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


Alan Turing

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Alan Turing gave us a mathematical model of digital computing that has completely withstood the test...
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I'm afraid that the following syllogism may be used by some in the future.

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The brain may be regarded as a kind of parasite of the organism.
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There are two modes of acquiring knowledge, namely by reasoning and experience. Reasoning draws a c...
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Consumption may be regarded as negative production.
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The numbers may be said to rule the whole world of quantity, and the four rules of arithmetic may be...
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Alan Turing is such an amazing, tragic story.
DAVID LAGERCRANTZ
The formulation of a problem is often more essential than its solution, which may be merely a matter...
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As far as I know, only a small minority of mathematicians, even of those with Platonist views, accep...
ABRAHAM ROBINSON
The formulation of the problem is often more essential than its solution, which may be merely a matt...
ALBERT EINSTEIN
You may be to call up the entire encyclopedia, but a brain with no heart and no reasoning .. well, n...
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The brain may be regarded as a kind of parasite of the organism, a pensioner, as it were, who dwells...
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Coincidence may be described as the chance encounter of two unrelated causal chains which
ARTHUR KOESTLER
Telling Alan Turing's story in a two-hour film was a tremendous challenge. It felt in some small...
GRAHAM MOORE
May the Christian church never be regarded as a special interest group. We're here because we love o...
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Many difficulties which nature throws in our way, may be smoothed away by the exercise of intelligen...
TITUS LIVIUS
Exercise should be regarded as tribute to the heart.
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What we call personality or character is a highly complex product of a long integrative process, a p...
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Everything we call real is made of things that cannot be regarded as real.
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Science itself, therefore, may be regarded as a minimal problem, consisting of the completest possib...
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As memory may be a paradise from which we cannot be driven, it may also be a hell from which we cann...
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As memory may be a paradise from which we cannot be driven, it may also be a hell from which we cann...
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The fathers of the field had been pretty confusing: John von Neumann speculated about computers and ...
E. W. DIJKSTRA
To lose one parent may be regarded as a misfortune; to lose both looks like carelessness.
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To lose one parent may be regarded as a misfortune... to lose both seems like carelessness.
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Lifestyle intervention, such as exercise and diet, may be effective treatment for ED.
ELIZABETH SELVIN
Alan Turing is so important to me and to the world, and his story is so important to be told, so it ...
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HIs chess-playing methods did the same thing — as did the games on the Colossi — and posed the q...
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In England, an inventor is regarded almost as a crazy man, and in too many instances, invention ends...
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Everything has two handles, one by which it may be borne, the other by which it may not
EPICTETUS
To lose one parent, Mr Worthing, may be regarded as a misfortune; to lose both looks like carelessne...
OSCAR WILDE
I wrote about Alan Turing, the great mathematician and code-breaker. He was an absolutely different ...
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MISCREANT, n. A person of the highest degree of unworth. Etymologically, the word means unbeliever, ...
AMBROSE BIERCE
A totally nondenominational prayer: Insofar as I may be heard by anything, which may or may not care...
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Doctor James Rowland Angell has said that 'any program may be regarded as educational (and here we m...
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A family is like a card game, on one hand, you can get a really bad hand and on the other, your hand...
GARY F EVANS...
Your meditations may be as profound, as exalted, as devout as you like; you may practise every pious...
JOHANNES TAULER
I think that May would be the earliest, based on two hurricanes that not only caused damage at some ...
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I think that May would be the earliest, based on two hurricanes that not only caused damage at some ...
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The basic commitment is that the basic structure of the North Stand will be completed for the one-da...
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The history of the human race, viewed as a whole, may be regarded as the realization of a hidden pla...
IMMANUEL KANT
The history of the human race, viewed as a whole may be regarded as the realization of a hidden plan...
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There may be some strict conditions on the merger, but nothing that's going to make anyone rethink t...
MARK RAVERA
Instead of being regarded as intelligent or knowledgeable, many a woman would rather be regarded as ...
MOKOKOMA MOKHONOANA
[She wasn't] a logically reasoning woman, but God is good, and hearts may count in heaven as high as...
