Mathematical Language Quotes & Sayings

We feel certain that the extraterrestrial message is a mathematical code of some kind. Probably a number code. Mathematics is the one language we might conceivably have in common with other forms of intelligent life in the universe. As I understand it, there is no reality more independent of our perception and more true to itself than mathematical reality. — Don DeLillo

It seems perfectly clear that Economy, if it is to be a science at all, must be a mathematical science. There exists much prejudice against attempts to introduce the methods and language of mathematics into any branch of the moral sciences. Most persons appear to hold that the physical sciences form the proper sphere of mathematical method, and that the moral sciences demand some other method-I know not what. — William Stanley Jevons

The physicist may be satisfied when he has the mathematical scheme and knows how to use for the interpretation of the experiments. But he has to speak about his results also to non-physicists who will not be satisfied unless some explanation is given in plain language. Even for the physicist the description in plain language will be the criterion of the degree of understanding that has been reached.
Physics and Philosophy — Werner Heisenberg

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. "Immortality" may be a silly word, but probably a mathematician has the best chance of whatever it may mean. — G.H. Hardy

It strikes me that mathematical writing is similar to using a language. To be understood you have to follow some grammatical rules. However, in our case, nobody has taken the trouble of writing down the grammar; we get it as a baby does from parents, by imitation of others. Some mathematicians have a good ear; some not (and some prefer the slangy expressions such as 'iff'). That's life. — Jean-Pierre Serre

As a graduate student, I wrote a long paper connecting the dots between mathematical models of learning and language development in children. It was published in a major journal. — Steven Pinker

Requirements in mathematical language are no use unless they are easier to read than the code. — David Parnas

All our surest statements about the nature of the world are mathematical statements, yet we do not know what mathematics "is" ... and so we find that we have adapted a religion strikingly similar to many traditional faiths. Change "mathematics" to "God" and little else might seem to change. The problem of human contact with some spiritual realm, of timelessness, of our inability to capture all with language and symbol-all have their counterparts in the quest for the nature of Platonic mathematics. — John D. Barrow

When a mathematician engaged in investigating physical actions and results has arrived at his own conclusions, may they not be expressed in common language as fully, clearly, and definitely as in mathematical formulae? If so, would it not be a great boon to such as well to express them so
translating them out of their hieroglyphics that we might also work upon them by experiment? — Michael Faraday

Python language is one example. As we noted above, it is also heavily used for mathematical and scientific papers, and will probably dominate that niche for some years yet. 18.3.3 — Eric S. Raymond

Consider a cognitive scientist concerned with the empirical study of the mind, especially the cognitive unconscious, and ultimately committed to understanding the mind in terms of the brain and its neural structure. To such a scientist of the mind, Anglo-American approaches to the philosophy of mind and language of the sort discussed above seem odd indeed. The brain uses neurons, not languagelike symbols. Neural computation works by real-time spreading activation, which is neither akin to prooflike deductions in a mathematical
logic, nor like disembodied algorithms in classical artificial intelligence, nor like derivations in a transformational grammar. — George Lakoff

The new mathematics is a sort of supplement to language, affording a means of thought about form and quantity and a means of expression,more exact,compact, and ready than ordinary language. The great body of physical science, a great deal of the essential facts of financial science, and endless social and political problems are only accessible and thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood that for complete initiation as an efficient citizen of one of the new great complex world wide states that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and write. — H.G.Wells

So is not mathematical analysis then not just a vain game of the mind? To the physicist it can only give a convenient language; but isn't that a mediocre service, which after all we could have done without; and, it is not even to be feared that this artificial language be a veil, interposed between reality and the physicist's eye? Far from that, without this language most of the initimate analogies of things would forever have remained unknown to us; and we would never have had knowledge of the internal harmony of the world, which is, as we shall see, the only true objective reality. — Henri Poincare

We shed as we pick up, like travellers who must carry everything in their arms, and what we let fall will be picked up by those behind. The procession is very long and life is very short. We die on the march. But there is nothing outside the march so nothing can be lost to it. The missing plays of Sophocles will turn up piece by piece, or be written again in another language. Ancient cures for diseases will reveal themselves once more. Mathematical discoveries glimpsed and lost to view will have their time again. You do not suppose, my lady, that if all of Archimedes had been hiding in the great library of Alexandria, we would be at a loss for a corkscrew? — Tom Stoppard

The universe cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth. This — Marcus Du Sautoy

I have tasted words, I have seen them. Never had her hands reached out in darkness and felt the texture of pure marble, never had her forehead bent forward and, as against a stone altar, felt safety. I am now saved. Her mind could not then so specifically have seen it, could not have said, Now I will reveal myself in words, words may now supercede a scheme of mathematical-biological definition. Words may be my heritage and with words ... A lady will be set back in the sky ... there was hope in a block of unsubstantiated marble, words could carve and set up solid altars ... Thought followed the wing that beat its silver into seven-branched larch boughs. — H.D.

