Yy S Fav Mathematical Proof Quotes

Zero has had a long history. The Babylonians invented the concept of zero; the ancient Greeks debated it in lofty terms (how could something be nothing?); the ancient Indian scholar Pingala paired Zero with the numeral 1 to get double digits; and both the Mayans and the Romans made Zero a part of their numeral systems. But Zero finally found its place around AD 498, when the Indian astronomer Aryabhatta sat up in bed one morning and exclaimed, "Sthanam sthanam dasa gunam" - which translates, roughly as, "place to place in ten times in value". With that, the idea of decimal based place value notion was born. Now Zero was on a roll: It spread to the Arab world, where it flourished; crossed the Iberian Peninsula to Europe (thanks to the Spanish Moors); got some tweaking from the Italians; and eventually sailed the Atlantic to the New World, where zero ultimately found plenty of employment (together with the digit 1) in a place called Silicon Valley. ~ Dan Ariely

According to PhD astrophysicists and qualified American science professors, the odds of the more than 2,500 prophecies found in the Bible being fulfilled by chance are 1 with 2,000 zeros after it. According to the mathematical science of probability, if a number has more than 50 zeros after it, the odds of that happening by chance is virtually impossible. This is irrefutable proof that the Bible is inspired by God! ~ Hugh Ross

In the Christian religion, though perhaps not in any other, we frequently find a conception of god that is selfcontradictory and therefore corresponds to nothing. That is the conception formed by the following three propositions taken together:
1. God is all-powerful.
2. God is all-benevolent.
3. There is much misery in the world.
A god who was all-powerful but left much misery in the world would not be all-benevolent. An all-benevolent god in a world containing much misery would not be an all-powerful god. A world containing a god who was both all-powerful and all-benevolent would contain no misery.
Here, then, we have a mathematical proof bearing on a common religious doctrine. Anyone who is confident that he frequently comes across misery in the world may conclude with equal confidence that there is no such thing as an all-powerful and all-benevolent god. And this mathematically disposes of official Christianity, as has long been known. ~ Richard Robinson

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

are not to have, in any object of use or ornament, what would be a contradiction in fact. You don't walk upon flowers in fact; you cannot be allowed to walk upon flowers in carpets. You don't find that foreign birds and butterflies come and perch upon your crockery; you cannot be permitted to paint foreign birds and butterflies upon your crockery. You never meet with quadrupeds going up and down walls; you must not have quadrupeds represented upon walls. You must use,' said the gentleman, 'for all these purposes, combinations and modifications (in primary colours) of mathematical figures which are susceptible of proof and demonstration. This is the new discovery. This is fact. This is taste.' The ~ Charles Dickens

These forays into the real world sharpened his view that scientists needed the widest possible education. He used to say, "How can you design for people if you don't know history and psychology? You can't. Because your mathematical formulas may be perfect, but the people will screw it up. And if that happens, it means you screwed it up." He peppered his lectures with quotations from Plato, Chaka Zulu, Emerson, and Chang-tzu.

But as a professor who was popular with his students - and who advocated general education - Thorne found himself swimming against the tide. The academic world was marching toward ever more specialized knowledge, expressed in ever more dense jargon. In this climate, being liked by your students was a sign of shallowness; and interest in real-world problems was proof of intellectual poverty and a distressing indifference to theory. ~ Michael Crichton

How could you,' Mackey asked, 'how could you, a mathematician, a man devoted to reason and logical proof. . . how could you believe that extra terrestrials are sending you messages? How could you believe that you are being recruited by aliens from outer space to save the world? How could you . . .?' "Nash looked up at last and fixed Mackey with an unblinking stare as cool and dispassionate as that of any bird or snake. 'Because,' Nash said slowly in his soft, reasonable southern drawl, as if talking to himself,'the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously. ~ Sylvia Nasar

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 ... " ~ John Edensor Littlewood

A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way. ~ G.H. Hardy

Mathematical knowledge ... is, in fact, merely verbal knowledge. "3" means "2+1", and "4" means "3+1". Hence it follows (though the proof is long) that "4" means the same as "2+2". Thus mathematical knowledge ceases to be mysterious. ~ Bertrand Russell

I am sorry for your disappointment,' he continued, glancing into her face. Their eyes having met, became, as it were, mutually locked together, and the single instant only which good breeding allows as the length of such a look, became trebled: a clear penetrating ray of intelligence had shot from each into each, giving birth to one of those unaccountable sensations which carry home to the heart before the hand has been touched or the merest compliment passed, by something stronger than mathematical proof, the conviction, 'A tie has begun to unite us.' Both faces also unconsciously stated that their owners had been much in each other's thoughts of late. Owen had talked to the young architect of his sister as freely as to Cytherea of the young architect. ~ Thomas Hardy

Science proceeds by inference, rather than by the deduction of mathematical proof. A series of observations is accumulated, forcing the deeper question: What must be true if we are to explain what is observed? What "big picture" of reality offers the best fit to what is actually observed in our experience? American scientist and philosopher Charles S. Peirce used the term "abduction" to refer to the way in which scientists generate theories that might offer the best explanation of things. The method is now more often referred to as "inference to the best explanation." It is now widely agreed to be the philosophy of investigation of the world characteristic of the natural sciences. ~ Alister E. McGrath

All mathematical proofs must be deductive. Each proof is a chain of deductive arguments, each of which has its premises and conclusion. ~ Morris Kline

God has the Big Book, the beautiful proofs of mathematical theorems are listed here. ~ Paul Erdos

