Quotes of All Topics . Occasions . Authors
Any impatient student of mathematics or science or engineering who is irked by having algebraic symbolism thrust upon him should try to get along without it for a week.
I also take it as granted that every created thing, and consequently the created monad also, is subject to change, and indeed that this change is continual in each one.
...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know
Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty and perfection.
No man speaketh, or should speak, of his prince, that which he hath not weighed whether it will consist with that veneration which should be preserved inviolate to him.
Very often in mathematics the crucial problem is to recognize and discover what are the relevant concepts; once this is accomplished the job may be more than half done.
Analytical geometry has never existed. There are only people who do linear geometry badly, by taking coordinates, and they call this analytical geometry. Out with them!
A heavy warning used to be given that pictures are not rigorous; this has never had its bluff called and has permanently frightened its victims into playing for safety.
After exponential quantities the circular functions, sine and cosine, should be considered because they arise when imaginary quantities are involved in the exponential.
... the student skit at Christmas contained a plaintive line: "Give us Master's exams that our faculty can pass, or give us a faculty that can pass our Master's exams."
Because government has tremendous power, it attracts people who are eager to game the system, obtaining by force of law what they could never achieve through consensus.
No man of science wants merely to know. He acquires knowledge to appease his passion for discovery. He does not discover in order to know, he knows in order to discover.
As for methods I have sought to give them all the rigour that one requires in geometry, so as never to have recourse to the reasons drawn from the generality of algebra.
It will be readily admitted, that a degree conferred by an university, ought to be a pledge to the public that he who holds it possesses a certain quantity of knowledge.
The proportion between the velocity with which men or animals move, and the weights they carry, is a matter of considerable importance, particularly in military affairs.
The most remarkable discovery ever made by scientists is science itself. The discovery must be compared in importance with the invention of cave-painting and of writing.
[Gauss calculated the elements of the planet Ceres] and his analysis proved him to be the first of theoretical astronomers no less than the greatest of 'arithmeticians.'
There is a quality of life which lies always beyond the mere fact of life; and when we include the quality in the fact, there is still omitted the quality of the quality.
Perhaps the methods I needed to complete the proof would not be invented for a hundred years. So even if I was on the right track, I could be living in the wrong century.
If you look at a shape like a straight line, what's remarkable is that if you look at a straight line from close by, from far away, it is the same; it is a straight line.
We have so exalted a notion of the human soul that we cannot bear to be despised, or even not to be esteemed by it. Man, in fact, places all his happiness in this esteem.
For since it is impossible for a created monad to have a physical influence on the inner nature of another, this is the only way in which one can be dependent on another.
Shall we keep our hands in our bosom, or stretch ourselves on our beds of laziness, while all the world about us is hard at work, in pursuing the designs of its creation?
If the earth were not round, heavy bodies would not tend from every side in a straight line towards the center of the earth, but to different points from different sides.
You insist that there is something a machine cannot do. If you tell me precisely what it is a machine cannot do, then I can always make a machine which will do just that.
One began to hear it said that World War I was the chemists' war, World War II was the physicists' war, World War III (may it never come) will be the mathematicians' war.
Ranganathan's 5 Laws: Books are for use. Books are for all. Every book its reader, or every reader his book. Save the time of the reader. A library is a growing organism.
Fermat never cared to publish his investigations, but was always perfectly ready, as we see from his letters, to acquaint his friends and contemporaries with his results.
The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.
I had many books and I had dreams of all kinds. Dreams in which were in a certain sense, how to say, easy to make because the near future was always extremely threatening.
Let it not be imagined that the life of a good Christian must be a life of melancholy and gloominess; for he only resigns some pleasures to enjoy others infinitely better.
Let no one say that I have said nothing new... the arrangement of the subject is new. When we play tennis, we both play with the same ball, but one of us places it better.
In turning from the smaller instruments in frequent use to the larger and more important machines, the economy arising from the increase of velocity becomes more striking.
The quantity of meaning compressed into small space by algebraic signs, is another circumstance that facilitates the reasonings we are accustomed to carry on by their aid.
As long as a branch of science offers an abundance of problems, so long it is alive; a lack of problems foreshadows extinction or the cessation of independent development.
Among mathematicians in general, three main categories may be distinguished; and perhaps the names logicians, formalists, and intuitionists may serve to characterize them.
If I could prove by logic that you would die in five minutes, I should be sorry you were going to die, but my sorrow would be very much mitigated by pleasure in the proof.
I think logicians hate my work, they detest it! And I'm like pornography, I'm sort of an unmentionable subject in the world of logic, because my results are so disgusting!
[Asked whether he would like to see an experimental demonstration of conical refraction] No. I have been teaching it all my life, and I do not want to have my ideas upset.
It is possible to believe in progress as a fact without believing in progress as an ethical principle; but in the catechism of many Americans, the one goes with the other.
No, I'm not interested in developing a powerful brain. All I'm after is just a mediocre brain, something like the President of the American Telephone and Telegraph Company.
Wisdom alone is true ambition's aim, wisdom is the source of virtue and of fame; obtained with labour, for mankind employed, and then, when most you share it, best enjoyed.
The only use of a knowledge of the past is to equip us for the present. The present contains all that there is. It is holy ground; for it is the past, and it is the future.
The vastest knowledge of today cannot transcend the buddhi of the Rishis in ancient India; and science in its most advanced stage now is closer to Vedanta than ever before.
By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.
If I believe in God and life after death and you do not, and if there is no God, we both lose when we die. However, if there is a God, you still lose and I gain everything.
Either God exists or He doesn't. Either I believe in God or I don't. Of the four possibilities, only one is to my disadvantage. To avoid that possibility, I believe in God.
Our faith in Mathematics is not likely to wane if we openly acknowledge that the personalities of even the greatest mathematicians may be as flawed as those of anyone else.
Because men believe not in Providence, therefore they do so greedily scrape and hoard. They do not believe in any reward for charity, therefore they will part with nothing.
So much the worse, it may be, for a particular meeting: but the meeting is the individual, which on evolution principles, must be sacrificed for the development of the race.