Mathematical Reality Quotes & Sayings

The mathematical question is "Why?" It's always why. And the only way we know how to answer such questions is to come up, from scratch, with these narrative arguments that explain it. So what I want to do with this book is open up this world of mathematical reality, the creatures that we build there, the questions that we ask there, the ways in which we poke and prod (known as problems), and how we can possibly craft these elegant reason-poems. — Paul Lockhart

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

The geometer offers to the physicist a whole set of maps from which to choose. One map, perhaps, will fit the facts better than others, and then the geometry which provides that particular map will be the geometry most important for applied mathematics. — G.H. Hardy

What is revealed through the psychedelic experience, I think, is a higher dimensional perspective on reality. And I use 'higher dimensional' in the mathematical sense. — Terence McKenna

You treat world history as a mathematician does mathematics, in which nothing but laws and formulas exist, no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal, shallow, mathematical present. — Hermann Hesse

Nothing can be more fatal to progress than a too confident reliance on mathematical symbols; for the student is only too apt to take the easier course, and consider the formula not the fact as the physical reality. — Lord Kelvin

Do mathematics have a relation to reality or are they only a mathematical symbol? — Fulton J. Sheen

My Third-World roots remind me that the vast majority of our fellow human beings live hungry, sick, and uneducated, and that most social scientists, even in that world, ignore that ugly reality. This is why my papers in mathematical sociology deal not with free choice among 30 flavors of ice-cream, but with social structure, social cohesion, and social marginality. — Mario Bunge

A mathematical formula for happiness:Reality divided by Expectations.There were two ways to be happy:improve your reality or lower your expectations. — Jodi Picoult

Our external physical reality is a mathematical structure. — Max Tegmark

So the bottom line is that if you believe in an external reality independent of humans, then you must also believe that our physical reality is a mathematical structure. Nothing else has a baggage-free description. In other words, we all live in a gigantic mathematical object-one that's more elaborate than a dodecahedron, and probably also more complex than objects with intimidating names such as Calabi-Yau manifolds, tensor bundles and Hilbert spaces, which appear in today's most advanced physics theories. Everything in our world is purely mathematical-including you. — Max Tegmark

This harmony that human intelligence believes it discovers in nature - does it exist apart from that intelligence? No, without doubt, a reality completely independent of the spirit which conceives it, sees it or feels it, is an impossibility. A world so exterior as that, even if it existed, would be forever inaccessible to us. But what we call objective reality is, in the last analysis, that which is common to several thinking beings, and could be common to all; this common part, we will see, can be nothing but the harmony expressed by mathematical laws. — Henri Poincare

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

The practical man demands an appearance of reality at least. Always dealing in the concrete, he regards mathematical terms not as symbols or thought but as images of reality. A system acceptable to the mathematician because of its inner consistency may appear to the practical man to be full of contradictions because of the incomplete manner in which it represents reality. — Tobias Dantzig

Mathematical Reasoning is not only exact; it has its own criteria of reality — Paul Feyerabend

I have a name for people who went to the extreme efficient market theory-which is "bonkers". It was an intellectually consistent theory that enabled them to do pretty mathematics. So I understand its seductiveness to people with large mathematical gifts. It just had a difficulty in that the fundamental assumption did not tie properly to reality. — Charlie Munger

The paradox of quantum physics in the 21st Century, awakens us to the realisation that "nothing matters" in and of itself. That nothing can be stated with certainty; but everything is just a mathematical probability occurring in an instance of space-time convergence, which forms our objective reality in the present moment. — Denis John George

if you take a positivist position, as I do, questions about reality don't have any meaning. All one can ask is whether imaginary time is useful in formulating mathematical models that describe what we observe. — Stephen Hawking

When people pose the question, are you "coxom", Tom Conrad? I like to pose a question back at them: Is J.K. Rowling actually a witch? Is Thomas Harris the no. 1 serial killer in the the US, did Yann Martell really spend a lifetime eating pie?
Of course, as far as I know J.K. Rowling is not a witch, but instead is a rather lovely and talented writer. As for that Thomas Harris (equally talented), I very much suspect he isn't actually a serial killer at all, or if he is, he's involved in the biggest case of double bluff ... ever! As for Yann Martell, well, as everyone with half a brain knows his book is actually concerned with a mathematical constant, so ignore the dumb pie joke. Hm :/ — Tom Conrad

Markets aren't real. They are mathematical models, created by imagining a self-contained world where everyone has exactly the same motivation and the same knowledge and is engaged in the same self-interested calculating exchange. Economists are aware that reality is always more complicated; but they are also aware that to come up with a mathematical model, one always has to make the world into a bit of a cartoon. — David Graeber

Fiction writing is art. It therefore, has few mathematical or scientific limits to its evolution. The writer must always push forward, experiment, and strive to reach new levels of storytelling. Good fiction comments on reality, but transports the reader to a sensational world of wonder and interest that far outweighs tangible existence. — Ron Gavalik

The stone that Dr. Johnson once kicked to demonstrate the reality of matter has become dissipated in a diffuse distribution of mathematical probabilities. The ladder that Descartes, Galileo, Newton, and Leibniz erected in order to scale the heavens rests upon a continually shifting, unstable foundation. — Morris Kline

The Difference Engine can in reality (as has been already partly explained) do nothing but add; and any other processes, not excepting those of simple subtraction, multiplication and division, can be performed by it only just to that extent in which it is possible, by judicious mathematical arrangement and artifices, to reduce them to a series of additions. — Ada Lovelace

