Number Theory Quotes

Topology and number theory are my faves. ~ Janna Levin

At a purely formal level, one could call probability theory the study of measure spaces with total measure one, but that would be like calling number theory the study of strings of digits which terminate. ~ Terence Tao

Godel showed how a statement about any mathematical formal system (such as the assertion that Principia Mathematica is contradiction-free) can be translated into a mathematical statement inside number theory (the study of whole numbers). In other words, any metamathematical statement can be imported into mathematics, and in its new guise the statement simply asserts (as do all statements of number theory) that certain whole numbers have certain properties or relationships to each other. But on another level, it also has a vastly different meaning that, on its surface, seems as far removed from a statement of number theory as would be a sentence in a Dostoevsky novel. ~ Douglas R. Hofstadter

Cardinal Arithmetics is much older than Number Theory. People used to exchange things way before there were numbers. Expressing numbers like 762 is already a sign of a very advanced civilization. ~ Saharon Shelah

My work on prime gaps lead to lots of media coverage, some good, some bad, some ugly, and some merely ridiculous. For example, a reporter of our university newspaper, who admitted that he is still learning English, wrote that "Prof. Goldston solved one of the most controversial problems in the prime number theory last month with support from his Turkish partner." ~ Daniel Goldston

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. ~ James Sanborn

[On Sophie Germain] When a person of the sex which, according to our customs and prejudices, must encounter infinitely more difficulties than men ... succeeds nevertheless in surmounting these obstacles and penetrating the most obscure parts of [number theory], then without doubt she must have the noblest courage, quite extraordinary talents and superior genius. ~ Carl Friedrich Gauss

Recreational number theory [ ... ] is that part of number theory that is too difficult to study. ~ Hendrik Lenstra

It is shown that the golden ratio plays a prominent role in the dimensions of all objects which exhibit five-fold symmetry. It is also showed that among the irrational numbers, the golden ratio is the most irrational and, as a result, has unique applications in number theory, search algorithms, the minimization of functions, network theory, the atomic structure of certain materials and the growth of biological organisms. ~ Richard A. Dunlap

Number theorists say that number theory is too complicated, so let's pretend that there is only one prime number, and then let's combine all these results. Surprisingly, sometimes it works. ~ Saharon Shelah

Two centuries ago Carl Friedrich Gauss, one of the greatest mathematicians and a founder of number theory, described his brainchild as "the queen of mathematics." Queens are regal, but they are also largely decorative, and this nuance was not lost on Gauss. ~ Ian Stewart

Music is part of Number Theory. Nowadays when a number-theorist applies for a grant, he says that it is good for security, but in those days, way before America, he would say that it's good for music. I will not comment whether we have progressed ... ~ Hendrik Lenstra

No part of mathematics is ever, in the long run, "useless." Most of number theory has very few "practical" applications. That does not reduce its importance, and if anything it enhances its fascination. No one can predict when what seems to be a most obscure theorem may suddenly be called upon to play some vital and hitherto unsuspected role. ~ C. Stanley Ogilvy

The only goal of science is the honour of the human spirit, and a question in number theory is worth a question concerning the system of the world. ~ Serge Lang

It is a matter for considerable regret that Fermat, who cultivated the theory of numbers with so much success, did not leave us with the proofs of the theorems he discovered. In truth, Messrs Euler and Lagrange, who have not disdained this kind of research, have proved most of these theorems, and have even substituted extensive theories for the isolated propositions of Fermat. But there are several proofs which have resisted their efforts. ~ Adrien-Marie Legendre

The fool's number is zero, but that's because he represents the infinite possibility of all things. He may become anything. See, he carries all of his possessions in a bundle on his back. He is ready for anything, to go anywhere, to become whatever he needs to be. Don't count out the fool, Pocket, simply because his number is zero. ~ Christopher Moore

Short-term travel has quadrupled: in 1980, the number of international tourist arrivals accounted for just 3.5 percent of the world's population, compared to almost 14 percent in 2010.16 Every year, an estimated 320 million people fly to attend professional meetings, conventions, and international gatherings - and their numbers are steadily growing.17 ~ Moises Naim

