M Quotes
Browse famous quotes beginning with M. This page is a child index of the full Popular Quotes A-Z directory.
“Mathematically speaking, the probable (that in 6,000,000,000 throws with a regular six-sided die the die will come up proximately 1 ,000,000,000 times) and the improbable (that in six throws with the same die the one will come approximately up six times) are not different in kind, but only in frequency, whereby the more frequent appears a priori more probable.
But the occasional occurrence of the improbable does not imply the intervention of a higher power, something in the nature of a miracle, as the layman is so ready to assume. The term "probability" includes improbability at the extreme limits of probability, and when the improbable does occur this is no cause for surprise, bewilderment or mystification.
Cf. Ernst Mally's Probability and Law, Hans Reichenbach The theory Probability, Whitehead and Russell's Principia Mathematica, von Mises' Probability, Statistics and Truth”
Source: Homo Faber
“Mathematically speaking, it seems impossible that there isn't life out our planet. If you flick on the news, it certainly seems like we have aliens among us.”
“Mathematically, debts grow exponentially at compound interest. Banks recycle the interest into new loans, so debts grow exponentially, faster than the economy can afford to pay.”
“Mathematicians - for what they do - are really poorly rewarded. And it's a very competitive field, almost as bad as being a concert pianist.”
“Mathematicians also make terrible salesmen. Physicists can discover the same thing as a mathematician and say 'We've discovered a great new law of nature. Give us a billion dollars.' And if it doesn't change the world, then they say, 'There's an even deeper thing. Give us another billion dollars.'”
“Mathematicians are a bit like the laconic Vermonter who, when asked if he's lived in the state his whole life, replies, "Not yet."”
Source: Irreligion: A Mathematician Explains Why the Arguments for God Just Don't Add Up
“Mathematicians are beginning to view order and chaos as two distinct manifestations of an underlying determinism. And neither state exists in isolation. The typical system can exist in a variety of states, some ordered, some chaotic. Instead of two opposed polarities, there is a continuous spectrum. As harmony and discord combine in musical beauty, so order and chaos combine in mathematical [and physical] beauty.”
“Mathematicians are inexorably drawn to nature, not just describing what is to be found there, but in creating echoes of natural laws.”
“Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different.”
“Mathematicians are like lovers. Grant a mathematician the least principle, and he will draw from it a consequence which you must also grant him, and from this consequence another.”
“Mathematicians are like managers - they want improvement without change.”
“Mathematicians are proud of the fact that, generally, they do their work with a piece of chalk and a blackboard. They value hand-done proofs above all else. A big question in mathematics today is whether or not computational proofs are legitimate. Some mathematicians won't accept computational proofs and insist that a real proof must be done by the human hand and mind, using equations.”
“Mathematicians aren't satisfied because they know there are no solutions up to four million or four billion, they really want to know that there are no solutions up to infinity.”
“Mathematicians boast of their exacting achievements, but in reality they are absorbed in mental acrobatics and contribute nothing to society.”
“Mathematicians call it “the arithmetic of congruences.” You can think of it as clock arithmetic. Temporarily replace the 12 on a clock face with 0. The 12 hours of the clock now read 0, 1, 2, 3, … up to 11. If the time is eight o’clock, and you add 9 hours, what do you get? Well, you get five o’clock. So in this arithmetic, 8 + 9 = 5; or, as mathematicians say, 8 + 9 ≡ 5 (mod 12), pronounced “eight plus nine is congruent to five, modulo twelve.”
Source: Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
“Mathematicians can and do fill in gaps, correct errors, and supply more detail and more careful scholarship when they are called on or motivated to do so. Our system is quite good at producing reliable theorems that can be solidly backed up. It's just that the reliability does not primarily come from mathematicians formally checking formal arguments; it comes from mathematicians thinking carefully and critically about mathematical ideas.”
“Mathematicians care no more for logic than logicians for mathematics.”
“Mathematicians come to the solution of a problem by the simple arrangement of the data, and reducing the reasoning to such simple operations, to judgments so brief, that they never lose sight of the evidence that serves as their guide.”
“Mathematicians create by acts of insights and intuition. Logic then sanctions the conquests of intuition.”
Source: Mathematics in Western Culture
“Mathematicians deal with large numbers sometimes, but never in their income.”