CHARLES DICKENS
The moment of truth, the sudden emergence of a new insight, is an act of intuition. Such intuitions ...
ARTHUR KOESTLER
If there is a Phase Two, it may not be as large. What we may see is funding support ... increased fo...
HAROLD MARTIN
Cold feet are often symptomatic of a legitimate intuition that you may be heading for the wrong plac...
SUZANNE FIELDS
Not only was Burroughs one of the three progenitors of the Beat movement ... but he may also be rega...
ISAAC GEWIRTZ
In one sense what may pass between the pope and myself may be trivialities. In another sense the fac...
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In another 10,000 or 20,000 years, I think the human brain may acquire a form that is quite differen...
BRUCE T. LAHN
The two operations of our understanding, intuition and deduction, on which alone we have said we mus...
RENE DESCARTES
From the consumer point of view, there may be questions about whether you'll have to be an AOL subsc...
CHARLENE LI
'The Imitation Game' is a celebration of Alan Turing's life and legacy, and Joan's f...
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There's no room for error. We are looking at facilities in this town and we may be looking at a bond...
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Steady, firm, and kind government of prisoners is the truest humanity and the best exercise of duty....
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We in this country, in this generation, are--by destiny rather than choice--the watchmen on the wall...
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We in this country, in this generation, areby destiny rather than choicethe watchmen on the walls of...
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She may have just been holding this for somebody, which we call a stash house.
LT. DARRELL SANDERS
Knowledge which is divorced from justice, may be called cunning rather than wisdom.
MARCUS TULLIUS CICERO
The biggest impact may be damage to the port facilities south of New Orleans. We have no way of know...
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Not like others? You may be inspired differently. Be bold, step out, follow YOUR intuition, no matte...
VAL UCHENDU
Patriotism or Nationalism without reasoning is what I call “Nationalist Fundamentalism”, which i...
ABHIJIT NASKAR
Now why should the cinema follow the forms of theater and painting rather than the methodology of la...
SERGEI EISENSTEIN
It's a clarion call. I use examples. There may be a number of businesses that may be beyond salvatio...
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As hard as it may seem to bound for success, you must never lose sight of the reasoning that kick st...
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Great investors need to have the right combination of intuition, business sense and investment talen...
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Temptation is like a knife, that may either cut the meat or the throat of a man; it may be his food ...
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It is strange how the memory of a man may float to posterity on what he would have himself regarded ...
WILLIAM OSLER
There are no plans to rebuild the dam. The Maclay family believes it does have a perfectly valid rig...
DAVID BLAIR
The combination of high-fat diets and the lack of exercise are probably the two key factors for the ...
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A swami may conceivably follow only the path of dry reasoning, of cold renunciation; but a yogi enga...
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I must down to the sea again, for the call of the running tide / Is a wild call and a clear call tha...
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For we may remark generally of our mathematical researches, that these auxiliary quantities, these l...
LOUIS POINSOT
Dull minds are never either intuitive or mathematical.
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All they have to do is call me and I will get something worked out. Even though we cover all those d...
DEANA STEVENS
I may have been lucky with some sort of intuition, but I believe in training a great deal.
DAVID SELBY
It might not be about perfection. Rather, it may be that that which is imperfect is that which has t...
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Some of this benefit we see now may be a combination of our increased awareness of heart disease in ...
LAURENCE SPERLING
That should be regarded as a loss, which is won at the expense of our reputation.
UNKNOWN
The joint military exercise aiming at boosting cooperation in war on terrorism will begin from May 1...
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The public must be put in its place, so that it may exercise its own powers, but no less and perhaps...
WALTER LIPPMANN
There is nothing respecting which a man may be so long unconscious as of the extent and strength of ...
FRANCIS JEFFREY
There is such a thing as legitimate warfare: war has its laws; there are things which may fairly be ...
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This may be the primary purpose of dogs: to restore our sense of wonder and to help us maintain it, ...
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Whatever may be the merits of a religious system, its effects upon the mass of mankind must depend i...
BENJAMIN ROBBINS CURTIS
Aristotle may be regarded as the cultural barometer of Western history. Whenever his influence domin...
AYN RAND
That's a good combination between me and McCoy. We know the way each other plays, so he may make a m...
