Quotes & Sayings About Mathematics And Truth

Solving a problem for which you know there's an answer is like climbing a mountain with a guide, along a trail someone else has laid. In mathematics, the truth is somewhere out there in a place no one knows, beyond all the beaten paths. And it's not always at the top of the mountain. It might be in a crack on the smoothest cliff or somewhere deep in the valley. — Yoko Ogawa

Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation. — Ivars Peterson

When we are young, we spend much time and pains in filling our note-books with all definitions of Religion, Love, Poetry, Politics, Art, in the hope that, in the course of a few years, we shall have condensed into our encyclopaedia the net value of all the theories at which the world has yet arrived. But year after year our tables get no completeness, and at last we discover that our curve is a parabola, whose arcs will never meet. — Ralph Waldo Emerson

It is mathematics which reveals every genuine truth, for it knows every hidden secret, and bears the key to every subtlety of letters; whoever then has the effrontery to study physics while neglecting mathematics, should know from the start that he will never make his entry into the portals of wisdom. — Thomas Bradwardine

When we say that the ancestors of the Blacks, who today live mainly in Black Africa, were the first to invent mathematics, astronomy, the calendar, sciences in general, arts, religion, agriculture, social organization, medicine, writing, technique, architecture; that they were the first to erect buildings out of 6 million tons of stone (the Great Pyramid) as architects and engineers - not simply as unskilled laborers; that they built the immense temple of Karnak, that forest of columns with its famed hypostyle hall large enough to hold Notre-Dame and its towers; that they sculpted the first colossal statues (Colossi of Memnon, etc.) - when we say all that we are merely expressing the plain unvarnished truth that no one today can refute by arguments worthy of the name. — Cheikh Anta Diop

Miri took genuine comfort in studying Mathematics that day. She could sort numbers into two simple ideas: true and not true. Unlike numbers, words were rarely just one thing. They moved and changed, camouflaging and leaping out unexpectedly. Words were slippery and alive; words wrestled out of her grip and became something new. Words were dangerous. — Shannon Hale

[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing-one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me. — Paul Halmos

I have often been surprised that Mathematics, the quintessence of Truth, should have found admirers so few and so languid. Frequent consideration and minute scrutiny have at length unravelled the cause: viz . that though Reason is feasted, Imagination is starved; whilst Reason is luxuriating in its proper Paradise, Imagination is wearily travelling on a dreary desert. — Samuel Taylor Coleridge

Look you wanna know the truth? I don't really care about the
stats or the cup or the trophy or anything like that. In fact even the games aren't that important to me. What matters to me is the perfect throw, making the perfect catch, the perfect step and block. Perfection. That's what it's about. It's those moments. When you can feel the perfection of creation. The beauty the physics you know the wonder of mathematics. The elations of action and reaction and that is the kind of perfection that I want to be connected to. — Samuel Anders

Mathematics is a form of poetry which transcends poetry in that it proclaims a truth; a form of reasoning which transcends reasoning in that it wants to bring about the truth it proclaims; a form of action, of ritual behavior, which does not find fulfilment in the act but must proclaim and elaborate a poetic form of truth. — Salomon Bochner

A Christian boy or girl can learn mathematics, for example, from a teacher who is not a Christian; and truth is truth however learned. But while truth is truth however learned, the bearing of truth, the meaning of truth, the purpose of truth, even in the sphere of mathematics, seem entirely different to the Christian from that which they seem to the non-Christian; and that is why a truly Christian education is possible only when Christian conviction underlies not a part but all, of the curriculum of the school. — John Gresham Machen

I know your race and mine are never on the best of terms." There was a cold smile in his voice if not on his face. "But I do only what you force me to. You rationalize, Keeton. You defend. You reject unpalatable truths, and if you can't reject them outright you trivialize them. Incremental evidence is never enough for you. You hear rumors of Holocaust; you dismiss them. You see evidence of genocide; you insist it can't be so bad. Temperatures rise, glaciers melt - species die - and you blame sunspots and volcanoes. Everyone is like this, but you most of all. You and your Chinese Room. You turn incomprehension into mathematics, you reject the truth without even knowing what it is. — Peter Watts

