Quotes of All Topics . Occasions . Authors
Those who profess contempt for men, and put them on a level with beasts, yet wish to be admired and believed by men, and contradict themselves by their own feelings--their nature, which is stronger than all, convincing them of the greatness of man more forcibly than reason convinces them of his baseness.
If we define a miracle as an effect of which the cause is unknown to us, then we make our ignorance the source of miracles! And the universe itself would be a standing miracle. A miracle might be perhaps defined more exactly as an effect which is not the consequence or effect of any known laws of nature.
The successful construction of all machinery depends on the perfection of the tools employed; and whoever is a master in the arts of tool-making possesses the key to the construction of all machines... The contrivance and construction of tools must therefore ever stand at the head of the industrial arts.
Detest it as lewd intercourse, it can deprive you of all your leisure, your health, your rest, and the whole happiness of your life. Having himself spent a lifetime unsuccessfully trying to prove Euclid's postulate that parallel lines do not meet, Farkas discouraged his son János from any further attempt.
1. 0 is a number. 2. The immediate successor of a number is also a number. 3. 0 is not the immediate successor of any number. 4. No two numbers have the same immediate successor. 5. Any property belonging to 0 and to the immediate successor of any number that also has that property belongs to all numbers.
We think very little of time present; we anticipate the future, as being too slow, and with a view to hasten it onward, we recall the past to stay it as too swiftly gone. We are so thoughtless, that we thus wander through the hours which are not here, regardless only of the moment that is actually our own.
St. Augustine teaches us that there is in each man a Serpent, an Eve, and an Adam. Our senses and natural propensities are the Serpent; the excitable desire is the Eve; and reason is the Adam. Our nature tempts us perpetually; criminal desire is often excited; but sin is not completed till reason consents.
I entered an omnibus to go to some place or other. At that moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with non-Euclidean geometry.
As professor of global peace studies at the International Islamic University of Malaysia I am committed to the ending of war also through criminalization of war, an approach that has not been sufficiently used in spite of the UN Charter outlawing war - with too many loopholes used buy aggressive countries.
Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. For, as has been pointed out several times, there is no such thing as a random number - there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method.
It is more important that a proposition be interesting than that it be true. This statement is almost a tautology. For the energy of operation of a proposition in an occasion of experience is its interest and is its importance. But of course a true proposition is more apt to be interesting than a false one.
If you have had your attention directed to the novelties in thought in your own lifetime, you will have observed that almost all really new ideas have a certain aspect of foolishness when they are first produced, and almost any idea which jogs you out of your current abstractions may be better than nothing.
Perhaps five or even ten per cent of men can do something rather well. It is a tiny minority who can do anything really well, and the number of men who can do two things well is negligible. If a man has any genuine talent, he should be ready to make almost any sacrifice in order to cultivate it to the full.
How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.
I believe that numbers and functions of Analysis are not the arbitrary result of our minds; I think that they exist outside of us, with the same character of necessity as the things of objective reality, and we meet them or discover them, and study them, as do the physicists, the chemists and the zoologists.
The scientific method of examining facts is not peculiar to one class of phenomena and to one class of workers; it is applicable to social as well as to physical problems, and we must carefully guard ourselves against supposing that the scientific frame of mind is a peculiarity of the professional scientist.
Evil is easily discovered; there is an infinite variety; good is almost unique. But some kinds of evil are almost as difficult to discover as that which we call good; and often particular evil of this class passes for good. It needs even a certain greatness of soul to attain to this, as to that which is good.
Blindness to the aesthetic element in mathematics is widespread and can account for a feeling that mathematics is dry as dust, as exciting as a telephone book... Contrariwise, appreciation of this element makes the subject live in a wonderful manner and burn as no other creation of the human mind seems to do.
Give us detailed, testable, mechanistic accounts for the origin of life, the origin of the genetic code, the origin of ubiquitous bio macromolecules and assemblages like the ribosome, and the origin of molecular machines like the bacterial flagellum, and intelligent design will die a quick and painless death.
To speak freely of mathematics, I find it the highest exercise of the spirit; but at the same time I know that it is so useless that I make little distinction between a man who is only a mathematician and a common artisan. Also, I call it the most beautiful profession in the world; but it is only a profession.
What (Stephen) Hawking says in his book The Grand Design is the universe exists because it needed to exist, and because it needed to exist, it therefore created itself. His conclusion merely restates his premise, which means his argument is circular. Nonsense is nonsense, even when spoken by famous scientists.
The human brain finds it extremely hard to cope with a new level of abstraction. This is why it was well into the eighteenth century before mathematicians felt comfortable dealing with zero and with negative numbers, and why even today many people cannot accept the square root of minus-one as a genuine number.
Let man then contemplate the whole of nature in her full and grand majesty... No idea approaches it. We may enlarge our conceptions beyond all imaginable space; we only produce atoms in comparison with the reality of things. It is an infinite sphere, the center of which is everywhere, the circumference nowhere.
There will certainly be no lack of human pioneers when we have mastered the art of flight....Let us create vessels and sails justed to the heavenly ether, and there will be plenty of people unafraid of the empty wastes. In the meantime we shall prepare, for the brave sky-travelers, maps of the celestial bodies.
[It] may be laid down as a general rule that, if the result of a long series of precise observations approximates a simple relation so closely that the remaining difference is undetectable by observation and may be attributed to the errors to which they are liable, then this relation is probably that of nature.