Without the physical world, Ideas will not exist. ~ Joey Lawsin

You will have your own examples of a work environment that seems to be firing on all cylinders. It will be a place where performance levels are consistently high, where turnover levels are low, and where a growing number of loyal customers join the fold every day. ~ Marcus Buckingham

First of all, there is absolutely an order that we have put together to create the maximum number of surprises, but that's just part of our storytelling. ~ Mitchell Hurwitz

We in the United States believe in the protection of minorities; we recognize the contributions that they can make and the leadership that they can provide; and we do not believe that any people - whether majority or minority, or individual human beings - are 'expendable' in the cause of theory or of policy. ~ Robert Kennedy

There are a lot of guys kind of on the bubble that can either be that sort who turn into journeyman kind of guys that will find a new spot or guys that can make a claim to be in one place for a long time. You can name a lot of names this year, an unusual number. And I think that most of them will be OK. ~ Steve Young

A philosopher's main task is to compulsively filibuster ~ Mohadesa Najumi

We know that there is no absolute knowledge, that there are only theories; but we forget this. The better educated we are, the harder we believe in axioms. ~ Lincoln Steffens

The cyclic universe theory predicts no gravitational waves from the early universe. ~ Stephen Hawking

Spencer: "Based on the number of drinks?"
Nick: "Based on the number of licks. ~ Aleksandr Voinov

I'm a fighter and I just want to fight better guys all the time, tougher guys so I just want to beat better guys and my goal is to be number one one day so if I get a chance to fight a better guy I'll do it, anytime, anywhere. ~ Alexander Gustafsson

To be "in charge" is certainly not only to carry out the proper measures yourself but to see that every one else does so too; to see that no one either willfully or ignorantly thwarts or prevents such measures. It is neither to do everything yourself nor to appoint a number of people to each duty, but to ensure that each does that duty to which he is appointed. ~ Florence Nightingale

The objective of nuclear-weapons policy should not be solely to decrease the number of weapons in the world, but to make the world safer - which is not necessarily the same thing. ~ Herman Kahn

That night Koch... tacked Chalmers down at a cocktail party for the conferencees and chastised him for his speech. It is precisely because philisophical approaches to consciousness have all failed that scientists must focue on the brain, Koch declared in his rapid-fire German-accented voice, his rubberneckers gathered. Chalmers's information-based theory of consciousness, Koch continued, liek all philosophical ideas, was untestable and therefore useless. "Why don't you just say that when you have a brain the Holy Ghost comes down and makes you conscious!" Koch exlaimed. Such a theory was unnecissarily complicated, Chalmers responded drily, and it would not accord with his own subjective experience. "But how do I know that your subjective experience is the same as mine?" Koch sputtered. "How do I even know you're conscious? ~ John Horgan

Father died last year. I don't subscribe to the theory by which we only become truly adult when our parents die; we never become truly adult. ~ Michel Houellebecq

What the world needs now is liberated men who have the qualities Silverstein cites, men who are 'empathetic and strong, autonomous and connected, responsible to self, to family and friends, to society, and capable of understanding how those responsibilities are, ultimately, inseparable.' Men need feminist thinking. It it the theory that supports their spiritual evolution and their shift away from the patriarchal model. Patriarchy is destroying the well-being of men, taking their lives daily. ~ Bell Hooks

Despite the digital age, there is a very large number of venues and spaces that are looking for plays, and many of them are looking for new plays. ~ Tom Stoppard

In a touch Buckland would have appreciated, this multipronged dispersal from Africa is sometimes called the Weak Garden of Eden theory. But this tale is actually better than the biblical version; we didn't lose Eden but learned to make other Edens across the world. ~ Sam Kean

The invisible government [bosses] is malign. But the evil doesn't come from the fact that it plays horse with the Newtonian theory of the constitution. What is dangerous about it is that we do not see it, cannot use it, and are compelled to submit to it. ~ Walter Lippmann

