process - having ideas, not having ideas, discovering patterns, making conjectures, constructing examples and counterexamples, devising arguments, and critiquing each other's work.

Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them.

I've dealt with numbers all my life, of course, and after a while you begin to feel that each number has a personality of its own. A twelve is very different from a thirteen, for example. Twelve is upright, conscientious, intelligent, whereas thirteen is a loner, a shady character who won't think twice about breaking the law to get what he wants. Eleven is tough, an outdoorsman who likes tramping through woods and scaling mountains; ten is rather simpleminded, a bland figure who always does what he's told; nine is deep and mystical, a Buddha of contemplation.

Prayers for the condemned man will be offered on an adding machine. Numbers constitute the only universal language.