Top 140 Mathematical Quotes

The further a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science.

I’m interested in complexity, in the mathematical sense, as well as the idiomatic sense. The idea of emergence – that it’s possible for complex patterns to arise out of many simple interactions – is fascinating.

One of the most important tools in critical thinking about numbers is to grant yourself permission to generate wrong answers to mathematical problems you encounter. Deliberately wrong answers!

Gamers have this tendency to turn games into mathematical equations, breaking them into lists of components like ‘presentation’ and ‘mechanics’ and judging each one on its own merits.

Much of what I make is geometric, and has a kind of almost mathematical logic to the form.

Music assists him in the use of harmonic and mathematical proportion.

We will never fully explain the world by appealing to something outside it that must simply be accepted on faith, be it an unexplained God or an unexplained set of mathematical laws.

The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing?

My intention here is to make it clear that not a single cell of my composition, here in regard to The Raven, is found by chance or intuition, that the composition moved towards perfection with the precision and inevitability of a mathematical equation.

I was very much on the mathematical side, where you probably do your best work before you’re forty-five. Having passed that significant date, I thought I would do something else.

I am a Leaper: a person who – thanks to some mathematical errors tied to the cosmic interactions of Earth and Sun and bad math on the part of some old timers long ago – is lost in time, born on a day that simply doesn’t exist three out of four years.

I regard it in fact as the great advantage of the mathematical technique that it allows us to describe, by means of algebraic equations, the general character of a pattern even where we are ignorant of the numerical values which will determine its particular manifestation.

It seems that jazz is more cerebral and more mathematical in a sense.

The orthodox believers in God are divided into two camps, one of which maintains that the existence of God is as demonstrable as any mathematical proposition, while the other asserts that his existence is not demonstrable to the intellect.

Art is based on very clear, mathematical principles like proportion and harmony. At the same time, physicists need to be inventive, to have ideas, to have some fantasy.

The circumstances of human society are too complicated to be submitted to the rigor of mathematical calculation.

I was a good student with mathematical ability and interests. As such, I took the usual college preparatory program in high school for one looking to become an engineer: all the available courses in mathematics and science.

Music rhythms are mathematical patterns. When you hear a song and your body starts moving with it, your body is doing math. The kids in their parents’ garage practicing to be a band may not realize it, but they’re also practicing math.

Statistics: the mathematical theory of ignorance.

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.

The special sphere of finance within economics is the study of allocation and deployment of economic resources, both spatially and across time, in an uncertain environment. To capture the influence and interaction of time and uncertainty effectively requires sophisticated mathematical and computational tools.

The mathematical framework of quantum theory has passed countless successful tests and is now universally accepted as a consistent and accurate description of all atomic phenomena.

I hope no man takes what I said about the living and dieing of men for mathematical demonstration.

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not.

I took a course on ‘Magic, Alchemy, and Astrology’ at Mount Holyoke, and it was a whole new awakening for me, a way of thinking about the world primarily in terms of concepts and words rather than mathematical formulas.

We’ve gone from the image of India as land of fakirs lying on beds of nails, and snake charmers with the Indian rope trick, to the image of India as a land of mathematical geniuses, computer wizards, software gurus.

There’s nothing really connecting the behavior of the Nile, metallurgy, and the behavior of prices except that I had the mathematical tools to explain them.

I don’t believe you can reduce the world to a mathematical formula. I start with the world, assume it’s complicated, and ask where can I get help from a whole range of disciplines.

Indeed, it is a proven mathematical theorem that a doughnut is topologically distinct from a sphere.

All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers.

How thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which, at the same time, assist in understanding earlier theories and in casting aside some more complicated developments.

Evolution has ensured that our brains just aren’t equipped to visualise 11 dimensions directly. However, from a purely mathematical point of view it’s just as easy to think in 11 dimensions, as it is to think in three or four.

All science requires mathematics. The knowledge of mathematical things is almost innate in us. This is the easiest of sciences, a fact which is obvious in that no one’s brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.

To a person of analytical ability, perceptive enough to realise that mathematical equipment was a powerful sword in economics, the world of economics was his or her oyster in 1935. The terrain was strewn with beautiful theorems begging to be picked up and arranged in unified order.

We have failed to protect science against speculative extensions of nature, continuing to assign physical and mathematical properties to hypothetical entities beyond what is observable in nature.

To my mathematical brain, the numbers alone make thinking about aliens perfectly rational. The real challenge is to work out what aliens might actually be like.

And for mathematical science, he that doubts their certainty hath need of a dose of hellebore.