WILLIAMS: The phrase, of course, is a variation of a line from the song "MacArthur Park." Any idea why the terrorists picked that particular song, Elizabeth?
BURGER: Brian, one theory is that it was chosen specifically to demoralize the United States, because it gets stuck in your head and everybody hates it. ~ Dave Barry

Because men
are killing the forests
the fairy tales are running away.
The spindle doesn't know
whom to prick,
the little girl's hands
that her father has chopped off,
haven't a single tree to catch hold of,
the third wish remains unspoken.
King Thrushbeard no longer owns one thing.
Children can no longer get lost.
The number seven means no more than exactly seven.
Because men have killed the forests,
the fairy tales are trotting off to the cities
and end badly. ~ Gunter Grass

From wherever the emissions come, they have the same effect: They trap much more heat from the sun, melt the ice, raise the sea level, cause stronger storms, floods, drought, bigger fires, generate millions of climate refugees, destabilize political systems, threaten the growing of food crops and cause a number of other catastrophic consequences which, taken together, threaten the basis for the future of human civilization on the Earth. ~ Al Gore

Teenage years are hard. And, having taught high school for a number of years, I think they're particularly hard on teenage girls. The most self-conscious human beings on the planet are teenage girls. ~ Rob Thomas

It goes without saying that a civilization which leaves so large a number of its participants unsatisfied and drives them into revolt neither has nor deserves the prospect of a lasting existence. ~ Sigmund Freud

Time decides the limits of existence. Nothing can be infinite if it exists in time. ~ Raheel Farooq

Songwriters can sort of get away with murder. You can throw out crazy theories and not have to back it up with data or graphs or research. ~ Andrew Bird

My theory is that one needs to be loved completely, unconditionally, and unfettered by parental disapproval, if one is to get happily through life which, after all, presents its own hurdles. ~ Arabella Weir

At first view it might seem not to square with the republican theory, to suppose either that a majority have not the right, or that a minority will have the force to subvert a government ... But theoretic reasoning in this, as in most other cases, must be qualified by the lessons of practice. ~ James Madison

I heard that in relativity theory, space and time are the same thing. Einstein discovered this when he kept showing up three miles late for his meetings. ~ Steven Wright

20% of management theories are responsible for 80% of results. That's assuming the Pareto Principle makes the cut. ~ Ryan Lilly

As a philosophy, utilitarianism is the argument you can objectively determine what is the greatest good for the greatest number of people and we need the state to achieve that end. ~ Stefan Molyneux

War is noble and heroic if a nation is defending its sovereignty from the invaders. War is disgraceful and unheroic, a despicable crime against humanity, if a dominant nation is invading another country and killing its innocent men, women, and children. The war, in the 21st century, is ostensibly the methodic game theory in offensive action that has no ethical and moral ground, whatsoever, but to intentionally kill and divide people, and, consequently, paralyze the political and economic stability of another nation. ( - Danny Castillones Sillada, The Existentialist Homo Technologicus) ~ Danny Castillones Sillada

Promise me you'll never go away.
Promise me you'll always stay. ~ Tegan Quin

The labourer seeks to maintain the total of his wages for a given time by performing more labour, either by working a greater number of hours, or by accomplishing more in the same number of hours. Thus, urged on by want, he himself multiplies the disastrous effects of division of labour. The result is: the more he works, the less wages he receives. And for this simple reason: the more he works, the more he competes against his fellow workmen, the more he compels them to compete against him, and to offer themselves on the same wretched conditions as he does so that, in the last analysis, he competes against himself as a member of the working class. ~ Karl Marx

It turns out from a number of more recent studies that reported happiness is strongly positively linked with the change or growth in GDP per capita from year to year. ~ Diane Coyle

It's a useful rule in Anglo-American communications that the English should double, and the Americans halve, the number of words they would normally employ. ~ Phyllis Bentley

Minimalism now is a reaction to what came before. It's absolutely of its time. Music moved into the set theory thing, and moved out of it. ~ Harrison Birtwistle

During my jury selection process, we went through over 360 jurors. It took six months, all New York residents. Of the 360 jurors, over half of them had been mugged one time. Quite a number of them, maybe 30 40, 50, had been mugged twice. ~ Bernhard Goetz