Quotes & Sayings About Mathematics In Nature

The Golden Number is a mathematical definition of a proportional function which all of nature obeys, whether it be a mollusk shell, the leaves of plants, the proportions of the animal body, the human skeleton, or the ages of growth in man. — R. A. Schwaller De Lubicz

In the Pythagorean system, thinking about numbers, or doing mathematics, was an inherently masculine task. Mathematics was associated with the gods, and with transcendence from the material world; women, by their nature, were supposedly rooted in this latter, baser realm. — Margaret Wertheim

Mowaljarlai rarely answered questions with an abstract explanation; he always told a story. His was not a fragmented world, divided into the convenient disciplinary languages and jargon that seem to be required for the understanding of concepts and principles in, for example, mathematics, physics, art and literature. Not only did he not have these languages; he thought this was a strange way to arrive at understanding the way in which the world lives in itself. It baffled him that whitefellas developed their knowledge by busting things up, reducing things to little pieces separate from everything else that contributes to their nature. For him, everything in creation is not only living and interconnected, but exists in a story and story cycle. Yet his knowledge of what whitefellas call 'science' was extraordinary."
p80-1. — Hannah Rachel Bell

Nature seems very conversant with the rules of pure mathematics, as our own mathematicians have formulated them in their studies, out of their own inner consciousness and without drawing to any appreciable extent on their experience of the outer world. — James Jeans

For we may remark generally of our mathematical researches, that these auxiliary quantities, these long and difficult calculations into which we are often drawn, are almost always proofs that we have not in the beginning considered the objects themselves so thoroughly and directly as their nature requires, since all is abridged and simplified, as soon as we place ourselves in a right point of view. — Louis Poinsot

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

Take this neat little equation here. It tells me all the ways an electron can make itself comfortable in or around an atom. That's the logic of it. The poetry of it is that the equation tells me how shiny gold is, how come rocks are hard, what makes grass green, and why you can't see the wind. And a million other things besides, about the way nature works. — Richard Feynman

Nature's great book is written in mathematics. — Galileo Galilei

In the one real, time-drenched universe, everything has a particular history precisely because it is finite, and not part of an infinite array. Moreover, the cosmological use of the infinite serves to mask the failure of a physical theory taken beyond the boundaries of its proper domain of application. The most notable instance is the inference in contemporary cosmology of an infinite initial singularity from the field equations of general relativity. Finally, the admission of the mathematical infinite into natural science effaces the difference, which we emphasize, between nature and mathematics. Nature works in time, with which mathematics has trouble. Mathematics offers, among other things, the infinite, which nature abhors. — Lee Smolin

While ritual, emotion and reasoning are all significant aspects of human nature, the most nearly unique human characteristic is the ability to associate abstractly and to reason. Curiosity and the urge to solve problems are the emotional hallmarks of our species; and the most characteristically human activities are mathematics, science, technology, music and the arts
a somewhat broader range of subjects than is usually included under the "humanities." Indeed, in its common usage this very word seems to reflect a peculiar narrowness of vision about what is human. Mathematics is as much a "humanity" as poetry. — Carl Sagan

I shall treat the nature and power of the Affects, and the power of the Mind over them, by the same Method by which, in the preceding parts, I treated God and the Mind, and I shall consider human actions and appetites just as if it were a Question of lines, planes, and bodies. — Baruch Spinoza

There is only one universal language, which is the language of numbers and proportions that are so striking and stunningly built into the Great Pyramid and to which our current science has no appropriate response. We can no longer ignore that this ancient civilization was aware of our units used in modern mathematics and physics and were even aware of our metric system. Our metric system originating in the eighteenth century, designed and implemented by a committee of mathematicians and physicists commissioned by the French revolutionary government. — Willem Witteveen

I should attempt to treat human vice and folly geometrically ... the passions of hatred, anger, envy, and so on, considered in themselves, follow from the necessity and efficacy of nature ... I shall, therefore, treat the nature and strength of the emotion in exactly the same manner, as though I were concerned with lines, planes, and solids. — Baruch Spinoza