So [in mathematics] we get to play and imagine whatever we want and make patterns and ask questions about them. But how do we answer these questions? It's not at all like science. There's no experiment I can do ... The only way to get at the truth about our imaginations is to use our imaginations, and that is hard work. — Paul Lockhart

Plato's sense that this was the only religion that would hold up nowadays was thoroughgoing. The only religion that could be really believed by anyone in his time, he said, is based on belief that the stars have intelligence, and that we and they have immortal souls of some sort.18 The more we learn - and mathematics is the queen of the soul's subjects - the more we will ascend toward self-knowledge and universal truth. This ascension is the drama of Plato's religion. — Jennifer Michael Hecht

The faith of scientists in the power and truth of mathematics is so implicit that their work has gradually become less and less observation, and more and more calculation ... But the facts which are accepted by virtue of these tests are not actually observed at all. — Susanne Katherina Langer

Mathematics and poetry are the two ways to drink the beauty of truth. — Amit Ray

Of these austerer virtues the love of truth is the chief, and in mathematics, more than elsewhere, the love of truth may find encouragement for waning faith. Every great study is not only an end in itself, but also a means of creating and sustaining a lofty habit of mind; and this purpose should be kept always in view throughout the teaching and learning of mathematics. — Bertrand Russell

When I was young, most teachers of philosophy in British and American universities were Hegelians, so that, until I read Hegel, I supposed there must be some truth to his system; I was cured, however, by discovering that everything he said on the philosophy of mathematics was plain nonsense. — Bertrand Russell

Finally, the dishonesty in the movement of the publication of a Greek philosophy, becomes very glaring, when we refer to the fact, purposely that by calling the theorem of the Square on the Hypotenuse, the Pythagorean theorem, it has concealed the truth for centuries from the world, who ought to know that the Egyptians taught Pythagoras and the Greeks, what mathematics they knew. — George G. M. James

All those formal systems, in mathematics and physics and the philosophy of science, which claim to give foundations for certain truth are surely mistaken. I am tempted to say that we do not look for truth, but for knowledge. But I dislike this form of words, for two reasons. First of all, we do look for truth, however we define it, it is what we find that is knowledge. And second, what we fail to find is not truth, but certainty; the nature of truth is exactly the knowledge that we do find. — Jacob Bronowski

Science and mathematics Run parallel to reality, they symbolize it, they squint at it, They never touch it: consider what an explosion Would rock the bones of men into little white fragments and unsky the world If any mind for a moment touch truth. — Robinson Jeffers

The Mathematics are Friends to Religion, inasmuch as they charm the Passions, restrain the Impetuosity of the Imagination, and purge the Mind from Error and Prejudice. Vice is Error, Confusion, and false Reasoning; and all Truth is more or less opposite to it. Besides, Mathematical Studies may serve for a pleasant Entertainment for those Hours which young Men are apt to throw away upon their Vices; the Delightfulness of them being such as to make Solitude not only easy, but desirable. — John Arbuthnot

We can ... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics. — Hans Reichenbach

It is said that there comes a point in every mathematics student's education when he hears himself saying to the teacher, "I think I understand"-- and that's the point at which he has hit a wall. Making sure that all gifted students hit their own personal walls is crucial for developing the empathy with the rest of the world. When they see their less lucky peers struggle academically, they need to be able to say "I know how it feels,"-- and be telling the truth. — Charles Murray

As regards authority I so proceed. Boetius says in the second prologue to his Arithmetic, 'If an inquirer lacks the four parts of mathematics, he has very little ability to discover truth.' And again, 'Without this theory no one can have a correct insight into truth.' And he says also, 'I warn the man who spurns these paths of knowledge that he cannot philosophize correctly.' And Again, 'It is clear that whosoever passes these by, has lost the knowledge of all learning.' — Roger Bacon

