Quotes of All Topics . Occasions . Authors
In each action we must look beyond the action at our past, present, and future state, and at others whom it affects, and see the relations of all those things. And then we shall be very cautious.
All men naturally hate each other. We have used concupiscence as best we can to make it serve the common good, but this is mere sham and a false image of charity, for essentially it is just hate.
When God works miracles, he does not do it in order to supply the wants of nature, but those of grace. Whoever thinks otherwise, must needs have a very mean notion of the wisdom and power of God.
Since we astronomers are priests of the highest God in regard to the book of nature, it befits us to be thoughtful, not of the glory of our minds, but rather, above all else, of the glory of God.
The heavenly motions... are nothing but a continuous song for several voices, perceived not by the ear but by the intellect, a figured music which sets landmarks in the immeasurable flow of time.
The mathematician, carried along on his flood of symbols, dealing apparently with purely formal truths, may still reach results of endless importance for our description of the physical universe.
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.
Our habitual experience is a complex of failure and success in the enterprise of interpretation. If we desire a record of uninterpreted experience, we must ask a stone to record its autobiography.
I didn't want to become a pure mathematician, as a matter of fact, my uncle was one, so I knew what the pure mathematician was and I did not want to be a pure - I wanted to do something different.
Although computer memory is no longer expensive, there's always a finite size buffer somewhere. When a big piece of news arrives, everybody sends a message to everybody else, and the buffer fills.
That something so obvious as the vanity of the world should be so little recognized that people find it odd and surprising to be told that it is foolish to seek greatness; that is most remarkable.
Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand... So Greek mathematics is 'permanent', more permanent even than Greek literature.
The most frequent complaint is that it's hard. True. it's a hard game to win Also, many people ask me how to use the secret debugging commands, apparently under the impression that I'll tell them.
Even private persons in due season, with discretion and temper, may reprove others, whom they observe to commit sin, or follow bad courses, out of charitable design, and with hope to reclaim them.
Culture is activity of thought, and receptiveness to beauty and humane feeling. Scraps of information have nothing to do with it. A merely well informed man is the most useless bore on God's earth.
It could be that the methods needed to take the next step may simply be beyond present day mathematics. Perhaps the methods I needed to complete the proof would not be invented for a hundred years.
Surely, if knowledge is valuable, it can never be good policy in a country far wealthier than Tuscany, to allow a genius like Mr. Dalton's, to be employed in the drudgery of elementary instruction.
The community of mathematicians is similar to an imaginary community of musical composers whose only satisfaction is obtained by the interchange among themselves of the musical scores they compose.
No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful.
Whence it follows that God is absolutely perfect, since perfection is nothing but magnitude of positive reality, in the strict sense, setting aside the limits or bounds in things which are limited.
A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details.
In conclusion, I submit that, far from science having buried God, not only do the results of science point towards his existence, but the scientific enterprise itself is validated by his existence.
The mathematical fraternity is a little like a self-perpetuating priesthood. The mathematicians of today teach the mathematicians of tomorrow and, in effect, decide whom to admit to the priesthood.
It would be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said, 'Yes, it is true, but you won't be able to understand the proof.'
Now in creative thought common sense is a bad master. Its sole criterion for judgement is that the new ideas shall look like the old ones. In other words it can only work by suppressing originality.
We desire truth, and find within ourselves only uncertainty. We seek happiness, and find only misery and death. We cannot but desire truth and happiness, and are incapable of certainty or happiness.
...for the truth is always older than all the opinions men have held regarding it; and one should be ignoring the nature of truth if we imagined that the truth began at the time it came to be known.
If you believe in God you are at no disadvantage in this life, and at considerable advantage in the next. If you do not believe, but find in the next that there was a next, you are most unfortunate!
If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by the laws.
A man becomes creative, whether he is an artist or scientist, when he finds a new unity in the variety of nature. He does so by finding a likeness between things which were not thought alike before.
To parents who despair because their children are unable to master the first problems in arithmetic I can dedicate my examples. For, in arithmetic, until the seventh grade I was last or nearly last.
So, Fabricius, I already have this: that the most true path of the planet [Mars] is an ellipse, which Dürer also calls an oval, or certainly so close to an ellipse that the difference is insensible.
The world of the future will be an even more demanding struggle against the limitations of our intelligence, not a comfortable hammock in which we can lie down to be waited upon by our robot slaves.
Sometimes I feel that a more rational explanation for all that has happened during my lifetime is that I am still only thirteen years old, reading Jules Verne or H. G. Wells, and have fallen asleep.
There is no more common error than to assume that, because prolonged and accurate mathematical calculations have been made, the application of the result to some fact of nature is absolutely certain.
If we do not know ourselves to be full of pride, ambition, lust, weakness, misery, and injustice, we are indeed blind. And if, knowing this, we do not desire deliverance, what can we say of a man...?
Those who write against vanity want the glory of having written well, and their readers the glory of reading well, and I who write this have the same desire, as perhaps those who read this have also.
The Council of the Royal Society is a collection of men who elect each other to office and then dine together at the expense of this society to praise each other over wine and give each other medals.
It is just as foolish to complain that people are selfish and treacherous as it is to complain that the magnetic field does not increase unless the electric field has a curl. Both are laws of nature.
To meet the shortage of supplies from America, due to lack of shipping, the representatives of the different supply departments were constantly in search of available material and supplies in Europe.
I am aware that a philosopher's ideas are not subject to the judgment of ordinary persons, because it is his endeavour to seek the truth in all things, to the extent permitted to human reason by God.
Some people have low susceptibility to advertising and marketing techniques. These are the people who aren't interested in money. Material acquisition does not serve their need for the power process.
The desire to explore thus marks out the mathematician. This is one of the forces making for the growth of mathematics. The mathematician enjoys what he already knows; he is eager for more knowledge.
Precisely because intelligent design does not turn the study of biological origins into a Bible-science controversy, intelligent design is a position around which Christians of all stripes can unite.
Above all things we must be aware of what I will call 'inert ideas' - that is to say, ideas that are merely received into the mind without being utilized, or tested, or thrown into fresh combinations.
Those great efforts of intellect, upon which the mind sometimes touches, are such that it cannot maintain itself there. It only leaps to them, not as upon a throne, forever, but merely for an instant.
There is nothing that we can see on earth which does not either show the wretchedness of man or the mercy of God. One either sees the powerlessness of man without God, or the strength of man with God.
No contradictions will arise as long as Finite Man does not mistake the infinite for something fixed, as long as he is not led by an acquired habit of mind to regard the infinite as something bounded.
To those who have chosen the profession of medicine, a knowledge of chemistry, and of some branches of natural history, and, indeed, of several other departments of science, affords useful assistance.
Puzzles are made of the things that the mathematician, no less than the child, plays with, and dreams and wonders about, for they are made of things and circumstances of the world he [or she] live in.