Three principles - the conformability of nature to herself, the applicability of the criterion of simplicity, and the "unreasonable effectiveness" of certain parts of mathematics in describing physical reality - are thus consequences of the underlying law of the elementary particles and their interactions. Those three principles need not be assumed as separate metaphysical postulates. Instead, they are emergent properties of the fundamental laws of physics. — Murray Gell-Mann

But in my opinion, all things in nature occur mathematically. — Rene Descartes

A totally new kind of education is needed in the world. The person who is born to be a poet is proving himself stupid in mathematics and the person who could have been a great mathematician is just cramming history and feeling lost. Everything is topsy-turvy because education is not according to your nature: it does not pay any respect to the individual. It forces everybody into a certain pattern. — Osho

Mathematics has always shown a curious ability to be applicable to nature, and this may express a deep link between our minds and nature. We are the Universe speaking out, a part of nature. So it is not so surprising that our systems of logic and mathematics sing in tune with nature. — George Zebrowski

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

One can understand nature only when one has learned the language and the signs in which it speaks to us; but this language is mathematics and these signs are methematical figures. — Galileo Galilei

All the sciences have a relation, greater or less, to human nature; and ... however wide any of them may seem to run from it, they still return back by one passage or another. Even Mathematics, Natural Philosophy, and Natural Religion, are in some measure dependent on the science of MAN; since they lie under the cognizance of men, and are judged of by their powers and faculties. — David Hume

It is exceptional that one should be able to acquire the understanding of a process without having previously acquired a deep familiarity with running it, with using it, before one has assimilated it in an instinctive and empirical way ... Thus any discussion of the nature of intellectual effort in any field is difficult, unless it presupposes an easy, routine familiarity with that field. In mathematics this limitation becomes very severe. — John Von Neumann

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

The distinction between mathematics and science is pretty well settled. It remains mysterious to us why mathematics that is invented for reasons having nothing to do with nature often turns out to be useful in physical theories. In a famous article,8 the physicist Eugene Wigner has written of the unreasonable effectiveness of mathematics. — Steven Weinberg

Bacon not only despised the syllogism, but undervalued mathematics, presumably as insufficiently experimental. He was virulently hostile to Aristotle , but he thought very highly of Democritus , Although he did not deny that the course of nature exemplifies a Divine purpose, he objected to any admixture of teleological explanation in the actual investigation of phenomena; everything, he held, should be explained as following necessarily from efficient causes . — Bertrand Russell

There is a noticeable general difference between the sciences and mathematics on the one hand, and the humanities and social sciences on the other. It's a first approximation, but one that is real. In the former, the factors of integrity tend to dominate more over the factors of ideology. It's not that scientists are more honest people. It's just that nature is a harsh taskmaster. You can lie or distort the story of the French Revolution as long as you like, and nothing will happen. Propose a false theory in chemistry, and it'll be refuted tomorrow. — Noam Chomsky

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

Mathematics is much more than a language for dealing with the physical world. It is a source of models and abstractions which will enable us to obtain amazing new insights into the way in which nature operates. — Melvin Schwartz

It is impossible to explain honestly the beauties of the laws of nature in a way that people can feel, without their having some deep understanding of mathematics. I am sorry, but this seems to be the case. — Richard Feynman

In terms of the mathematician's beliefs about the nature of mathematics and its influence on their research, the study revealed that four of the mathematicians leaned towards Platonism, in contrast to the popular notion that Platonism is an exception today. A detailed discussion of this aspect of the research is beyond the scope of this paper; however, I have found that beliefs regarding the nature of mathematics not only influenced how these mathematicians conducted research but also were deeply connected to their theological beliefs (Sriraman, 2004a). — Bharath Sriraman

Before an experiment can be performed, it must be planned - the question to nature must be formulated before being posed. Before the result of a measurement can be used, it must be interpreted - nature's answer must be understood properly. These two tasks are those of the theorist, who finds himself always more and more dependent on the tools of abstract mathematics. Of course, this does not mean that the experimenter does not also engage in theoretical deliberations. The foremost classical example of a major achievement produced by such a division of labor is the creation of spectrum analysis by the joint efforts of Robert Bunsen, the experimenter, and Gustav Kirchhoff, the theorist. Since then, spectrum analysis has been continually developing and bearing ever richer fruit. — Max Planck

Highly complex numbers like the Comma of Pythagoras, Pi and Phi (sometimes called the Golden Proportion), are known as irrational numbers. They lie deep in the structure of the physical universe, and were seen by the Egyptians as the principles controlling creation, the principles by which matter is precipitated from the cosmic mind.

