Quotes & Sayings About Mathematical Proof

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

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

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

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

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

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

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

You'll often see posts about people beating the CAP theorem. They haven't. What they have done is create a system where some capabilities are CP, and some are AP. The mathematical proof behind the CAP theorem holds. Despite many attempts at school, I've learned that you don't beat math. — Sam Newman

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

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

The proof given by Wright, that non-adaptive differentiation will occur in small populations owing to "drift," or the chance fixation of some new mutation or recombination, is one of the most important results of mathematical analysis applied to the facts of neo-mendelism. It gives accident as well as adaptation a place in evolution, and at one stroke explains many facts which puzzled earlier selectionists, notably the much greater degree of divergence shown by island than mainland forms, by forms in isolated lakes than in continuous river-systems. — Julian Huxley

It is my experience that proofs involving matrices can be shortened by 50% if one throws the matrices out. — Emil Artin

A mathematical proof must be perspicuous. — Ludwig Wittgenstein

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

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

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

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. — Charles Proteus Steinmetz

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

[On Archimedes mathematical results:] It is not possible to find in all geometry more difficult and intricate questions, or more simple and lucid explanation ... No investigation of yours would succeed in attaining the proof, and yet, once seen you immediately believe you would have discovered it. — Proclus

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

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

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

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

Euclid ... manages to obtain a rigorous proof without ever dealing with infinity, by reducing the problem [of the infinitude of primes] to the study of finite numbers. This is exactly what contemporary mathematical analysis does. — Lucio Russo

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

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

All truths in science must be demonstrated either through experiment or through mathematical proof. The idea that something must be so because Newton or Einstein said so is simply not scientific. — Dalai Lama XIV

We are not very pleased when we are forced to accept a mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context. — Hermann Weyl

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

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. — John Ashworth Ratcliffe

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

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

The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or interrelations between various objects. The goal of a proof is to make such a statement convincing by presenting a reasoning subdivided into small steps each of which is justified as an "elementary" convincing argument. — Yuri Manin

But he needed to be certain before committing to something so - the word, certain, arrested his thoughts. A person can't be absolutely certain about anything, not certainty in the sense of a mathematical proof. He wasn't certain about Kate. He saw her, observed her, wanted to be with her. Somehow, he just knew. For reasons already set in his heart, the way he was wired, Josh knew Kate was a person he wanted in his life. She was the proof. Would it be the same way with God? — H.L. Wegley

Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science which have been by slow degrees vouchsafed to man, and are still granted in these latter times by the Differential Calculus, now superseded by the Higher Algebra, all of which must have existed in that sublimely omniscient Mind from eternity. — Mary Somerville

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