Top 1200 Mathematical Proof Quotes & Sayings - Page 3

Like music or art, mathematical equations can have a natural progression and logic that can evoke rare passions in a scientist. Although the lay public considers mathematical equations to be rather opaque, to a scientist an equation is very much like a movement in a larger symphony. Simplicity. Elegance. These are the qualities that have inspired some of the greatest artists to create their masterpieces, and they are precisely the same qualities that motivate scientists to search for the laws of nature. LIke a work of art or a haunting poem, equations have a beauty and rhythm all their own.

Faith in God means believing absolutely in something with no proof whatsoever. Faith in humanity means believing absolutely in something with a huge amount of proof to the contrary. We are the true believers.

In the "commentatio" (note presented to the Russian Academy) in which his theorem on polyhedra (on the number of faces, edges and vertices) was first published Euler gives no proof. In place of a proof, he offers an inductive argument: he verifies the relation in a variety of special cases. There is little doubt that he also discovered the theorem, as many of his other results, inductively.

Acceptance without proof is the fundamental characteristic of Western religion, rejection without proof is the fundamental characteristic of Western science.

For those who believe, no proof is necessary. For those who don't believe, no proof is possible.

Although mathematical notation undoubtedly possesses parsing rules, they are rather loose, sometimes contradictory, and seldom clearly stated. [...] The proliferation of programming languages shows no more uniformity than mathematics. Nevertheless, programming languages do bring a different perspective. [...] Because of their application to a broad range of topics, their strict grammar, and their strict interpretation, programming languages can provide new insights into mathematical notation.

I don’t believe in god. There’s no proof he exists. In a world where there isn’t even proof of the future, the past exists. Even if it’s tainted with misunderstandings and delusions, if the people themselves believe in it, the past is the truth to them. And, if you base your actions or your life around it, in a way, it’s a type of god itself.

The Reader may here observe the Force of Numbers, which can be successfully applied, even to those things, which one would imagine are subject to no Rules. There are very few things which we know, which are not capable of being reduc'd to a Mathematical Reasoning, and when they cannot, it's a sign our Knowledge of them is very small and confus'd; and where a mathematical reasoning can be had, it's as great folly to make use of any other, as to grope for a thing in the dark when you have a Candle standing by you.

There's a mathematical way to get success.

After the bare requisites to living and reproducing, man wants most to leave some record of himself, a proof, perhaps, that he has really existed. He leaves his proof on wood, on stone or on the lives of other people. This deep desire exists in everyone, from the boy who writes dirty words in a public toilet to the Buddha who etches his image in the race mind. Life is so unreal. I think that we seriously doubt that we exist and go about trying to prove that we do.

We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of science are mathematics and logic; the mathematical set puts out the logical eye, the logical set puts out the mathematical eye; each believing that it sees better with one eye than with two. Note that De Morgan, himself, only had sight with only one eye.

O was infinitely more moving when her body was covered with marks, of whatever kind, if only because these marks made it impossible for her to cheat and immediately proclaimed, the moment they were seen, that anything went as far as she was concerned. For to know this was one thing, but to see the proof of it, and to see the proof constantly renewed, was quite another.

This report has been difficult to write because it involves something that doesn't officially exist. It is well known that ever since the first flying saucer was reported in June 1947 the Air Force has officially said that there is no proof that such a thing as an interplanetary spaceship exists. But what is not well known is that this conclusion is far from being unanimous among the military and their scientific advisors because of the one word, proof; so the UFO investigations continue.

A mathematical equation stands forever.

It's like a mathematical law, Grace.

The art of music is good, for the reason, among others, that it produces pleasure; but what proof is it possible to give that pleasure is good? If, then, it is asserted that there is a comprehensive formula, including all things which are in themselves good, and that whatever else is good, is not so as an end, but as a mean, the formula may be accepted or rejected, but is not a subject of what is commonly understood by proof.

Mathematics is not only real, but it is the only reality. That is that entire universe is made of matter, obviously. And matter is made of particles. It's made of electrons and neutrons and protons. So the entire universe is made out of particles. Now what are the particles made out of They're not made out of anything. The only thing you can say about the reality of an electron is to cite its mathematical properties. So there's a sense in which matter has completely dissolved and what is left is just a mathematical structure.

I don't think there's a problem. First of all, I don't think music turns people into social liabilities. Because you hear a lyric - there's no medical proof that a person hearing a lyric is going to act out the lyric. There's also no medical proof that if you hear any collection of vowels and consonants, that the hearing of that collection is going to send you to Hell.

The laws of nature are but the mathematical thoughts of God.

But as the work proceeded I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was not more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.

Originally, the burden of proof was on physicists to prove that time travel was possible. Now the burden of proof is on physicists to prove there must be a law forbidding time travel.

I actually wanted to be an astronaut, but I don't have a mathematical brain.

Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries? What particular goals will there be toward which the leading mathematical spirits of coming generations will strive? What new methods and new facts in the wide and rich field of mathematical thought will the new centuries disclose?

The man who is anybody and who does anything is surely going to be criticized, vilified, and misunderstood. This is a part of the penalty for greatness, and every great man understands it; and understands, too, that it is no proof of greatness. The final proof of greatness lies in being able to endure contumely without resentment.

The source of Pyrrhonism comes from failing to distinguish between a demonstration, a proof and a probability. A demonstration supposes that the contradictory idea is impossible; a proof of fact is where all the reasons lead to belief, without there being any pretext for doubt; a probability is where the reasons for belief are stronger than those for doubting.

The scientist believes in proof without certainty, the bigot in certainty without proof.

