A Quote by Margaret Wertheim
Mathematicians are proud of the fact that, generally, they do their work with a piece of chalk and a blackboard. They value hand-done proofs above all else. A big question in mathematics today is whether or not computational proofs are legitimate. Some mathematicians won't accept computational proofs and insist that a real proof must be done by the human hand and mind, using equations.
Related Quotes
In the broad light of day mathematicians check their equations and their proofs, leaving no stone unturned in their search for rigour. But, at night, under the full moon, they dream, they float among the stars and wonder at the miracle of the heavens. They are inspired. Without dreams there is no art, no mathematics, no life.
I think it is said that Gauss had ten different proofs for the law of quadratic reciprocity. Any good theorem should have several proofs, the more the better. For two reasons: usually, different proofs have different strengths and weaknesses, and they generalise in different directions - they are not just repetitions of each other.
It is the facts that matter, not the proofs. Physics can progress without the proofs, but we can't go on without the facts ... if the facts are right, then the proofs are a matter of playing around with the algebra correctly.
Believers who have formulated such proofs [for God's existence] ... would never have come to believe as a result of such proofs
Only professional mathematicians learn anything from proofs. Other people learn from explanations.
Historical refutation as the definitive refutation.- In former times, one sought to prove that there is no God - today one indicates how the belief that there is a God arose and how this belief acquired its weight and importance: a counter-proof that there is no God thereby becomes superfluous.- When in former times one had refuted the 'proofs of the existence of God' put forward, there always remained the doubt whether better proofs might not be adduced than those just refuted: in those days atheists did not know how to make a clean sweep.
I am obliged to interpolate some remarks on a very difficult subject: proof and its importance in mathematics. All physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof.
The most painstaking phase comes when the manuscript is set in 'type' for the first time and the first proofs of the book are printed. These initial copies are called first-pass proofs or galleys.
Mathematicians need proofs to keep them honest. All technical areas of human activity need reality checks. It is not enough to believe that something works, that it is a good way to proceed, or even that it is true. We need to know why it's true. Otherwise, we won't know anything at all.
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.
There is no scientific proof that only scientific proofs are good proofs; no way to prove by the scientific method that the scientific method is the only valid method.
It is the invariable habit of bureaucracies, at all times and everywhere, to assume...that every citizen is a criminal. Their one apparent purpose, pursued with a relentless and furious diligence, is to convert the assumption into a fact. They hunt endlessly for proofs, and, when proofs are lacking, for mere suspicions. The moment they become aware of a definite citizen, John Doe, seeking what is his right under the law, they begin searching feverishly for an excuse for withholding it from him.
Paul Erdos has a theory that God has a book containing all the theorems of mathematics with their absolutely most beautiful proofs, and when he wants to express particular appreciation of a proof he exclaims, "This is from the book!"
As far as I know, Clifford Pickover is the first mathematician to write a book about areas where math and theology overlap. Are there mathematical proofs of God? Who are the great mathematicians who believed in a deity? Does numerology lead anywhere when applied to sacred literature? Pickover covers these and many other off-trail topics with his usual verve, humor, and clarity. And along the way the reader will learn a great deal of serious mathematics.
Those who have racked their brains to discover new proofs have perhaps been induced to do so by a compulsion they could not quite explain to themselves. Instead of giving us their new proofs they should have explained to us the motivation that constrained them to search for them.
I am falsely accused, without proof, of using my position for personal profit. Many who accuse me have lifestyles and spending habits that make them walking proofs of that crime.
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