Each part of our genome is unique. We would not be alive if there was not a single mathematical solution for our chromosomes. We would just be scrambled goo.

The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic.

I did what I could to inflate the rumor I was on my way to stardom. What I was on my way to, by any mathematical standards known to man, was oblivion, by way of obscurity.

Design and technology should be the subject where mathematical brainboxes and science whizzkids turn their bright ideas into useful products.

Internet players have successfully addressed the all-in play from a mathematical perspective. For example, it’s fairly common to see a net player move all-in over the top from the big blind with a hand like K-Q when they have less than twenty big blinds remaining. And for good reason – it works!

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

There has to be a mathematical explanation for how bad that tie is.

Learning certain things purely through memory is related to the developmental forces that are present between the sixth or seventh year and the fourteenth year of life. This quality of human nature is what mathematical instruction should be based on.

I write in a mathematical manner. For some of my songs, I rhyme every syllable. It’s a science.

No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful.

The blockchain does one thing: It replaces third-party trust with mathematical proof that something happened.

You kind of alluded to it in your introduction. I mean, for the last 300 or so years, the exact sciences have been dominated by what is really a good idea, which is the idea that one can describe the natural world using mathematical equations.

A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.

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

In a few decades of reconstruction, even the mathematical natural sciences, the ancient archetypes of theoretical perfection, have changed habit completely!

The thing that got me started on the science that I’ve been building now for about 20 years or so was the question of okay, if mathematical equations can’t make progress in understanding complex phenomena in the natural world, how might we make progress?

I had become interested in economics, an interest that was transformed into a lifetime dedication when I met with the mathematical theory of general economic equilibrium.

On the mathematical side, you could in principle build a society in which people were fulfilling their needs and flourishing as human beings in a higher way than in a consumer society, provided you had the right investments in the opportunity to flourish in less materialistic ways.

I approach an action sequence almost like a mathematical problem. Sometimes you get these action sequences that you read and go, ‘Oh my God, this is huge, how do I do it?’ and I go, ‘Just a step at a time. Sit down and plot each piece of it out.’

A single neuron in the brain is an incredibly complex machine that even today we don’t understand. A single ‘neuron’ in a neural network is an incredibly simple mathematical function that captures a minuscule fraction of the complexity of a biological neuron.

All my family has very good mathematical abilities – like, so dorky. I was the dork then in school – on any maths exams I’d get 100%. I just knew how to do maths and most people would hate it, but for some reason it just came.

I’m obviously attuned to pick up mathematics whenever I can see it. But in Mozart there is a lot of conscious use of mathematical symbolism and numbers in order to try and give messages.

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.

By a combination of formal training and self study, the latter continuing systematically well into the 1940s, I was able to gain a broad base of knowledge in economics and political science, together with reasonable skills in advanced mathematics, symbolic logic, and mathematical statistics.

A mathematical proof is beautiful, but when you’re finished, it’s really only about one thing. A story can be about many things.

Some people are better at maths than others: no one thinks you can be ‘taught’ to be a mathematical genius. And no one thinks of teaching, in that context, as a kind of forcing of the will. But there seems to be an idea of writing as an intuitive pastime which is being dishonestly subjected to counterintuitive methods.

There’s a very mathematical, mechanical side to architecture, and I probably lean more toward that aspect of it, though I’m terrible at numbers. But that side appeals to me more than the decorating aspect.

The time was not yet ripe for the growth of mathematical science among us, and any development that might have taken place in that direction was rudely stopped by the civil war.

Well, gauge theory is very fundamental to our understanding of physical forces these days. But they are also dependent on a mathematical idea, which has been around for longer than gauge theory has.

I have my hopes, & very distinct ones, too, of one day getting cerebral phenomena such that I can put them into mathematical equations: in short, a law or laws for the mutual actions of the molecules of the brain (equivalent to the law of gravitation for the planetary & sideral world).

There’s barely any aspect of our modern lives that hasn’t had a mathematical contribution at some point and yet, if you asked the average person, they might think that maths is just difficult, irrelevant and uninteresting.

Mathematical science shows what is. It is the language of unseen relations between things. But to use and apply that language, we must be able fully to appreciate, to feel, to seize the unseen, the unconscious.

Game theory is a branch of, originally, applied mathematics, used mostly in economics and political science, a little bit in biology, that gives us a mathematical taxonomy of social life, and it predicts what people are likely to do and believe others will do in cases where everyone’s actions affect everyone else.

Whatever may be the merits of a religious system, its effects upon the mass of mankind must depend in an important degree upon its teachers. All instruction and all truth, except simple mathematical truth, is modified by the medium through which it is conveyed.