Source: Prelude to Foundation
“Mathematicians do not write for the circulating library.”
Source: The Principles of Success in Literature
“Mathematicians enjoy thinking about the simplest possible things, and the simplest possible things are imaginary.”
“Mathematicians finally developed a financial model to accurately compare apples and oranges. Any two kinds of fruit can be compared, although guavas still cause minor rounding errors.”
Source: No Hope for Gomez!
“Mathematicians grow very old; it is a healthy profession. The reason you live long is that you have pleasant thoughts. Math and physics are very pleasant things to do.”
“Mathematicians have a certain type of mind, and climbers have a certain type of mind, because climbing poses these incredibly interesting problems for them.”
“Mathematicians have sought knowledge in figures, Philosophers in systems, Logicians in subtleties, and Metaphysicians in sounds. It is not in any nor in all of these. He that studies only men, will get the body of knowledge without the soul, and he that studies only books, the soul without the body.”
Source: Lacon: Or Many Things in Few Words Addressed to Those who Think
“Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.”
“Mathematicians may flatter themselves that they possess new ideas which mere human language is as yet unable to express.”
Source: The Scientific Papers of James Clerk Maxwell
“Mathematicians may flatter themselves that they possess new ideas which mere human language is as yet unable to express. Let them make the effort to express these ideas in appropriate words without the aid of symbols, and if they succeed they will not only lay us laymen under a lasting obligation, but, we venture to say, they will find themselves very much enlightened during the process, and will even be doubtful whether the ideas as expressed in symbols had ever quite found their way out of the equations into their minds.”
Source: The Scientific Papers of James Clerk Maxwell
“Mathematicians need proofs to keep them honest. All technical areas of human activity need reality checks. It is not enough to believe that something works, that it is a good way to proceed, or even that it is true. We need to know why it's true. Otherwise, we won't know anything at all.”
Source: Letters to a Young Mathematician
“Mathematicians seem to have no difficulty in creating new concepts faster than the old ones become well understood.”
“Mathematicians stand on each other's shoulders.”
“Mathematicians stand on each others' shoulders and computer scientists stand on each others' toes.”
“Mathematicians tend to prefer a worst-case analysis, a kind of paranoia that is especially understandable if you live in Israel!”
“Mathematicians themselves set up standards of generality and elegance in their exposition which are a bar to understand.”
“Mathematicians use intuition, conjecture and guesswork all the time except when they are in the classroom.”
“Mathematicians, like cows in the dark, all look alike to me.”
“Mathematics - the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human affairs.”
Source: The Usefulness of Mathematical Learning Explained and Demonstrated: Being Mathematical Lectures Read in the Publick Schools at the University of Cambridge
“Mathematics - this may surprise or shock some - is never deductive in creation.”
“Mathematics ... is indispensable as an intellectual technique. In many subjects, to think at all is to think like a mathematician.”
“Mathematics allows for no hypocrisy and no vagueness.”
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don't happen to have all the data. In mathematics we have all the data, brought together in the full light of demonstration, and yet we don't understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
“Mathematics and art are quite different. We could not publish so many papers that used, repeatedly, the same idea and still command the respect of our colleagues.”
“Mathematics and logic have been proved to be one; a fact from which it seems to follow that mathematics may successfully deal with non-quantitative problems in a much broader sense than was suspected to be possible.”
“Mathematics and poetry are the two ways to drink the beauty of truth.”
“Mathematics and thought are ontologically the same thing. Have you understood? You are a thinking entity inhabiting a world created from thought. “God” doesn’t make the world out of nothing. God makes the world out of thought, his own thought. God is himself thought, and you yourself are an eternal, necessary node of God. This reality is just “God”, in all of his different monadic nodes, thinking about things and calculating the best answer to everything.”
Source: Do the Math: Why Math Is Nothing Like How You Imagine
“Mathematics are one of the fundamentaries of educationalizing our youth.”
“Mathematics are the result of mysterious powers which no one understands, and which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty's sake and pulls it down to earth.”
Source: Selected papers
“Mathematics are well and good but Nature keeps dragging us around by the nose.”
“Mathematics as a science, commenced when first someone, probably a Greek, proved propositions about "any" things or about "some" things, without specifications of definite particular things.”
Source: An Introduction to Mathematics