A Quote by Aristotle

It is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician demonstrative proofs.

Aristotle

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Accept Demand Equally Foolish Mathematician Probable Reasoning

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Aristotle
Greek - Philosopher
384 BC - 322 BC

It is the mark of an educated mind to expect that amount of exactness which the nature of the particular subject admits. It is equally unreasonable to accept merely probable conclusions from a mathematician and to demand strict demonstration from an orator.

Aristotle

The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing.

George Polya

A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories.

Stefan Banach

Now all orators effect their demonstrative proofs by allegation either of enthymems or examples, and, besides these, in no other way whatever.

Aristotle

Philosophers of genius, children, and the people are equally wise - because they ask equally foolish questions. Foolish to a civilized man who has a well-furnished European apartment with an excellent toilet and a well-furnished dogma.

Yevgeny Zamyatin

Geometry is beautifully logical, and it teaches you how to think and prove that things are so, step by step by step. Proofs are excellent lessons in reasoning. Without logic and reasoning, you are dependent on jumping to conclusions or - worse - having empty opinions.

Marilyn vos Savant

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

Abram Samoilovitch Besicovitch

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.

Margaret Wertheim

The great mathematician fully, almost ruthlessly, exploits the domain of permissible reasoning and skirts the impermissible. That his recklessness does not lead him into a morass of contradictions is a miracle in itself: certainly it is hard to believe that our reasoning power was brought, by Darwin's process of natural selection, to the perfection which it seems to possess.

Eugene Wigner

I have hardly ever known a mathematician who was capable of reasoning.

Plato

Before God we are all equally wise - and equally foolish.

Albert Einstein

Since a given system can never of its own accord go over into another equally probable state but into a more probable one, it is likewise impossible to construct a system of bodies that after traversing various states returns periodically to its original state, that is a perpetual motion machine.

Ludwig Boltzmann

Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning.

John Locke

An axiomatic system establishes a reverberating relationship between what a mathematician assumes (the axioms) and what he or she can derive (the theorems). In the best of circumstances, the relationship is clear enough so that the mathematician can submit his or her reasoning to an informal checklist, passing from step to step with the easy confidence the steps are small enough so that he cannot be embarrassed nor she tripped up.

David Berlinski

I am ready to reject all belief and reasoning, and can look upon no opinion even as more probable or likely than another.

David Hume

Whoever builds his faith exclusively on demonstrative proofs and deductive arguments, builds a faith on which it is impossible to rely. For he is affected by the negativities of constant objections. Certainty(al-yaqin) does not derive from the evidences of the mind but pours out from the depths of the heart.

Ibn Arabi

A Quote by Aristotle

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