One can think of any given axiom system as being like a computer with a certain limited amount of memory or processing power. One could switch to a computer with even more storage, but no matter how large an amount of storage space the computer has, there will still exist some tasks that are beyond its ability.
Science would be ruined if (like sports) it were to put competition above everything else, and if it were to clarify the rules of competition by withdrawing entirely into narrowly defined specialties. The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
I am in the utmost perplexity, yand have wished a hundred times, that if there is a A God, nature would manifest him without ambiguity, and that if there is not, every imaginary sign of his existence might vanish : in short, let nature speak distinctly, or be totally silent, and I shall know what course to take.
The wisdom of the Lord is infinite as are also His glory and His power. Ye heavens, sing His praises; sun, moon, and planets, glorify Him in your ineffable language! Praise Him, celestial harmonies, and all ye who can comprehend them! And thou, my soul, praise thy Creator! It is by Him and in Him that all exist.
Everything useful in mathematics has been devised for a purpose. Even if you don't know it, the guy who did it first, he knew what he was doing. Banach didn't just develop Banach spaces for the sake of it. He wanted to put many spaces under one heading. Without knowing the examples, the whole thing is pointless.
The future mathematician ... should solve problems, choose the problems which are in his line, meditate upon their solution, and invent new problems. By this means, and by all other means, he should endeavor to make his first important discovery: he should discover his likes and dislikes, his taste, his own line.
A first fact should surprise us, or rather would surprise us if we were not used to it. How does it happen there are people who do not understand mathematics? If mathematics invokes only the rules of logic, such as are accepted by all normal minds...how does it come about that so many persons are here refractory?
The mechanical brain does not secrete thought "as the liver does bile," as the earlier materialists claimed, nor does it put it out in the form of energy, as the muscle puts out its activity. Information is information, not matter or energy. No materialism which does not admit this can survive at the present day.
Often the great scientists, by turning the problem around a bit, changed a defect to an asset. For example, many scientists when they found they couldn't do a problem finally began to study why not. They then turned it around the other way and said, "But of course, this is what it is" and got an important result.
While asleep, I had an unusual experience. There was a red screen formed by flowing blood, as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention. That hand wrote a number of elliptic integrals. They stuck to my mind. As soon as I woke up, I committed them to writing.
If we take seriously the word-flesh Christology of Chalcedon (i.e., the doctrine that Christ is fully human and fully divine) and view Christ as the telos toward which God is drawing the whole of creation, then any view of the sciences that leaves Christ out of the picture must be seen as fundamentally deficient.
All great amusements are dangerous to the Christian life; but among all those which the world has invented there is none more to be feared than the theater. It is a representation of the passions so natural and so delicate that it excites them and gives birth to them in our hearts, and, above all, to that of love.
One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.
If we except the great name of Newton (and the exception is one that the great Gauss himself would have been delighted to make) it is probable that no mathematician of any age or country has ever surpassed Gauss in the combination of an abundant fertility of invention with an absolute vigorousness in demonstration.
Some of what these pamphlets [of astrological forecasts] say will turn out to be true, but most of it time and experience will expose as empty and worthless. The latter part will be forgotten literally: written on the winds while the former will be carefully entered in people's memories, as is usual with the crowd.
Nothing is so intolerable to man as being fully at rest, without passion, without business, without entertainment, without care. It is then that he recognizes that he is empty, insufficient, dependent, ineffectual. From the depths of his soul now comes at once boredom, gloom, sorrow, chagrin, resentment and despair.
In addition to its use in arithmetic and science, the Hindu-Arabic number system is the only genuinely universal language on Earth, apart perhaps for the Windows operating system, which has achieved the near universal adoption of a conceptually and technologically poor product by the sheer force of market dominance.
Let's stick to the practical and the concrete: Would you like it if people lived in a virtual world? If machines were smarter than people? If, in the future, people, animals and plants were products of technology? If you don't like these ideas, then for you the computer and biological sciences clearly are dangerous.
Gentlemen, as we study the universe we see everywhere the most tremendous manifestations of force. In our own experience we know of but one source of force, namely will. How then can we help regarding the forces we see in nature as due to the will of some omnipresent, omnipotent being? Gentlemen, there must be a GOD.
There is nothing so insupportable to man as to be in entire repose, without passion, occupation, amusement, or application. Then it is that he feels his own nothingness, isolation, insignificance, dependent nature, powerless, emptiness. Immediately there issue from his soul ennui, sadness, chagrin, vexation, despair.
Combinatorial analysis, in the trivial sense of manipulating binomial and multinomial coefficients, and formally expanding powers of infinite series by applications ad libitum and ad nauseamque of the multinomial theorem, represented the best that academic mathematics could do in the Germany of the late 18th century.
Do they think that they have given us great pleasure by telling us that they hold our soul to be no more than wind or smoke, and saying it moreover in tones of pride and satisfaction? Is this then something to be said gaily? Is it not on the contrary something to be said sadly, as being the saddest thing in the world?
Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course. There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology.
What a glorious title, Nature, a veritable stroke of genius to have hit upon. It is more than a cosmos, more than a universe. It includes the seen as well as the unseen, the possible as well as the actual, Nature and Nature's God, mind and matter. I am lost in admiration of the effulgent blaze of ideas it calls forth.
For when a ship is floating calmly along, the sailors see its motion mirrored in everything outside, while on the other hand they suppose that they are stationary, together with everything on board. In the same way, the motion of the earth can unquestionably produce the impression that the entire universe is rotating.