High Frontier places a bullet-proof vest on our bare chest. High Frontier is as non-aggressive as a bullet-proof vest. There is no way to kill anyone with High Frontier - all that High Frontier can do is to keep others from killing us.

The heart of our karate is real fighting.There can be no proof without real fighting. Without proof there is no trust. Without trust there is no respect. This is a definition in the world of martial arts.

We shall see that the mathematical treatment of the subject [of electricity] has been greatly developed by writers who express themselves in terms of the 'Two Fluids' theory. Their results, however, have been deduced entirely from data which can be proved by experiment, and which must therefore be true, whether we adopt the theory of two fluids or not. The experimental verification of the mathematical results therefore is no evidence for or against the peculiar doctrines of this theory.

Mathematical Analysis is as extensive as nature herself.

To die for God is not a proof of faith in God. To die for an unknown and repulsive convict who is a victim of injustice, that is a proof of faith in God.

A proof is that which convinces a reasonable man; a rigorous proof is that which convinces an unreasonable man.

Has the mathematical abilities of a Clydesdale.

The world is not looking for more doctrinal proof of the reality of God! It is not looking for greater proof of the resurrection or better arguments about creation. The world is looking for Christians who can stand up to every crisis, fear, trouble and difficulty and remain calm and at rest in the midst of it all. The world needs to see God's children trusting wholly in their Lord.

What I realized is that if we're going to be able to have a theory about what happens in, for example, nature there has to ultimately be some rule by which nature operates. But the issue is does that rule have to correspond to something like a mathematical equation, something that we have sort of created in our human mathematics? And what I realized is that now with our understanding of computation and computer programs and so on, there is actually a much bigger universe of possible rules to describe the natural world than just the mathematical equation kinds of things.

Music is a science, in many ways it's mathematical.

As soon as a man stands up and says he is right or his church is right, and all others are wrong, he is himself all wrong. He does not know that upon the proof of all the others depends the proof of his own. Love and charity for the whole human race, that is the test of true religiousness. I do not mean the sentimental statement that all men are brothers, but that one must feel the oneness of human life.

We humans have a wide range of abilities that help us perceive and analyze mathematical content. We perceive abstract notions not just through seeing but also by hearing, by feeling, by our sense of body motion and position. Our geometric and spatial skills are highly trainable, just as in other high-performance activities. In mathematics we can use the modules of our minds in flexible ways - even metaphorically. A whole-mind approach to mathematical thinking is vastly more effective than the common approach that manipulates only symbols.

Nature is written in mathematical language.

Science has proof without any certainty. Creationists have certainty without any proof.

In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must be familiar with the forms of expression peculiar to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression.

There is no perfect mathematical formula for pricing a business.

A prevalent fallacy is the assumption that a proof of an afterlife would also be a proof of the existence of a deity. This is far from being the case. If, as I hold, there is no good reason to believe that a god either created or presides over this world, there is equally no good reason to believe that a god created or presides over the next world, on the unlikely supposition that such a thing exists.

As a man may be born with a mathematical faculty, and by training that faculty year after year may immensely increase his mathematical capacity, so may a man be born with certain faculties within him, faculties belonging to the soul, which he can develop by training and by discipline.

I don't like to think of it as 'stolen'. They have no proof that I didn't plan on giving it back." "You're kidding, right?" He shrugged. "You have no proof either." She squinted back at him. "Were you planning on giving it back?" "Maybe." An orange light blinked on in the corner of Cinder's vision-her cyborg programming picking up on the lie.

Kant, discussing the various modes of perception by which the human mind apprehends nature, concluded that it is specially prone to see nature through mathematical spectacles. Just as a man wearing blue spectacles would see only a blue world, so Kant thought that, with our mental bias, we tend to see only a mathematical world.

Wisdom is not finally tested in schools, Wisdom cannot be pass'd from one having it to another not having it, Wisdom is of the soul, is not susceptible of proof, is its own proof, Applies to all stages and objects and qualities and is content, Is the certainty of the reality and immortality of things, and the excellence of things; Something there is in the float of the sight of things that provokes it out of the soul.

Fourier is a mathematical poem.

There's nothing mathematical to my writing. It's a feeling.

Those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or definitions, it is not true that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.

The mathematical expectation of the speculator is zero.

GRAVITATION, n. The tendency of all bodies to approach one another with a strength proportioned to the quantity of matter they contain-the quantity of matter they contain being ascertained by the strength of their tendency to approach one another. This is a lovely and edifying illustration of how science, having made A the proof of B, makes B the proof of A.

Never preach a sermon without a text from the Bible, a text containing the theme which you can elaborate. The text is the best proof in support of your argument. A sermon without a text is an argument without a proof.

Grown people know that they do not always know the why of things, and even if they think they know, they do not know where and how they got the proof. Hence the irritation they show when children keep on demanding to know if a thing is so and how the grown folks got the proof of it. It is so troublesome because it is disturbing to the pigeonhole way of life.

Mathematical reasoning may be regarded.

If we want proof of God's love for us, then we must look first at the Cross where God offered up His Son as a sacrifice for our sins. Calvary is the one objective, absolute, irrefutable proof of God's love for us.

Proof, being the highest level of reproduction activity, has an important interiorization aspect: as Yuri Manin stresses in his book Provable and Unprovable, a proof becomes such only after it is accepted (as the result of a highly rigorous process) ... Manin describes the act of acceptance as a social act; however, the importance of its personal, psychological component can hardly be overestimated.

I knew that he was as reliable as a mathematical formula.

Achievement of your happiness is the only moral purpose of your life, and that happiness, not pain or mindless self-indulgence, is the proof of your moral integrity, since it is the proof and the result of your loyalty to the achievement of your values.

Statistics: the mathematical theory of ignorance.