We shed as we pick up, like travelers who must carry everything in their arms, and what we let fall will be picked up by those behind. The procession is very long and life is very short. We die on the march. But there is nothing outside the march so nothing can be lost to it. The missing plays of Sophocles will turn up piece by piece, or be written again in another language. Ancient cures for diseases will reveal themselves once more. Mathematical discoveries glimpsed and lost to view will have their time again. — Tom Stoppard

This book reminds me of James Gleick's Chaos. The ideas and stories in Loving and Hating Mathematics are timely, interesting, and sometimes even profound. The authors, writing for nonspecialists, take pains to explain technical ideas in nontechnical language, and the book should interest general readers as well as a large mathematical audience. — Steven G. Krantz

Whether we like it or not, if we are to pursue a career in science, eventually we have to learn the "language of nature": mathematics. Without mathematics, we can only be passive observers to the dance of nature rather than active participants. As Einstein once said, "Pure mathematics is, in its way, the poetry of logical ideas." Let me offer an analogy. One may love French civilization and literature, but to truly understand the French mind, one must learn the French language and how to conjugate French verbs. The same is true of science and mathematics. Galileo once wrote, "[The universe] cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles, and other geometrical figures, without which means it is humanly impossible to understand a single word. — Michio Kaku

[In the Royal Society, there] has been, a constant Resolution, to reject all the amplifications, digressions, and swellings of style: to return back to the primitive purity, and shortness, when men deliver'd so many things, almost in an equal number of words. They have exacted from all their members, a close, naked, natural way of speaking; positive expressions; clear senses; a native easiness: bringing all things as near the Mathematical plainness, as they can: and preferring the language of Artizans, Countrymen, and Merchants, before that, of Wits, or Scholars. — Thomas Sprat

We should expect nothing less from the language that was originally given by God, to His human family. Hebrew was the method that God chose for mankind to speak to Him, and Him to them. Adam spoke Hebrew - and your Bible confirms this. Everyone who got off the ark spoke one language - Hebrew.
Even Abraham spoke Hebrew. Where did Abraham learn to speak Hebrew? Abraham was descended from Noah's son, Shem. (Ge 11:10-26) Shem's household was not affected by the later confusion of languages, at Babel. (Ge 11:5-9) To the contrary, Shem was blessed while the rest of Babel was cursed. (Ge 9:26) That is how Abraham retained Hebrew, despite residing in Babylon.
So, Shem's language can be traced back to Adam. (Ge 11:1) And, Shem (Noah's son) was still alive when Jacob and Esau was 30 years of age. Obviously, Hebrew (the original language) was clearly spoken by Jacob's sons. (Ge 14:13) — Michael Ben Zehabe

Philosophy [nature] is written in that great book which ever is before our eyes
I mean the universe
but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth. — Galileo Galilei

Destruction is creation. Become as a little child. Language as space, a kind of mathematical notation, geometric locations in the lab of memory. Reading. Maps. Codes, substitutions, the secret names of things. The glorious inrush of a word. The joy of chatter. Every color's wavelength, by number. — Kim Stanley Robinson

Time is said to have only one dimension, and space to have three dimensions ... The mathematical quaternion partakes of both these elements; in technical language it may be said to be 'time plus space', or 'space plus time': and in this sense it has, or at least involves a reference to, four dimensions. And how the One of Time, of Space the Three, Might in the Chain of Symbols girdled be. — William Rowan Hamilton

I think that modern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language. — Werner Heisenberg

probably heard that math is the language of science, or the language of Nature is mathematics. Well, it's true. The more we understand the universe, the more we discover its mathematical connections. Flowers have spirals that line up with a special sequence of numbers (called Fibonacci numbers) that you can understand and generate yourself. Seashells form in perfect mathematical curves (logarithmic spirals) that come from a chemical balance. Star clusters tug on — Arthur Benjamin

The precision provided (or enforced) by programming languages and their execution can identify lacunas, ambiguities, and other areas of potential confusion in conventional [mathematical] notation. — Kenneth E. Iverson

The world of physics is essentially the real world construed by mathematical abstractions, and the world of sense is the real world construed by the abstractions which the sense-organs immediately furnish. To suppose that the "material mode" is a primitive and groping attempt at physical conception is a fatal error in epistemology. — Susanne K. Langer

Adam was told to name the animals. Adam studied each kind and gave them a name based on his observations. Every animal "kind" has some behavior or characteristic that is unique to that animal type. When you know the Hebrew name for an animal, you get a peek at how a perfect man, speaking a perfect language, understood that perfect animal. — Michael Ben Zehabe

I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply our notes of our observations. This view has been held, in one form or another, by many philosophers of high reputation from Plato onwards, and I shall use the language which is natural to a man who holds it. — G.H. Hardy

My suggestion is that at each state the proper order of operation of the mind requires an overall grasp of what is generally known, not only in formal logical, mathematical terms, but also intuitively, in images, feelings, poetic usage of language, etc. — David Bohm

But why has our physical world revealed such extreme mathematical regularity that astronomy superhero Galileo Galilei proclaimed nature to be "a book written in the language of mathematics," and Nobel Laureate Eugene Wigner stressed the "unreasonable effectiveness of mathematics in the physical sciences" as a mystery demanding an explanation? — Max Tegmark