I think of myth and magic as the hieroglyphics of the human psyche. They are a special language that circumvents conscious thought and goes straight to the subconscious.
Non-fiction uses the medium of information. It tells us what we need to know.
Science fiction primarily uses the medium of physics and mathematics. It tells us how things work, or could work.
Horror taps into the darker imagery of the psychology, telling us what we should fear.
Fantasy, magic and myth, however, tap into the spiritual potential of the human life. Their medium is symbolism, truth made manifest in word pictures, and they tell us what things mean on a deep, internal level. I have always been a meaning-maker. I have always been someone who strives to make sense of everything and perhaps that is where my life as a storyteller first began. Life doesn't always make sense, but story must. And so I write stories, and the world comes right again. — Ripley Patton

The laws of Nature are written in the language of mathematics. Math is a way to describe reality and figure out how the world works, a universal language that has become the gold standard of truth. In our world, increasingly driven by science and technology, mathematics is becoming, ever more, the source of power, wealth, and progress. Hence those who are fluent in this new language will be on the cutting edge of progress. — Edward Frenkel

That's because, if correct, a mathematical formula expresses an eternal truth about the universe. Hence no one can claim ownership of it; it is ours to share. Rich or poor, black or white, young or old - no one can take these formulas away from us. Nothing in this world is so profound and elegant, and yet so available to all. — Edward Frenkel

The membership relation for sets can often be replaced by the composition operation for functions. This leads to an alternative foundation for Mathematics upon categories
specifically, on the category of all functions. Now much of Mathematics is dynamic, in that it deals with morphisms of an object into another object of the same kind. Such morphisms (like functions) form categories, and so the approach via categories fits well with the objective of organizing and understanding Mathematics. That, in truth, should be the goal of a proper philosophy of Mathematics. — Saunders Mac Lane

But the science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value; just as logic has its own peculiar truth and value, independently of the subjects to which we may apply its reasonings and processes. — Ada Lovelace

The world is colors and motion, feelings and thoughts and what does math have to do with it? Not much, if 'math' means being bored in high school, but in truth mathematics is the one universal science. Mathematics is the study of pure pattern and everything in the cosmos is a kind of pattern. — Rudy Rucker

We have heard much about the poetry of mathematics, but very little of it has as yet been sung. The ancients had a juster notion of their poetic value than we. The most distinct and beautiful statements of any truth must take at last the mathematical form. We might so simplify the rules of moral philosophy, as well as of arithmetic, that one formula would express them both. — Henry David Thoreau

If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics ... — Roger Bacon

I only know that when I study mathematics, I transport myself to another world, a world of exquisite beauty and truth. And in that world I am the person I like to be. — Dora Musielak

Do we use models to help us find the truth? Or do we know the truth first, and then develop the mathematics to explain it? — Arthur C. Clarke

We come astonishingly close to the mystical beliefs of Pythagoras and his followers who attempted to submit all of life to the sovereignty of numbers. Many of our psychologists, sociologists, economists and other latter-day cabalists will have numbers to tell them the truth or they will have nothing ... We must remember that Galileo merely said that the language of nature is written in mathematics. He did not say that everything is. And even the truth about nature need not be expressed in mathematics. For most of human history, the language of nature has been the language of myth and ritual. These forms, one might add, had the virtues of leaving nature unthreatened and of encouraging the belief that human beings are part of it. It hardly befits a people who stand ready to blow up the planet to praise themselves too vigorously for having found the true way to talk about nature. — Neil Postman

A famous Japanese Zen master, Hakuun Yasutani Roshi, said that unless you can explain Zen in words that a fisherman will comprehend, you don't know what you're talking about. Some fifty years ago a UCLA professor told me the same thing about applied mathematics. We like to hide from the truth behind foreign-sounding words or mathematical lingo. There's a saying: The truth is always encountered but rarely perceived. If we don't perceive it, we can't help ourselves and we can't much help anyone else. — Jeff Bridges