Science proceeds by inference, rather than by the deduction of mathematical proof. A series of observations is accumulated, forcing the deeper question: What must be true if we are to explain what is observed? What "big picture" of reality offers the best fit to what is actually observed in our experience? American scientist and philosopher Charles S. Peirce used the term "abduction" to refer to the way in which scientists generate theories that might offer the best explanation of things. The method is now more often referred to as "inference to the best explanation." It is now widely agreed to be the philosophy of investigation of the world characteristic of the natural sciences. — Alister E. McGrath

Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover. — Bertrand Russell

All such uncertainties about undecidability and inconsistency apply only to mathematical structures with infinitely many elements. Are infinities, undecidability and potential inconsistency really inherent in the ultimate physical reality, or are they merely mirages, artifacts of our playing with fire and using powerful mathematical tools that are more convenient to work with than those that actually describe our Universe? More specifically, how well defined do mathematical structures need to be to be real, i.e., to be members of the Level IV multiverse? — Max Tegmark

Mathematics is an escape from reality. — Stanislaw Ulam

Not only in geometry, but to a still more astonishing degree in physics, has it become more and more evident that as soon as we have succeeded in unraveling fully the natural laws which govern reality, we find them to be expressible by mathematical relations of surprising simplicity and architectonic perfection. It seems to me to be one of the chief objects of mathematical instruction to develop the faculty of perceiving this simplicity and harmony. — Hermann Weyl

I do not know if God is a mathematician, but mathematics is the loom upon which God weaves the fabric of the universe....The fact that reality can be described or approximated by simple mathematical expressions suggests to me that nature has mathematics at its core. — Clifford A. Pickover

There is indeed a fundamental beauty in mathematical abstractions. They so attracted the Greek philosopher Plato that he declared that all those things that we can see and touch are, in fact, mere shadows of the true reality and that the real things of this universe can be found only through the use of pure reason. Plato's knowledge of mathematics was relatively naive, and many of the cherished purities of Greek mathematics have been shown to be flawed. — David Salsburg

The further we analyse the manner in which such an engine performs its processes and attains its results, the more we perceive how distinctly it places in a true and just light the mutual relations and connexion of the various steps of mathematical analysis; how clearly it separates those things which are in reality distinct and independent, and unites those which are mutually dependent. — Ada Lovelace

It turned out keeping reality bound by mathematical laws was a useful hack preventing the Devil from existing. — Scott Alexander

What distinguishes a mathematical model from, say, a poem, a song, a portrait or any other kind of "model," is that the mathematical model is an image or picture of reality painted with logical symbols instead of with words, sounds or watercolors. — John L. Casti

In a universe governed by God there are no chance events. Indeed, there is no such thing as chance. Chance does not exist. It is merely a word we use to describe mathematical possibilities. But chance itself has no power because it has no being. Chance is not an entity that can influence reality. Chance is not a thing. It is nothing. — R.C. Sproul

317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way. — G.H. Hardy

The play is independent of the pages on which it is printed, and 'pure geometries' are independent of lecture rooms, or of any other detail of the physical world. — G.H. Hardy

Sense of beauty, perception, and the mathematical universe are all part of the same texture. — Neeti Sinha

That man is a reality, mankind an abstraction; that men cannot be treated as units in operations of political arithmetic because they behave like the symbols for zero and the infinite, which dislocate all mathematical operations; that the end justifies the means only within very narrow limits; that ethics is not a function of social utility, and charity not a petty bourgeois sentiment but the gravitational force which keeps civilization in its orbit. — Arthur Koestler

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

True technique will know how to maintain the illusion of liberty, choice, and individuality; but these will have been carefully calculated so that they will be integrated into the mathematical reality merely as appearances! — Jacques Ellul

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

Mathematical parallels. It's plausible to hypothesize that these patterns will be reflected in events and people in each dimension. That people who have met in one quantum reality will be likely to meet in another. Certain things that happen will happen over and over, in different ways, but more often than you could explain by chance alone. — Claudia Gray

What appear to be the most valuable aspects of the theoretical physics we have are the mathematical descriptions which enable us to predict events. These equations are, we would argue, the only realities we can be certain of in physics; any other ways we have of thinking about the situation are visual aids or mnemonics which make it easier for beings with our sort of macroscopic experience to use and remember the equations. — Celia Green

There are patterns within the dimensions," Paul insisted, never looking up again. "Mathematical parallels. It's plausible to hypothesize that these patterns will be reflected in events and people in each dimension. That people who have met in one quantum reality will be likely to meet in another. Certain things that happen will happen over and over, in different ways, but more often than you could explain by chance alone."
"In other words," I said, "you're trying to prove the existence of fate."
I was joking, but Paul nodded slowly, like I'd said something intelligent. "Yes. That's it exactly. — Claudia Gray

If all consciousness is subject to essential laws in a manner similar to that in which spatial reality is subject to mathematical laws, then these essential laws will be of most fertile significance in investigating facts of the conscious life of human and brute animals. — Edmund Husserl

As we discussed in Chapter 7, we physicists still haven't found a mathematical structure that can describe all aspects of reality, including gravity, but so far, there's no indication that string theory or any of the other most actively pursued candidates for such a description are any less mathematical than quantum field theory. — Max Tegmark

There exists, if I am not mistaken, an entire world which is the totality of mathematical truths, to which we have access only with our mind, just as a world of physical reality exists, the one like the other independent of ourselves, both of divine creation. — Charles Hermite

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

He means that even though there is a mathematical possibility that dinosaurs and humans coexist, that possible reality would collapse because the likelihood is so astronomically small. — Liana Brooks