Quotes of All Topics . Occasions . Authors
Equal weights at equal distances are in equilibrium and equal weights at unequal distances are not in equilibrium but incline towards the weight which is at the greater distance.
I spent my time very nicely in many ways, but not fully satisfactory. Then I became Professor in France, but realized that I was not - for the job that I should spend my life in.
Imagination magnifies small objects with fantastic exaggeration until they fill our soul, and with bold insolence cuts down great things to its own size, as when speaking of God.
I condemn equally those who choose to praise man, those who choose to condemn him and those who choose to divert themselves, and I can only approve of those who seek with groans.
La dernie' re chose qu'on trouve en faisant un ouvrage, est de savoir celle qu'il faut mettre la premie' re. The last thing one discovers in composing a work iswhat to put first.
Let us now speak according to natural lights. If there is a God, He is infinitely incomprehensible. . . . We are then incapable of knowing of either what He is or if He is. . . .
That science has long been neglected and declining in England, is not an opinion originating with me, but is shared by many, and has been expressed by higher authority than mine.
I don't say that bodies like flint, which are commonly called inanimate, have perceptions and appetition; rather they have something of that sort in them, as worms are in cheese.
In my opinion a mathematician, in so far as he is a mathematician, need not preoccupy himself with philosophy-an opinion, moreover, which has been expressed by many philosophers.
If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of the same universe at a succeeding moment.
There must be something unique about man because otherwise, evidently, the ducks would be lecturing about Konrad Lorenz, and the rats would be writing papers about B. F. Skinner.
There are three signs of senility. The first sign is that a man forgets his theorems. The second sign is that he forgets to zip up. The third sign is that he forgets to zip down.
Mathematics, in the development of its ideas, has only to take account of the immanent reality of its concepts and has absolutely no obligation to examine their transient reality.
Therefore, I have attacted [the problem of the catenary] which I had hitherto not attempted, and with my key [the differential calculus] happily opened its secret. Acta eruditorum
It follows from what we have just said, that the natural changes of monads come from an internal principle, since an external cause would be unable to influence their inner being.
It is the peculiar beauty of this method, gentlemen, and one which endears it to the really scientific mind, that under no circumstance can it be of the smallest possible utility.
The subjectivist states his judgements, whereas the objectivist sweeps them under the carpet by calling assumptions knowledge, and he basks in the glorious objectivity of science.
Though I had success in my research both when I was mad and when I was not, eventually I felt that my work would be better respected if I thought and acted like a 'normal' person.
Clearly the price considered most likely by the market is the true current price: if the market judged otherwise, it would quote not this price, but another price higher or lower.
Babbage ... gave the name to the [Cambridge] Analytical Society, which he stated was formed to advocate 'the principles of pure d-ism as opposed to the dot-age of the university.'
That the state of knowledge in any country will exert a directive influence on the general system of instruction adopted in it, is a principle too obvious to require investigation.
The fatigue produced on the muscles of the human frame does not altogether depend on the actual force employed in each effort, but partly on the frequency with which it is exerted.
I am accustomed, as a professional mathematician, to living in a sort of vacuum, surrounded by people who declare with an odd sort of pride that they are mathematically illiterate.
Projective geometry has opened up for us with the greatest facility new territories in our science, and has rightly been called the royal road to our particular field of knowledge.
The ultimate reason of things must lie in a necessary substance, in which the differentiation of the changes only exists eminently as in their source; and this is what we call God.
... numbers have neither substance, nor meaning, nor qualities. They are nothing but marks, and all that is in them we have put into them by the simple rule of straight succession.
Discovery is the privilege of the child: the child who has no fear of being once again wrong, of looking like an idiot, of not being serious, of not doing things like everyone else.
In the history of the concept of number has been adjective (three cows, three monads) and noun (three, pure and simple), and now ... number seems to be more like a verb (to triple).
Now where there are no parts, there neither extension, nor shape, nor divisibility is possible. And these monads are the true atoms of nature and, in a word, the elements of things.
Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build my arithmetic.
All suggested accounts of the origin of the solar system are subject to serious objections. The conclusion in the present state of the subject would be that the system cannot exist.
Germany expected that at the most a day or so would see Belgian resistance broken and the dash on Paris begun. It was not safe to start such a forward rush with Belgium unconquered.
The 'chess machine', by which admiring title he had been known, revealed the great drawback of a machine: it had not sufficient flexibility to adapt itself to altered circumstances.
Nations are not ruined by one act of violence, but gradually and in an almost imperceptible manner by the depreciation of their circulating currency, through its excessive quantity.
I am not here concerned with intent, but with scientific standards, especially the ability to tell the difference between a fact, an opinion, a hypothesis, and a hole in the ground.
Similarly, computer literacy courses tend to produce computer people who know a lot about computers or a piece of software but they don't help people become fluent with the machine.
He [John von Neumann] had the invaluable faculty of being able to take the most difficult problem and separate it into its components, whereupon everything looked brlliantly simple.
I'm afraid that the following syllogism may be used by some in the future. Turing believes machines think Turing lies with men Therefore machines do not think Yours in distress, Alan
When the weather changes, nobody believes the laws of physics have changed. Similarly, I don't believe that when the stock market goes into terrible gyrations its rules have changed.
So we can only know God well by knowing our iniquities. Therefore those who have known God, without knowing their wretchedness, have not glorified Him, but have glorified themselves.
The origins of disputes between philosophers is, that one class of them have undertaken to raise man by displaying his greatness, and the other to debase him by showing his miseries.
Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry.
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.
Men act like brutes in so far as the sequences of their perceptions arise through the principle of memory only, like those empirical physicians who have mere practice without theory.
Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.
We are a scientific civilization. That means a civilization in which knowledge and its integrity are crucial. Science is only a Latin word for knowledge ... Knowledge is our destiny.
That series of inventions by which man from age to age has remade his environment is a different kind of evolution -- not biological, but cultural evolution . . . "The Ascent of Man.
I have made the most important discovery of my career, the most important discovery of my life: It is only in the mysterious equations of love that any logic or reasons can be found.
Sometimes, properties of a fixed hyperbolic surface can be better understood by studying the moduli space that parameterises all hyperbolic structures on a given topological surface.
I often don't know what I'll be working on next year or a year from now. There is often a chance meeting, or something that I worked on 10 years ago suddenly becomes important again.