Today scientists recognize the Comma of Pythagoras, Pi and the Golden Proportion as well as the closely related Fibonacci sequence are universal constants that describe complex patterns in astronomy, music and physics. ...

To the Egyptians these numbers were also the secret harmonies of the cosmos and they incorporated them as rhythms and proportions in the construction of their pyramids and temples. — Jonathan Black

Pure concepts of the understanding. So the Humean problem is completely solved, though in a way that would have surprised its inventor. The solution secures an a priori origin for the pure concepts of the understanding, and for the universal laws of nature it secures a status as valid laws of the understanding; but it does this in such a way as to limit the use of these concepts to experience only, and it grounds them in a relation between the understanding and experience that is the complete reverse of anything that Hume envisaged - instead of the concepts being derived from experience, that experience is derived from them. My line of argument yields the following result: All synthetic a priori principles are simply principles of possible experience; they can never be applied to things in themselves, but only to appearances as objects of experience. Hence pure mathematics as well as pure natural science can never bear on anything except appearances — Anonymous

In modern science laws of nature are usually phrased in mathematics. They can be either exact or approximate, but they must have been observed to hold without exception - if not universally, then at least under a stipulated set of conditions. For — Stephen Hawking

The laws of nature are written by the hand of God in the language of mathematics. — Galileo Galilei

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

We therefore find that the triangles and rectangles herein described, enclose a large majority of the temples and cathedrals of the Greek and Gothic masters, for we have seen that the rectangle of the Egyptian triangle is a perfect generative medium, its ratio of five in width to eight in length 'encouraging impressions of contrast between horizontal and vertical lines' or spaces; and the same practically may be said of the Pythagorean triangle — Samuel Colman

Consider Rutherford playing his thoroughly unlikely hunch about alpha backscattering, Heisenberg remembering an obscure remark of Einstein's and concluding that nature only performed in consonance with his mathematics, Lawrence flipping compulsively through obscure foreign journals: Were this thinking not in the framework of scientific work, it would be considered paranoid. In scientific work, creative thinking demands seeing things not seen previously, or in ways not previously imagined; and this necessitates jumping off from "normal" positions, and taking risks by departing from reality. — Richard Rhodes

It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem. — Mark Kac

Modern bodybuilding is ritual, religion, sport, art, and science, awash in Western chemistry and mathematics. Defying nature, it surpasses it. — Camille Paglia

This world is of a single piece; yet, we invent nets to trap it for our inspection. Then we mistake our nets for the reality of the piece. In these nets we catch the fishes of the intellect but the sea of wholeness forever eludes our grasp. So, we forget our original intent and then mistake the nets for the sea.

Three of these nets we have named Nature, Mathematics, and Art. We conclude they are different because we call them by different names. Thus, they are apt to remain forever separated with nothing bonding them together. It is not the nets that are at fault but rather our misunderstanding of their function as nets. They do catch the fishes but never the sea, and it is the sea that we ultimately desire. — Martha Boles

When Mathematics unfold through Origamis,
when video games target Medicine and Education,
when architecture embraces nature,
when we defy gravity,
when physics dance, and dance clubs play Einstein,
when we stop playing war,
when TV starts saying something,
when we produce without wasting,
when engineering meets humanity's primary needs,
when all of these are not just casualties,
but a standard we all live UP to:
Then we'll know.
I'll know:
we really live in the 21st century — Natasha Tsakos

Let us say, in a word, that the correlation between the laws of mathematics and of physics is the evidence of the rational character of nature. Nature may be reduced to motions; and motions can be understood only as force, activity. But the laws which connect motions are fundamentally mathematical laws,- laws of reason. Hence force, activity, can be understood only as rational, as spiritual. Nature is thus seen to mean Activity, and Activity is seen to mean Intelligence — John Dewey