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Idiosyncratic belief systems which are shared by only a few adherents are likely to be regarded as d...
ANTHONY STORR
The suffering may be moral or physical; and in my opinion it is just as absurd to call a man a cowar...
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The long concatenations of simple and easy reasoning which geometricians use in achieving their most...
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I think a strong claim can be made that the process of scientific discovery may be regarded as a for...
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We might be wise to follow the insight of the enraptured heart rather than the more cautious reasoni...
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It's been a long time coming. Thank God for this day.
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Here I am trying to build a life and I have nothing to build it with. It's wrong, just wrong.
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If you really want the truth, leave no stone unturned.
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There ain't no compensation for what they done to me. But I'm not bitter.
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What matters are the applications.
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I'm going to Disneyland!
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He's a great kid.
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I figure lots of predictions is best. People will forget the ones I get wrong and marvel over the re...
ALAN COX
Live fast, die old, and make very sure everyone knows you were there.
ALAN COX
The promoter is all you need for activation and silencing. It's the main site of action where everyt...
ALAN COWMAN
The promoter is all you need for activation and silencing. It's the main site of action where everyt...
ALAN COWMAN
The promoter is all you need for activation and silencing.
ALAN COWMAN
This is the first time anyone has actually been able to infiltrate an antigenic variation program. W...
ALAN COWMAN
It's like a leopard being able to change its spots. New forms come up, and the immune system beats t...
ALAN COWMAN
I still believe there's someone out there for our film.
ALAN COOKE
If we'd made it in the conventional way, we would have lost a lot of the feeling that came from thin...
ALAN COOKE
We wanted to make something that spoke from the heart to the heart.
ALAN COOKE
From the beginning there was an element of fate about the project.
ALAN COOKE
It's an individual taking a journey, that's the perspective. It happened here, but it could happen a...
ALAN COOKE
In the 13 years I served, we never had a problem. But I feel we are going downhill.
ALAN COOKE
We know it's going to be a difficult challenge, we're under no illusion.
ALAN COOKE
It is a niche opportunity for National Savings, it won't have a big impact on us.
ALAN COOK
Ultimately, they still had to sell. You have to give them credit for realizing they weren't going to...
ALAN COOK
The problem before was that the chapter was in over its head with this building,
ALAN COOK
In our discussions, part of the plan is to put into writing a memorandum of understanding that the m...
ALAN COOK
He likes to dribble a lot, ... so I told our defenders to just stay on his back, don't let him turn....
ALAN COOK
All of the paintings in the Museum Art Online collection are known to have a status of world-wide fa...
ALAN COOK
If what you are claiming is true, I would have shouted it from the rooftops. I would have gone to th...
ALAN COLMES
If what you are claiming is true, I would have shouted it from the rooftops. I would have gone to th...
ALAN COLMES
You know what bothers me more? Whether or not a member of the White House leaked the identity of a C...
ALAN COLMES
sure beats being plucked off the top of your home by a helicopter.
ALAN COLMES
I take personal responsibility.
ALAN COLMES
Also, interestingly enough, some of the things he was accused of believing ...actually were not his ...
ALAN COLMES
the real smear here, is against the Democrats who are held up as these evil people... Heaven forbid ...
ALAN COLMES
I still believe that the Democrats have it right about health care, education, the war in Iraq and, ...
ALAN COLMES
Genius, scholar, and war hero though he is, you have to admit - or maybe you should think about admi...
ALAN COLMES
Democrats need to be not only gracious in defeat, but positive about the future.
ALAN COLMES
Can we make money from this? That remains to be seen.
ALAN COLMAN
Singapore is gaining a lot of credibility as a good place to work. It has actually been easier for m...
ALAN COLMAN
It has undoubtedly harmed the image not just in Singapore, where I directly feel it has impacted our...
ALAN COLMAN
Although Singapore has a relatively limited pool of scientists as compared to the U.K., it has maxim...
ALAN COLMAN
They are a big catch. They are prominent researchers, very successful in the U.S..
ALAN COLMAN
Practice, it is said, makes perfect. But is it ethical to practice? And I absolutely think it is not...
ALAN COLMAN