Mathematical Quotes

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.

A pure mathematical series would be one in which each term is derived from the preceding term by a rule.

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

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.

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 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.

As long as there is a mathematical chance, we have to keep on going.

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 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.

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.

I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.

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.

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.

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

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 received my undergraduate degree in engineering in 1939 and a Master of Science degree in mathematical physics in 1941 at Steven Institute of Technology.

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.

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.

To emphasize only the beautiful seems to me to be like a mathematical system that only concerns itself with positive numbers.

Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.

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.

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.

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

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.

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.

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.

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?

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!

There’s never been a mathematical equation that says a good experience making a movie equates to a good movie, or a bad experience on a set is going to lead to a bad movie.

Eccentric doesn’t bother me. ‘Eccentric’ being a poetic interpretation of a mathematical term meaning something that doesn’t follow the lines – that’s okay.

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

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

I always thought it was strange when these artists like Kurt Cobain or whoever would get really famous and say, ‘I don’t understand why this is happening to me.’ There is a mathematical formula to why you got famous. It isn’t some magical thing that just started happening.

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.

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.

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.

I was in charge of the Bureau of Labor Statistics. So I had some of the most brilliant mathematical statistical minds in the country, who would put together the modern technology, if you like, of understanding the economy and tracking it and trying to influence it.

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.

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.

The immediacy of mystic experience simply means that we know God just as we know other objects. God is not a mathematical entity or a system of concepts mutually related to one another and having no reference to experience.

Ignorance and superstition ever bear a close and mathematical relation to each other.

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.

I spend quite a lot of time thinking about how curated our information is. What we watch, what we read, what we buy, often who we talk to, is all shaped and influenced by some kind of a mathematical algorithm.

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.

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.

When I speak of the beauty of a game of chess, then naturally this is subjective. Beauty can be found in a very technical, mathematical game for example. That is the beauty of clarity.

You can get a certain amount of pleasure as a mathematical spectator, reading and watching some of the most beautiful arguments that have been created in the history of humanity. But that’s too passive.

Video games as a storytelling medium are, from a mathematical standpoint, a branching narrative. You start at one place, you can go in multiple different directions, and there’s a multitude of different endings.

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.

Things like the financial markets – a proper grounding in mathematics could help the common man. I believe that if people are more familiar with mathematical concepts… it can help deal with modern life, which is increasingly complex.

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.

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.

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.

Formal logic is mathematics, and there are philosophers like Wittgenstein that are very mathematical, but what they’re really doing is mathematics – it’s not talking about things that have affected computer science; it’s mathematical logic.

Mathematical discoveries, like springtime violets in the woods, have their season which no man can hasten or retard.

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

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.

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.

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.

From Roger Bacon, the 13th century Franciscan who pioneered the scientific method, to George Lemaitre, the 20th century Belgian priest who first developed a mathematical foundation for the ‘Big Bang,’ people of faith have played a key role in advancing scientific understanding.

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.

I never, ever drink while writing. Never have from the start, and I’m happy that I never have to. A lot of my stuff is plot-driven and mathematical, and I think you need a clean and sober mind to pin down the logistics of that.

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.

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

Ever since the Enlightenment, people thought that we were living in a rational universe. They thought that God was a mathematician and that the function of the scientist was to figure out the mathematical rules whereby the universe was created.

There’s a human element here you start to lose when you start rattling off the best mathematical equation to get the out.

In terms of merit, sports has mathematical statistics. That’s how you know who the best player is.

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

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.

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.

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.

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.

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.

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 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.

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.

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

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.

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.

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

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.’

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.

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.

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.

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

It’s my belief that you can take everyone down a logical path if you take them slowly enough, and the trouble is that mathematical brains can get scrambled a little bit on the way. You get a bad teacher, it messes you up for the rest of the journey.

I did long-term re-insurance claims. Asbestos, health hazards, pollution. It was very boring. But I’ve got quite a mathematical brain and it paid well.

The big mathematical challenge for flying robots is making them move in six dimensions: x, y, z, pitch, yaw and roll. We create 3-D obstacle courses in the lab – windows, doors, hula-hoops taped to posts – and ask the robots to fly through. It looks like a Harry Potter Quidditch match.

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.

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.

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.

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.

Some people are great at the pure mathematical things – like Bill Gates, he’s great at math things. He loves to do puzzles. Me, I like to look at an overall landscape and try to figure out, how do you solve a problem?

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.

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.

Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.

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

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.

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

I know this world is ruled by infinite intelligence. Everything that surrounds us- everything that exists – proves that there are infinite laws behind it. There can be no denying this fact. It is mathematical in its precision.

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.

Statistics: the mathematical theory of ignorance.

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.

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.

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.