Top 1200 Mathematical Analysis Quotes & Sayings - Page 17

Honestly, I find the analysis of dreams is one of the dullest things. I say this as a therapist kid. I find them deeply uninteresting, as a window to the soul.

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.

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.

Greatness, in the last analysis, is largely bravery - courage in escaping from old ideas and old standards and respectable ways of doing things.

Eternity is said not to be an extension of time but an absence of time, and sometimes it seemed to me that her abandonment touched that strange mathematical point of endlessness, a point with no width, occupying no space.

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.

Success on any major scale requires you to accept responsibility... in the final analysis, the one quality that all successful people have... is the ability to take on responsibility.

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.

Pep and his staff work very hard, not just on the training pitch but also with the analysis of opponents, and now, of course, we understand more how he wants to play.

the full analysis of the notions of saying something and understanding what one said inevitably involves a concept which, as I will show in detail, essentially corresponds to the Cartesian idea of thought.

The more important the subject and the closer it cuts to the bone of our hopes and needs, the more we are likely to err in establishing a framework for analysis.

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.

All art is in the last analysis an endeavor to condense as out of the flying vapor of the world an image of human perfection, and for its own and not for the art's sake.

I believe that the visit of the Queen to the United States is an admirable occasion to produce an historical, truthful, sincere, genuine analysis of how the British Monarchy evolved into its present situation.

The Internet has improved a lot in the last few years, but still, you wouldn't want to depend on Web sources for historical analysis. There's just something hard to beat about a book.

[The infinitely small] neither have nor can have theory; it is a dangerous instrument in the hands of beginners [ ... ] anticipating, for my part, the judgement of posterity, I would dare predict that this method will be accused one day, and rightly, of having retarded the progress of the mathematical sciences.

There are certain pressures and things that change your life to a degree that, in the cost benefit analysis that constantly goes on, sometimes makes you think, 'Maybe I should just leave.'

In the last analysis, of course, an oath will encourage fidelity in office only to the degree that officeholders continue to believe that they cannot escape ultimate accountability for a breach of faith.

In enabling mechanism to combine together general symbols in successions of unlimited variety and extent, a uniting link is established between the operations of matter and the abstract mental processes of the most abstract branch of mathematical science.

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!

It's really important when we're writing our opinions to be transparent about what our decision method in the case is and how we get from Point A to B to C in the analysis.

Like works of literature, mathematical ideas help expand our circle of empathy, liberating us from the tyranny of a single, parochial point of view. Numbers, properly considered, make us better people.

Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.

The physicist who states a law of nature with the aid of a mathematical formula is abstracting a real feature of a real material world, even if he has to speak of numbers, vectors, tensors, state-functions, or whatever to make the abstraction.

Page after page of professional economic journals are filled with mathematical formulas leading the reader from sets of more or less plausible but entirely arbitrary assumptions to precisely stated but irrelevant theoretical conclusions.

As the briefer, my job is to carry CIA`s best information and best analysis to the president of the United States and make sure he understands it.

The more one analyses people, the more all reasons for analysis disappear. Sooner or later one comes to that dreadful universal thing called human nature.

The soul, considered with its Creator, is like one of those mathematical lines that may draw nearer to another for all eternity without a possibility of touching it; and can there be a thought so transporting as to consider ourselves in these perpetual approaches to Him, who is not only the standard of perfection, but of happiness?

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.

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.

The usefulness of mathematics in furthering the sciences is commonly acknowledged: but outside the ranks of the experts there is little inquiry into its nature and purpose as a deliberate human activity. Doubtless this is due to the inevitable drawback that mathematical study is saturated with technicalities from beginning to end.

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.

Seriously, these days I tend to shut up in terms of external analysis and DO try to let things speak for themselves, while still trying to get some depth into them.

The mathematical life of a mathematician is short. Work rarely improves after the age of twenty-five or thirty. If little has been accomplished by then, little will ever be accomplished.

Now what is history? It is the centuries of systematic explorations of the riddle of death, with a view to overcoming death. That's why people discover mathematical infinity and electromagnetic waves, that's why they write symphonies.

I am giving this winter two courses of lectures to three students, of which one is only moderately prepared, the other less than moderately, and the third lacks both preparation and ability. Such are the onera of a mathematical profession.

Success on any major scale requires you to accept responsibility in the final analysis. The one quality that all successful people have is the ability to take on responsibility.

Hydrodynamics procreated complex analysis, partial differential equations, Lie groups and algebra theory, cohomology theory and scientific computing.

In our constitutional system, the extent of political controversies, including the protests, surrounding a given issue is utterly unrelated to the analysis of legality and should have no effect on any court.

So much of the work is intuitive. The resistance you detect is just that, a kind of evasion, a sense that too much analysis will inhibit creativity.

I would say that many architects are very logical. They start their process from analysis and from rational processes to try and find the 'right' answer, like solving a mathematic equation.

Traditionally, scientists have treated the laws of physics as simply 'given,' elegant mathematical relationships that were somehow imprinted on the universe at its birth, and fixed thereafter. Inquiry into the origin and nature of the laws was not regarded as a proper part of science.

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.

A mind is accustomed to mathematical deduction, when confronted with the faulty foundations of astrology, resists a long, long time, like an obstinate mule, until compelled by beating and curses to put its foot into that dirty puddle.

In that disputable point of persecuting men for conscience sake, I see such dreadful consequences rising, I would be as fully convinced of the truth of it, as a mathematical demonstration, before I would venture to act upon it or make it a part of my religion.

Experience has shown repeatedly that a mathematical theory with a rich internal structure generally turns out to have significant implications for the understanding of the real world, often in ways no one could have envisioned before the theory was developed.

I see philosophy as a fairly abstract activity, as concerned mainly with the analysis of criticism and concepts, and of course most usefully of scientific concepts.

I don't want to make a cheap analysis, but when you have, like I did, a father incapable of showing emotion, who spends his life telling you that no one will love you if you aren't perfect, it leaves scars.

Silk Road to Ruin has all the analysis and it's structured very well. I rely on my notes more and I use direct quotes. But there's nothing like writing about it right away.

I certainly do care about measuring educational results. But what is an 'educational result?' The twinkling eyes of my students, together with their heartfelt and beautifully expressed mathematical arguments are all the results I need.

When you get into statistical analysis, you don't really expect to achieve fame. Or to become an Internet meme. Or be parodied by 'The Onion' - or be the subject of a cartoon in 'The New Yorker.' I guess I'm kind of an outlier there.

In the final analysis, all explanations of meaning, various as they are, serve to indicate how something is 'appropriate' in and to our practices, our lives in effect.

There's been essentially the same analysis over and over again and very little allowance made for different views and interpretations and reflections.

The mathematician's best work is art, a high perfect art, as daring as the most secret dreams of imagination, clear and limpid. Mathematical genius and artistic genius touch one another.

There are certain pressures and things that change your life to a degree that, in the cost benefit analysis that constantly goes on, sometimes makes you think, 'Maybe I should just leave.

I think that a society cannot live without a certain number of irrational beliefs. They are protected from criticism and analysis because they are irrational.

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.

I have sought to offer humanists a detailed analysis of a technology sufficiently magnificent and spiritual to convince them that the machines by which they are surrounded are cultural artifacts worthy of their attention and respect.

The merit of painting lies in the exactness of reproduction. Painting is a science and all sciences are based on mathematics. No human inquiry can be a science unless it pursues its path through mathematical exposition and demonstration.

The whole of the developments and operations of analysis are now capable of being executed by machinery ... As soon as an Analytical Engine exists, it will necessarily guide the future course of science.