A Quote by Paul Halmos
Mathematics - this may surprise or shock some - is never deductive in creation.
Related Quotes
Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.
I don't like the phrase shock value. Surprise is essential in comedy, and if people are shocked by what I consider merely surprising, then that's their shock. But there is no joke without surprise.
Humor is based on surprise, and surprise is a milder way of saying shock. It's surprise that makes the joke.
Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.
Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.
It isn't enough to shock. It's easy to shock. Real surprise is what I'm after.
A first fact should surprise us, or rather would surprise us if we were not used to it. How does it happen there are people who do not understand mathematics? If mathematics invokes only the rules of logic, such as are accepted by all normal minds...how does it come about that so many persons are here refractory?
My kind [vampires] does not surprise easily," he said. "You surprised me, this morning. I have thus used up my full quota of shock and consternation for some interval." I stared at him. "You made a *joke*." "I have heard this kind of thing may happen.
This word "description" may be disconcerting when used to refer to what is generally called a translation. But when one wishes to render a verbal creation (as opposed to a didactic statement) from one language to another, he is confronted with two equally unsatisfactory choices. He may, according to his talents, elaborate a similar, but never identical creation, or he may describe that creation as completely as possible in his own language.
Now, some people do this for shock value. Shock is just another uptown word for surprise. Granted it has a different quality to it, but a joke is about surprising someone. I'm a great believer in context. You can joke about anything. I do like finding out where the line is drawn, deliberately crossing it and bringing some of them with me across the line, and having them be happy that I did.
Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.
Mathematics is not a deductive science - that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.
The science of pure mathematics, in its modern developments, may claim to be the most original creation of the human spirit.
May not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life.
Inferences of Science and Common Sense differ from those of deductive logic and mathematics in a very important respect, namely, when the premises are true and the reasoning correct, the conclusion is only probable.
I've never had a surprise birthday party. I've had every other type of surprise. I've had surprise beatings, surprise drug tests, surprise daughter I think.
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