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. ~ Timothy Gowers

Here are the basic principles of Constructivism as practiced by Kronecker and codified by J.H. Poincare and L.E.J. Brouwer and other major figures in Intuitionism: (1) Any mathematical statement or theorem that is more complicated or abstract than plain old integer-style arithmetic must be explicitly derived (i.e. 'constructed') from integer arithmetic via a finite number of purely deductive steps. (2) The only valid proofs in math are constructive ones, with the adjective here meaning that the proof provides a method for finding (i.e., 'constructing') whatever mathematical entities it's concerned with. ~ David Foster Wallace

It is an unfortunate fact that proofs can be very misleading. Proofs exist to establish once and for all, according to very high standards, that certain mathematical statements are irrefutable facts. What is unfortunate about this is that a proof, in spite of the fact that it is perfectly correct, does not in any way have to be enlightening. Thus, mathematicians, and mathematics students, are faced with two problems: the generation of proofs, and the generation of internal enlightenment. To understand a theorem requires enlightenment. If one has enlightenment, one knows in one's soul why a particular theorem must be true. ~ Herbert S. Gaskill

I had made an empirical discovery and it carried all the weight of a mathematical proof. ~ Paul Auster

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. ~ David Hilbert

A mathematical proof is beautiful, but when you're finished, it's really only about one thing. A story can be about many things. ~ Bonnie Jo Campbell

If we leave that general descriptive talk where everything which looks like a poem can be called a poem and turn instead to normative talk, we will of course not recognize as a poem everything that looks like a poem. A real poem has to be a successful poem, a successful speech act. In approximately the same way that only a mathematical proof which really proves something can be called a mathematical proof. It is not enough that it looks like a proof. The proof has to prove. For the poem it is not enough to look like a poem. It has to achieve something. ~ Lars Gustafsson

Poverty is a mathematical proof of the fact that mankind is a big failure! ~ Mehmet Murat Ildan

Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? Where does the proof use the hypothesis? ~ Paul Halmos

I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations. ~ David Hilbert

A mathematical proof must be perspicuous. ~ Ludwig Wittgenstein

It followed that every act, whether the finding of a new proof for a complex mathematical problem or a twist of vision that turned one school of art into another was a result of endless failure. ~ Jon Courtenay Grimwood

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." ~ Eyvind Kang

A journey is an achievement, Maria, just as much as a mathematical proof. ~ Sara Sheridan

No human investigation can claim to be scientific if it doesn't pass the test of mathematical proof. ~ Leonardo Da Vinci

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. ~ Hermann Weyl

A felicitous but unproved conjecture may be of much more consequence for mathematics than the proof of many a respectable theorem. ~ Atle Selberg

Perspective is an Art Mathematical which demonstrates the manner and properties of all radiations direct, broken and reflected. ~ John Dee

He closed his hand around my wrist and pressed my hand flat against his chest. The way I see it, Elle, scars are proof we can survive. ~ Megan Hart

In law, we talk about a beautiful summation, or a beautiful judgment: and what we mean by that, of course, is the loveliness of not only its logic but its expression. And similarly, in math, when we talk about a beautiful proof, what we're recognizing is the simplicity of the proof, its ... elementalness, I suppose: its inevitability. ~ Hanya Yanagihara

We are born atheist and we remain so until someone lies to us. ~ Aron Ra

Nothing, to my way of thinking, is a better proof of a well ordered mind than a man's ability to stop just where he is and pass some time in his own company. ~ Seneca.

I peeled his fingers from my lips. "That was unnecessary." I said. "I was only surprised at your statement, after you have consistently disclaimed any interest in the matter. In fact, I too have discovered the identity of the person in question." "Oh, you have, have you?" "Yes, I have." We studied one another warily. "Would you care to enlighten me?" Emerson inquired. "No. I think I know; but if I am wrong you will never let me hear the end of it. Perhaps you will enlighten me." "No." "Ha! You are not sure either." "I said as much." Again we exchanged measuring glances. "You have no proof," I said. "That is the difficulty. And you - " "Not ~ Elizabeth Peters

[ ... ] assuming that the true opinion abides in the mind, but abides as a prejudice, a belief independent of, and proof against, argument - this is not the way in which truth ought to be held by a rational being. This is not knowing the truth. Truth, thus held, is but one superstition the more, accidentally clinging to the words which enunciate a truth. ~ John Stuart Mill

Another time somebody gave a talk about poetry. He talked about the structure of the poem and the emotions that come with it; he divided everything up into certain kinds of classes. In the discussion that came afterwards, he said, "Isn't that the same as in mathematics, Dr. Eisenhart?" Dr. Eisenhart was the dean of the graduate school and a great professor of mathematics. He was also very clever. He said, "I'd like to know what Dick Feynman thinks about it in reference to theoretical physics." He was always putting me on in this kind of situation. I got up and said, "Yes, it's very closely related. In theoretical physics, the analog of the word is the mathematical formula, the analog of the structure of the poem is the interrelationship of the theoretical bling-bling with the so-andso"–and I went through the whole thing, making a perfect analogy. The speaker's eyes were _beaming_ with happiness. Then I said, "It seems to me that no matter _what_ you say about poetry, I could find a way of making up an analog with _any_ subject, just as I did for theoretical physics. I don't consider such analogs meaningful. ~ Richard P. Feynman

We are the same, you and I. Whether samurai or night-hawk, the Suruga Dainagon or member of the Toudouza, it makes no difference. My sword is the proof ... ~ Takayuki Yamaguchi