In mathematical analysis we call x the undetermined part of line a: the rest we don't call y, as we do in common life, but a-x. Hence mathematical language has great advantages over the common language. — Georg C. Lichtenberg

The mathematical sciences wield their particular language made of digits and signs, no less subtle than any other. — Jorge Luis Borges

Ever since his first ecstasy or vision of Christminster and its possibilities, Jude had meditated much and curiously on the probable sort of process that was involved in turning the expressions of one language into those of another. He concluded that a grammar of the required tongue would contain, primarily, a rule, prescription, or clue of the nature of a secret cipher, which, once known, would enable him, by merely applying it, to change at will all words of his own speech into those of the foreign one. His childish idea was, in fact, a pushing to the extremity of mathematical precision what is everywhere known as Grimm's Law - an aggrandizement of rough rules to ideal completeness. Thus he assumed that the words of the required language were always to be found somewhere latent in the words of the given language by those who had the art to uncover them, such art being furnished by the books aforesaid. — Thomas Hardy

The strange word nymphomation, used to denote a complex mathematical procedure where numbers, rather than being added together or multiplied or whatever, were actually allowed to breed with each other to produce new numbers. — Jeff Noon

Without computers, in the 17th century, we could classify the entire animal kingdom ... there was this idea of the speciation, right? And now, all a search engine is is essentially the mathematical speciation of ideas - and these things really derive from the way that language is used and the way words relate. — Joshua Cohen

Of the properties of mathematics, as a language, the most peculiar one is that by playing formal games with an input mathematical text, one can get an output text which seemingly carries new knowledge. The basic examples are furnished by scientific or technological calculations: general laws plus initial conditions produce predictions, often only after time-consuming and computer-aided work. One can say that the input contains an implicit knowledge which is thereby made explicit. — Yuri Manin

Hurry was not a concept that could be symbolized in the Martian language and therefore must be presumed to be unthinkable. Speed, velocity, simultaneity, acceleration, and other mathematical abstractions having to do with the pattern of eternity were part of Martian mathematics, but not of Martian emotion. — Robert A. Heinlein

Nature is written in mathematical language. — Galileo Galilei

Science is complex and chilling. The mathematical language of science is understood by very few. The vistas it presents are scary-an enormous universe ruled by chance and impersonal rules, empty and uncaring, ungraspable and vertiginous. How comfortable to turn instead to a small world, only a few thousand years old, and under God's personal; and immediate care; a world in which you are His peculiar concern. — Isaac Asimov

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. — George Polya

One can prove or refute anything at all with words. Soon people will perfect language technology to such an extent that they'll beproving with mathematical precision that twice two is seven. — Anton Chekhov

Riemann concluded that electricity, magnetism, and gravity are caused by the crumpling of our three-dimensional universe in the unseen fourth dimension. Thus a "force" has no independent life of its own; it is only the apparent effect caused by the distortion of geometry. By introducing the fourth spatial dimension, Riemann accidentally stumbled on what would become one of the dominant themes in modern theoretical physics, that the laws of nature appear simple when expressed in higher-dimensional space. He then set about developing a mathematical language in which this idea could be expressed. — Michio Kaku

One cannot inquire into the foundations and nature of mathematics without delving into the question of the operations by which the mathematical activity of the mind is conducted. If one failed to take that into account, then one would be left studying only the language in which mathematics is represented rather than the essence of mathematics. — L. E. J. Brouwer

The properties of executability and universality associated with programming languages can be combined, in a single language, with the well-known properties of mathematical notation which make it such an effective tool of thought. — Kenneth E. Iverson

So mathematical truth prefers simple words since the language of truth is itself simple. — Tycho Brahe

Our experience teaches us that there are indeed laws of nature, regularities in the way things behave, and that these laws are best expressed using the language of mathematics. This raises the interesting possibility that mathematical consistency might be used to guide us, along with experimental observation, to the laws that describe physical reality, and this has proved to be the case time and again throughout the history of science. We will see this happen during the course of this book, and it is truly one of the wonderful mysteries of our universe that it should be so. — Brian Cox

In the eighteenth century, philosophers considered the whole of human knowledge, including science, to be their field and discussed questions such as: Did the universe have a beginning? However, in the nineteenth and twentieth centuries, science became too technical and mathematical for the philosophers, or anyone else except a few specialists. Philosophers reduced the scope of their inquiries so much that Wittgenstein, the most famous philosopher of this century, said, "The sole remaining task for philosophy is the analysis of language." What a comedown from the great tradition of philosophy from Aristotle to Kant! — Stephen Hawking

Indeed, as Professor Felten notes, eavesdropping on calls can be quite difficult due to language differences, meandering conversations, the use of slang or deliberate codes, and other attributes that either by design or accident obfuscate the meaning. "The content of calls are far more difficult to analyze in an automated fashion due to their unstructured nature," he argued. By contrast, metadata is mathematical: clean, precise, and thus easily analyzed. And as Felten put it, it is often "a proxy for content": — Glenn Greenwald