Among the thousand-and-one faces whereby form chooses to reveal itself to us, the one that fascinates me more than any other, and continues to fascinate me, is the structure hidden in mathematical things.

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

As far as I know, only a small minority of mathematicians, even of those with Platonist views, accept the idea that there may be mathematical facts which are true but unknowable.

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.

I make fractals. They’re like mathematical pictures. My stepdad is actually a rocket scientist, so in his free time, he gave me a fractal program for fun. He showed me how to use it when I was about nine or 10, and I made thousands of fractals.

The building blocks of mathematical thinking are requisite for more advanced conceptualization. If a student is not ready to move on, then the teacher must take time to assist that learner.

I’m left-brained, so I’m all about a mathematical approach to language. I’ve always been interested in that.

Most people don’t have time to master the very mathematical details of theoretical physics.

In 1688, Edward Lloyd opened a coffeehouse on London’s seafront popular among underwriters, men in powdered wigs with mathematical minds and steely constitutions who offered to compensate owners if their boats were lost at sea.

In this age of specialization, I sometimes think of myself as the last ‘generalist’ in economics, with interests that range from mathematical economics down to current financial journalism. My real interests are research and teaching.

Lower-income immigrant families might receive more in benefits than they pay in taxes. But that mathematical equilibrium is temporary, and an artifact of the way the tax-and-transfer system is structured to help lower-income families and to support families with kids.

Without troublesome work, no one can have any concrete, full idea of what pure mathematical research is like or of the profusion of insights that can be obtained from it.

When you have different kinds of scientific and mathematical minds approaching problems, you will get more solutions. This leads to more innovation and more creative design.

We have elected to put our money and faith in a mathematical framework that is free of politics and human error.

In the 1940s, economics started getting highly mathematical. It was basically because economists weren’t smart enough to write down models of real behavior that they started writing down models of highly rational behavior – and they kind of forgot about humans.

The traditional mathematician recognizes and appreciates mathematical elegance when he sees it. I propose to go one step further, and to consider elegance an essential ingredient of mathematics: if it is clumsy, it is not mathematics.

The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law.

I’m not sure whether it counts as a talent, but I love playing ‘Magic: The Gathering.’ It’s mathematical and intellectually challenging, and makes me feel nostalgic for when I played as a kid.

The ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously.

I think the rise of quantitative econometrics and a highly mathematical approach to risk management was the obverse of a decline in interest in financial history.

Here at Wisconsin we didn’t get an undergraduate course in mathematical logic until the ’60s.

The most important single thing about string theory is that it’s a highly mathematical theory, and the mathematics holds together in a very tight and consistent way. It contains in its basic structure both quantum mechanics and the theory of gravity. That’s big news.

It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but, with a little mathematical fiddling, you can show the relationship.

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.

I’m always trying to calculate the mathematical probability of certain outcomes.

The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.

If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper.

Wind depends on temperature. Temperature depends on pressure. And pressure depends on wind. It’s an intricate mathematical tapestry that is far too intertwined to unpick by hand.

In the lab, we could not see or physically describe the mathematical objects that we called quarks, which we suspected were the key to unlocking the dynamics of the strong force that binds together the clump of protons and neutrons at the center of the atom.

Alan Turing gave us a mathematical model of digital computing that has completely withstood the test of time. He gave us a very, very clear description that was truly prophetic.

One of the pleasing things about science is that we do all climb towards the heavens on the shoulders of our predecessors. Economics, like physics, has its heroes, and the letter ‘H’ that I used in my mathematical equations was not there to honor Sir William Hamilton, but rather Harold Hotelling.

Dr. Karel Culik is an outstanding applied mathematician, a specialist in algebra, logic, computer sciences and mathematical linguistics. In 1965, he visited the linguistics research program at MIT, and we have worked together on several projects since.

The computer can’t tell you the emotional story. It can give you the exact mathematical design, but what’s missing is the eyebrows.

I would finally renounce my delusional hypotheses and revert to thinking of myself as a human of more conventional circumstances and return to mathematical research.

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

Thus, the more succinctly a train of thought was expounded, and the more comprehensive the unity of its basic idea, the closer it would approximate to the prerequisites of the mathematical way of thinking.

Never had any mathematical conversations with anybody, because there was nobody else in my field.

A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.

I tried reading Hilbert. Only his papers published in mathematical periodicals were available at the time. Anybody who has tried those knows they are very hard reading.

I do not love to be printed on every occasion, much less to be dunned and teased by foreigners about mathematical things or to be thought by our own people to be trifling away my time about them when I should be about the king’s business.

