Mathematical Proof Quotes
The best sayings about Mathematical Proof that you can share on Instagram, Pinterest, Facebook and other social networks!
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I read in the proof sheets of Hardy on Ramanujan: "As someone said, each of the positive integers was one of his personal friends." My reaction was, "I wonder who said that; I wish I had." In the next proof-sheets I read (what now stands), "It was Littlewood who said..."
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We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?"
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Mathematics consists in proving the most obvious thing in the least obvious way.
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In a way, composing on the melodic level is an expression of a melodic truth, almost like a geometric truth. If it has clarity, other people will recognize it. There's no way of isolating it in a gallery on a white wall and saying, "This is a work of art. This is a mathematical proof."
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A proof tells us where to concentrate our doubts.
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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.
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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.
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A mathematical proof must be perspicuous.
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There was, I think, a feeling that the best science was that done in the simplest way. In experimental work, as in mathematics, there was "style" and a result obtained with simple equipment was more elegant than one obtained with complicated apparatus, just as a mathematical proof derived neatly was better than one involving laborious calculations. Rutherford's first disintegration experiment, and Chadwick's discovery of the neutron had a "style" that is different from that of experiments made with giant accelerators.
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To divide a cube into two other cubes, a fourth power, or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.
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When you can measure what you are speaking about, and express it in numbers, you know something about it.
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Besides it is an error to believe that rigour is the enemy of simplicity. On the contrary we find it confirmed by numerous examples that the rigorous method is at the same time the simpler and the more easily comprehended. The very effort for rigor forces us to find out simpler methods of proof.
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A witty statesman said, you might prove anything by figures.
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I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible.
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Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science.
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A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details.
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Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions.
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Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? ... Where does the proof use the hypothesis?
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Poverty is a mathematical proof of the fact that mankind is a big failure!
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No human investigation can claim to be scientific if it doesn't pass the test of mathematical proof.
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Absence of proof is not proof of absence.
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I have had my results for a long time: but I do not yet know how I am to arrive at them.
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Mathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt to draw absolute conclusions. All mathematical truths are relative, conditional. In E. T. Bell Men of Mathematics, New York: Simona and Schuster, 1937.
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Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning.
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Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.
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Geometry enlightens the intellect and sets one's mind right. All of its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence.
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What a mathematical proof actually does is show that certain conclusions, such as the irrationality of , follow from certain premises, such as the principle of mathematical induction. The validity of these premises is an entirely independent matter which can safely be left to philosophers.
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It is my experience that proofs involving matrices can be shortened by 50% if one throws the matrices out.
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A mathematician's reputation rests on the number of bad proofs he has given.
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About Thomas Hobbes: He was 40 years old before he looked on geometry; which happened accidentally. Being in a gentleman's library, Euclid's Elements lay open, and "twas the 47 El. libri I" [Pythagoras' Theorem]. He read the proposition "By God", sayd he, "this is impossible:" So he reads the demonstration of it, which referred him back to such a proposition; which proposition he read. That referred him back to another, which he also read. Et sic deinceps, that at last he was demonstratively convinced of that truth. This made him in love with geometry.
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