Mathematics, as much as music or any other art, is one of the means by which we rise to a complete self-consciousness. The significance of mathematics resides precisely in the fact that it is an art; by informing us of the nature of our own minds it informs us of much that depends on our minds. — Antoine Thomson D'Abbadie

Mathematics would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude. — Friedrich Nietzsche

Now, in the development of our knowledge of the workings of Nature out of the tremendously complex assemblage of phenomena presented to the scientific inquirer, mathematics plays in some respects a very limited, in others a very important part. As regards the limitations, it is merely necessary to refer to the sciences connected with living matter, and to the ologies generally, to see that the facts and their connections are too indistinctly known to render mathematical analysis practicable, to say nothing of the complexity. — Oliver Heaviside

One of the biggest problems of mathematics is to explain to everyone else what it is all about. The technical trappings of the subject, its symbolism and formality, its baffling terminology, its apparent delight in lengthy calculations: these tend to obscure its real nature. A musician would be horrified if his art were to be summed up as "a lot of tadpoles drawn on a row of lines"; but that"s all that the untrained eye can see in a page of sheet music ... In the same way, the symbolism of mathematics is merely its coded form, not its substance. — Ian Stewart

Perhaps, you know, new laws, new domains of potential openness are occurring as the universe ages, and complexity previously disallowed is now possible, and we are that complexity. We are nature moving out of its genetic phase - a phase under the control of chemical genes, which are physical structures, in to an epigenetic phase, a phase of culture ruled by codes, transformable culturally confined codes - mathematics, religion, philosophy, art, dance, humor. — Terence McKenna

In abstract mathematics, of course operations alter those particular relations which are involved in the considerations of number and space, and the results of operations are those peculiar results which correspond to the nature of the subjects of operation. — Ada Lovelace

Nature is written in mathematical language. — Galileo Galilei

The book of nature is written in the language of mathematics. — Galileo Galilei

In this book, you will encounter various interesting geometries that have been thought to hold the keys to the universe. Galileo Galilei (1564-1642) suggested that "Nature's great book is written in mathematical symbols." Johannes Kepler (1571-1630) modeled the solar system with Platonic solids such as the dodecahedron. In the 1960s, physicist Eugene Wigner (1902-1995) was impressed with the "unreasonable effectiveness of mathematics in the natural sciences." Large Lie groups, like E8-which is discussed in the entry "The Quest for Lie Group E8 (2007)"- may someday help us create a unified theory of physics. in 2007, Swedish American cosmologist Max Tegmark published both scientific and popular articles on the mathematical universe hypothesis, which states that our physical reality is a mathematical structure-in other words, our universe in not just described by mathematics-it is mathematics. — Clifford A. Pickover

The focus of history and philosophy of science scholar Arthur Miller's (2010) "137: Jung and Pauli and the Pursuit of Scientific Obsession" is Jung and Pauli's
mutual effort to discover the cosmic number or fine structure constant, which is a fundamental physical constant dealing with electromagnetism, or, from a different perspective, could be considered the philosopher's stone of the mathematical universe.
This was indeed one of Pauli and Jung's collaborative passions, but it was not the only concentration of their relationship. Quantum physics could be seen as the natural progression from ancient alchemy, through chemistry, culminating in the abstract world of subatomic particles, wave functions, and mathematics. [Ancient Egypt and Modern Psychotherapy] — Todd Hayen

Obviously, the final goal of scientists and mathematicians is not simply the accumulation of facts and lists of formulas, but rather they seek to understand the patterns, organizing principles, and relationships between these facts to form theorems and entirely new branches of human thought. For me, mathematics cultivates a perpetual state of wonder about the nature of mind, the limits of thoughts, and our place in this vast cosmos. — Clifford A. Pickover

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

Magic is that which it is; it is by itself, like the mathematics; for it is the exact and absolute science of Nature and its laws . Magic is the science of the Ancient Magi: and the Christian religion, which has imposed silence on the lying oracles, and put an end to the prestiges of the false Gods , itself reveres those Magi who came from the East, guided by a Star , to adore the Saviour of the world in His cradle. — Albert Pike

Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos [mathematics], where pure thought can dwell in its natural home ... — Bertrand Russell

It is convenient for the old men to blame Eve. To insist we are damned because a country girl talked to the snake one afternoon long ago. Children must starve in Somalia for that, and old women be abandoned in our greatest cities. It's why we will finally be thrown into the lakes of molten lead. Because she was confused by happiness that first time anyone said she was beautiful. Nevertheless, she must be the issue, so people won't notice that rocks and galaxies, mathematics and rust are also created in His image. — Jack Gilbert

I don't want to convince you that mathematics is useful. It is, but utility is not the only criterion for value to humanity. Above all, I want to convince you that mathematics is beautiful, surprising, enjoyable, and interesting. In fact, mathematics is the closest that we humans get to true magic. How else to describe the patterns in our heads that - by some mysterious agency - capture patterns of the universe around us? Mathematics connects ideas that otherwise seem totally unrelated, revealing deep similarities that subsequently show up in nature. — Ian Stewart

The fallacy that dynamic processes must be modeled as if the system is in continuous equilibrium is probably the most important reason for the intellectual failure of neoclassical economics. Mathematics, science and engineering developed tools long ago to model outside of equilibrium processes. This dynamic approach to thinking about the economy should become second nature to economists. — Steve Keen

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

Galileo wrote that 'the book of nature is written in the language of mathematics; without its help it is impossible to comprehend a single word of it. — Steven Pinker

Look, this island is an attempt to re-create a natural environment from the past. To make an isolated world where extinct creatures roam freely. Correct?" "Yes." "But from my point of view, such an undertaking is impossible. The mathematics are so self-evident that they don't need to be calculated. It's rather like my asking you whether, on a billion dollars in income, you had to pay tax. You wouldn't need to pull out your calculator to check. You'd know tax was owed. And, similarly, I know overwhelmingly that one cannot successfully duplicate nature in this way, or hope to isolate it. — Michael Crichton

For most people, the major hurdle in grasping modern insights into the nature of the universe is that these developments are usually phrased using mathematics. — Brian Greene

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

Mathematics, natural science, laws, arts, even morality, etc. do not completely fill the soul; there is always a space left over reserved for pure and speculative reason, the emptiness of which prompts us to seek in vagaries, buffooneries, and mysticism for what seems to be employment and entertainment, but what actually is mere pastime undertaken in order to deaden the troublesome voice of reason, which, in accordance with its nature, requires something that can satisfy it and does not merely subserve other ends or the interests of our inclinations. — Immanuel Kant

There is an old debate," Erdos liked to say, "about whether you create mathematics or just discover it. In other words, are the truths already there, even if we don't yet know them?" Erdos had a clear answer to this question: Mathematical truths are there among the list of absolute truths, and we just rediscover them. Random graph theory, so elegant and simple, seemed to him to belong to the eternal truths. Yet today we know that random networks played little role in assembling our universe. Instead, nature resorted to a few fundamental laws, which will be revealed in the coming chapters. Erdos himself created mathematical truths and an alternative view of our world by developing random graph theory. Not privy to nature's laws in creating the brain and society, Erdos hazarded his best guess in assuming that God enjoys playing dice. His friend Albert Einstein, at Princeton, was convinced of the opposite: "God does not play dice with the universe. — Albert-Laszlo Barabasi

Emotion is not a defect in an otherwise perfect reasoning machine. Reason, unfettered from human feeling, has led to as many horrors as any crusader's zeal. What use is pity in a world devoted to maximizing efficiency and productivity? Scientific husbandry tells us to weed out the sick, the infirm, the weak. The ruthless efficiency of euthanasia initiatives and ethnic cleansing are but the programmatic application of Nietzsche's point: from any quantifiable cost-benefit analysis, the principles of animal husbandry should apply to the human race. Charles Darwin himself acknowledged that strict obedience to "hard reason" rather than sympathy for fellow humans would represent a sacrifice of "the noblest part of our nature."6 It is the human heart resonating with empathy, not the logical brain attuned to the mathematics of efficiency, that revolts at cruelty and inhumanity. In — Terryl L. Givens