Bitcoin may herald the dawning of a new age in currency. It holds superior traits as a form of ‘good money.’ As a tangible form of asset (its core tangibility being its mathematical basis), it could become an incredibly important building block for the 21st century’s global economy.

One of the pleasures of looking at the world through mathematical eyes is that you can see certain patterns that would otherwise be hidden.

I believe sanity and realism can be restored to the teaching of Mathematical Statistics most easily and directly by entrusting such teaching largely to men and women who have had personal experience of research in the Natural Sciences.

As for everything else, so for a mathematical theory: beauty can be perceived but not explained.

Einstein was very attracted to Mozart. There’s a mathematical, classical structure to the music, and I think he identified with that very strongly. I think there also is a connection between being a genius and a polymath.

The universal medicine for the Soul is the Supreme Reason and Absolute Justice; for the mind, mathematical and practical Truth; for the body, the Quintessence, a combination of light and gold.

Mathematics has beauty and romance. It’s not a boring place to be, the mathematical world. It’s an extraordinary place; it’s worth spending time there.

We have overcome the notion that mathematical truths have an existence independent and apart from our own minds. It is even strange to us that such a notion could ever have existed.

Cyberspace. A consensual hallucination experienced daily by billions of legitimate operators, in every nation, by children being taught mathematical concepts.

In teaching, I wanted to offer a general pharmacology course based on chemical principles, biochemical classification and mathematical modelling. In the event I achieved neither of my ambitions.

Poker isn’t the roulette wheel of pure chance, nor is it the chess of mathematical elegance and perfect information. Apart from the underlying mathematics, poker depends on the nuanced reading of human intention, interactions, and deceptions.

Some people are born with a brain that has this weird, magical mathematical thing that makes them an amazing jazz musician.

I perceive myself as rather uninhibited, with a certain mathematical facility and more interest in the broad aspect of a problem than the delicate nuances. I am more interested in discovering what is over the next rise than in assiduously cultivating the beautiful garden close at hand.

It is a curious historical fact that modern quantum mechanics began with two quite different mathematical formulations: the differential equation of Schroedinger and the matrix algebra of Heisenberg. The two apparently dissimilar approaches were proved to be mathematically equivalent.

Scientology is not written with disrespect toward God. It doesn’t worship something that is evil. It is scientific, mathematical, and spiritual. The black community has to check it out and see what’s there. I’m not saying it’s for everyone, but you have to take a look.

Out of fifty mathematical papers presented in brief at such a meeting, it is a rare mathematician indeed who really understands what more than half a dozen are about.

Logical positivists have never taken psychology into account in their epistemology, but they affirm that logical beings and mathematical beings are nothing but linguistic structures.

Ultimately, my Ph.D. is in mathematical physics, focusing on quantum field theory and curved space-time, and I worked with Stephen Hawking.

I think part of the appeal of mathematical logic is that the formulas look mysterious – You write backward Es!

I chose to deal with the science of cryptography. Cryptography began in mathematics. Codes were developed, even from Caesar’s time, based on number theory and mathematical principles. I decided to use those principles and designed a work that is encoded.

My brother is a genius. When we went to Italy, he was on the local television channel as a prodigy, who could solve very sophisticated mathematical equations. He was only seven or eight years old but he could solve mathematical problems for fourteen year olds.

Through the very culture of representation through form, we have come to see that the abstract – like the mathematical – is actually expressed in and through all things, although not determinately.

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.

Every child needs to become literate in one or more languages, and every child should become comfortable in the major scholarly disciplines – historical, scientific, mathematical, and artistic-humanistic thinking. Beyond that, I am not in favour of a uniform system. I think there should be some choices.

The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved.

There are times when success doesn’t make sense on a purely mathematical basis. I’ve played absolutely perfectly before, put in a masterful performance, and then my perfect play evaporated because one guy lost his mind and got lucky. Of course, I’ve also won that way.

We do learn a thing or two from art. It may not be the one-to-one instruction of a moral lesson or the rote learning of a grammatical rule or mathematical concept. But the habits of mind art cultivates are important.

One of the things I’ve always liked about my husband is he’s very good at lots of stuff. He was an English teacher when I met him. He wrote poetry and played the guitar. As time went on, he decided to go into economics, so he’s very analytical and mathematical in addition to his artsy side.

I’m very attracted to schematic structures. My brother is a chemical engineer, he has a very mathematical mind, and he’s also a visual artist. I think we have a lot in common. And my first film had a very tight structure, narratively.