The true man of science will know nature better by his finer organization; he will smell, taste, see, hear, feel, better than other men. His will be a deeper and finer experience. We do not learn by inference and deduction and the application of mathematics to philosophy, but by direct intercourse and sympathy. It is with science as with ethics,
we cannot know truth by contrivance and method; the Baconian is as false as any other, and with all the helps of machinery and the arts, the most scientific will still be the healthiest and friendliest man, and possess a more perfect Indian wisdom. — Henry David Thoreau

There are all sorts of things embodied in the LEGO brick - geometry and mathematics and truth and proportion and shape and colour ... It is a faintly spiritual activity that everybody connects with. — James May

Religion has the same relation to man's heavenly condition that mathematics has to his earthly one: both the one and the other are merely the rules of the game. Belief in God and belief in numbers: local truth and truth of location. — Vladimir Nabokov

Outside observers often assume that the more complicted a piece of mathematics is, the more mathematicians admire it. Nothing could be further from the truth. Mathematicians admire elegance and simplicity above all else, and the ultimate goal in solving a problem is to find the method that does the job in the most efficient manner. Though the major accolades are given to the individual who solves a particular problem first, credit (and gratitude) always goes to those who subsequently find a simpler solution. — Keith Devlin

To all of us who hold the Christian belief that God is truth, anything that is true is a fact about God, and mathematics is a branch of theology. — Hilda Phoebe Hudson

A man craves ultimate truths. Every mortal mind, I think, is that way. But what is ultimate truth? It's the end of the road, where there is no more mystery, no more hope. And no more questions to ask, since all the answers have been given. But there is no such place.
The Universe is a labyrinth made of labyrinths. Each leads to another. And wherever we cannot go ourselves, we reach with mathematics. Out of mathematics we build wagons to carry us into the nonhuman realms of the world. — Stanislaw Lem

Q. You do not consider your statement a disloyal one?
A. No, sir. Scientific truth is beyond loyalty and disloyalty.
Q. Can you prove that this mathematics is valid?
A. Only to another mathematician.
Q. Your claim then is that your truth is of so esoteric a nature that it is beyond the understanding of a plain man. It seems to me that truth should be clearer than that, less mysterious, more open to the mind.
A. It presents no difficulties to some minds. The physics of energy transfer, which we know as thermodynamics, has been clear and true through all the history of man since the mythical ages, yet there may be people present who would find it impossible to design a power engine. People of high intelligence, too. — Isaac Asimov

See skulking Truth to her old cavern fled, Mountains of Casuistry heap'd o'er her head! Philosophy, that lean'd on Heav'n before, Shrinks to her second cause, and is no more. Physic of Metaphysic begs defence, And Metaphysic calls for aid on Sense! See Mystery to Mathematics fly! — Alexander Pope

Mathematics is, I believe, the chief source of the belief in eternal and exact truth, as well as a sensible intelligible world. — Bertrand Russell

All the truths of mathematics are linked to each other, and all means of discovering them are equally admissible. — Adrien-Marie Legendre

In mathematics or physics, infinity is greater than one or two or any number countable. In how many ways can the world be destroyed based on ordered knowledge? You may be able to count this. But the truth is, you "really" don't know. These possibilities in your mind hold a set of unpredictable orders. One effect may be causative of another of another. It could be a culmination of effects you know as events where events are sets and subsets of potential possibilities.
In how many ways can the world be destroyed based on unordered possibilities? — Dew Platt

The thing I want you especially to understand is this feeling of divine revelation. I feel that this structure was "out there" all along I just couldn't see it. And now I can! This is really what keeps me in the math game
the chance that I might glimpse some kind of secret underlying truth, some sort of message from the gods. — Paul Lockhart

The science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value. — Ada Lovelace