To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in. — Richard Feynman

When we find that God's ways always coincide with our own ways, it's time to question who we're really worshipping, God or ourselves. The latter moves the nature of godliness from the King to our servant to a slave, a deduction into the realm of selfhood and then the lower, slavehood. It's a spiritual mathematics in that men who need God in his godhood are humble yet strong and spiritually ambitious while men who need a slave in their selfhood are ultimately paralyzed and will remain paralyzed. — Criss Jami

Certainly one of the most important things I learned is that numbers can be deceiving. There is a logic to mathematics, but there is also the underlying human element that must be considered. Numbers can't lie, but the people who create those numbers can and do. As so many people have learned, forgetting to include human nature in an equation can be devastating. — Harry Markopolos

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

The usefulness of mathematics in furthering the sciences is commonly acknowledged: but outside the ranks of the experts there is little inquiry into its nature and purpose as a deliberate human activity. Doubtless this is due to the inevitable drawback that mathematical study is saturated with technicalities from beginning to end. — Herbert Turnbull

Logic, too, also rests on assumptions that do not correspond to anything in the real world, e.g., on the assumption that there areequal things, that the same thing is identical at different points in time: but this science arose as a result of the opposite belief (that such things actually exist in the real world). And it is the same with mathematics, which would certainly never have arisen if it had been understood from the beginning that there is no such thing in nature as a perfectly straight line, a true circle, and absolute measure. — Friedrich Nietzsche

Because the observer's only freedom is the choice of which question to pose (Shall I look up at the sky?), it is here that the mind of the observer has a chance to affect the dynamics of the brain. An examination of the mathematics, Stapp argued, shows that "the conscious intentions of a human being [reflected in the choices he makes about what question to put to nature] can influence the activities of his brain....Each conscious event picks out from the multitude of...possibilities that comprise the quantum brain the subensemble that is compatible with the conscious experience." The physical event reduces the state of the brain to that branch of it that is compatible with the particular experience or observation. — Jeffrey M. Schwartz

It is the same with mathematics, which would certainly not have arisen if it had been known from the beginning that in Nature there are no exactly straight lines, no real circle, no absolute standard of size. — Friedrich Nietzsche

First of all, when we are all finished, and we have a mathematical theory by which we can compute consequences, what can we do? It really is an amazing thing. In order to figure out what an atom is going to do in a given situation we make up rules with marks on paper, carry them into a machine which has switches that open and close in some complicated way, and the result will tell us what the atom is going to do! If the way that these switches open and close were some kind of model of the atom, if we thought that the atom had switches in it, then I would say that I understood more or less what is going on. I find it quite amazing that it is possible to predict what will happen by mathematics, which is simply following rules which really have nothing to do with what is going on in the original thing. The closing and opening of switches in a computer is quite different from what is happening in nature. — Anonymous

As science has become more abstract and remote from everyday experience, the role of metaphor in our descriptions of the world has become more central. The language that nature speaks, as Galileo long pointed out, is mathematics. The language that ordinary human beings speak, especially those of us who are not fluent in mathematics, is metaphor. Lightman ends his discussion with another metaphor: "We are blind men, imagining what we don't see." That is a good description of theoretical physics. — Freeman Dyson

I know, indeed, and can conceive of no pursuit so antagonistic to the cultivation of the oratorical faculty ... as the study of Mathematics. An eloquent mathematician must, from the nature of things, ever remain as rare a phenomenon as a talking fish, and it is certain that the more anyone gives himself up to the study of oratorical effect the less will he find himself in a fit state to mathematicize. — James Joseph Sylvester

Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of constraint and freedom that is the very essence of human nature. — Hermann Weyl

Science attempts to find logic and simplicity in nature. Mathematics attempts to establish order and simplicity in human thought. — Edward Teller

There is a beauty in discovery. There is mathematics in music, a kinship of science and poetry in the description of nature, and exquisite form in a molecule. Attempts to place different disciplines in different camps are revealed as artificial in the face of the unity of knowledge. All literate men are sustained by the philosopher, the historian, the political analyst, the economist, the scientist, the poet, the artisan and the musician. — Glenn T. Seaborg

One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That's so unlike the true nature of mathematics. — Leon Henkin