... I left Caen, where I was living, to go on a geologic excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go to some place or other. At the 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 those of non-Eudidean geometry. I did not verify the idea; I should not have had time, as upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for convenience sake, I verified the result at my leisure.

...to many it is not knowledge but the quest for knowledge that gives greater interest to thought—to travel hopefully is better than to arrive.

La pensée n'est qu'un écliar au milieu d'une longue nuit. Mais c'est cet éclair qui est tout.
Thought is only a flash in the middle of a long night. But this flash means everything.

A poet is, after all, a sort of scientist, but engaged in a qualitative science in which nothing is measurable. He lives with data that cannot be numbered, and his experiments can be done only once. The information in a poem is, by definition, not reproducible. ... He becomes an equivalent of scientist, in the act of examining and sorting the things popping in [to his head], finding the marks of remote similarity, points of distant relationship, tiny irregularities that indicate that this one is really the same as that one over there only more important. Gauging the fit, he can meticulously place pieces of the universe together, in geometric configurations that are as beautiful and balanced as crystals.

A society made up of individuals who were capable of original thought would probably be unendurable. The pressure of ideas would simply drive it frantic.

A subtle thought that is in error may yet give rise to fruitful inquiry that can establish truths of great value.

Act as if you are going to live for ever and cast your plans way ahead. You must feel responsible without time limitations, and the consideration of whether you may or may not be around to see the results should never enter your thoughts.

All great discoveries are made by men whose feelings run ahead of their thinking.

All the fifty years of conscious brooding have brought me no closer to answer the question, “What are light quanta?” Of course today every rascal thinks he knows the answer, but he is deluding himself.

An equation means nothing to me unless it expresses a thought of God.

And from my pillow, looking forth by light
Of moon or favouring stars, I could behold
The antechapel where the statue stood
Of Newton with his prism and silent face,
The marble index of a mind for ever
Voyaging through strange seas of Thought, alone.

As the component parts of all new machines may be said to be old[,] it is a nice discriminating judgment, which discovers that a particular arrangement will produce a new and desired effect. ... Therefore, the mechanic should sit down among levers, screws, wedges, wheels, etc. like a poet among the letters of the alphabet, considering them as the exhibition of his thoughts; in which a new arrangement transmits a new idea to the world.

Be not afeard.
The isle is full of noises,
Sounds, and sweet airs, that give delight and hurt not.
Sometimes a thousand twangling instruments
Will hum about mine ears; and sometime voices
That if I then had waked after long sleep
Will make me sleep again; and then, in dreaming
The clouds methought would open and show riches
Ready to drop upon me, that, when I waked,
I cried to dream again.

Behold the mighty dinosaur,
Famous in prehistoric lore,
Not only for his power and strength
But for his intellectual length.
You will observe by these remains
The creature had two sets of brains—
One in his head (the usual place),
The other at his spinal base.
Thus he could reason 'A priori'
As well as 'A posteriori'.
No problem bothered him a bit
He made both head and tail of it.
So wise was he, so wise and solemn,
Each thought filled just a spinal column.
If one brain found the pressure strong
It passed a few ideas along.
If something slipped his forward mind
'Twas rescued by the one behind.
And if in error he was caught
He had a saving afterthought.
As he thought twice before he spoke
He had no judgment to revoke.
Thus he could think without congestion
Upon both sides of every question.
Oh, gaze upon this model beast
Defunct ten million years at least.

Both religion and natural science require a belief in God for their activities, to the former He is the starting point, and to the latter the goal of every thought process. To the former He is the foundation, to the latter, the crown of the edifice of every generalized world view.

But nothing of a nature foreign to the duties of my profession [clergyman] engaged my attention while I was at Leeds so much as the, prosecution of my experiments relating to electricity, and especially the doctrine of air. The last I was led into a consequence of inhabiting a house adjoining to a public brewery, where first amused myself with making experiments on fixed air [carbon dioxide] which found ready made in the process of fermentation. When I removed from that house, I was under the necessity making the fixed air for myself; and one experiment leading to another, as I have distinctly and faithfully noted in my various publications on the subject, I by degrees contrived a convenient apparatus for the purpose, but of the cheapest kind. When I began these experiments I knew very little of chemistry, and had in a manner no idea on the subject before I attended a course of chymical lectures delivered in the Academy at Warrington by Dr. Turner of Liverpool. But I have often thought that upon the whole, this circumstance was no disadvantage to me; as in this situation I was led to devise an apparatus and processes of my own, adapted to my peculiar views. Whereas, if I had been previously accustomed to the usual chemical processes, I should not have so easily thought of any other; and without new modes of operation I should hardly have discovered anything materially new.

But, indeed, the science of logic and the whole framework of philosophical thought men have kept since the days of Plato and Aristotle, has no more essential permanence as a final expression of the human mind, than the Scottish Longer Catechism.

Can a society in which thought and technique are scientific persist for a long period, as, for example, ancient Egypt persisted, or does it necessarily contain within itself forces which must bring either decay or explosion?

Chemical research conducts to the knowledge of philosophical truth, and forms the mind to philosophical enlargement and accuracy of thought, more happily than almost any other species of investigation in which the human intellect can be employed.

Discovery consists of seeing what everybody has seen and thinking what nobody has thought.

Doubtless it is true that while consciousness is occupied in the scientific interpretation of a thing, which is now and again “a thing of beauty,” it is not occupied in the aesthetic appreciation of it. But it is no less true that the same consciousness may at another time be so wholly possessed by the aesthetic appreciation as to exclude all thought of the scientific interpretation. The inability of a man of science to take the poetic view simply shows his mental limitation; as the mental limitation of a poet is shown by his inability to take the scientific view. The broader mind can take both.

During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical. The question now is, not whether this or that hypothesis is better or worse to the pure thought, but whether it accords with observed phenomena in those consequences which can be shown necessarily to follow from it, if it be true

Einstein, twenty-six years old, only three years away from crude privation, still a patent examiner, published in the Annalen der Physik in 1905 five papers on entirely different subjects. Three of them were among the greatest in the history of physics. One, very simple, gave the quantum explanation of the photoelectric effect—it was this work for which, sixteen years later, he was awarded the Nobel prize. Another dealt with the phenomenon of Brownian motion, the apparently erratic movement of tiny particles suspended in a liquid: Einstein showed that these movements satisfied a clear statistical law. This was like a conjuring trick, easy when explained: before it, decent scientists could still doubt the concrete existence of atoms and molecules: this paper was as near to a direct proof of their concreteness as a theoretician could give. The third paper was the special eory of relativity, which quietly amalgamated space, time, and matter into one fundamental unity. This last paper contains no references and quotes no authority. All of them are written in a style unlike any other theoretical physicist's. They contain very little mathematics. There is a good deal of verbal commentary. The conclusions, the bizarre conclusions, emerge as though with the greatest of ease: the reasoning is unbreakable. It looks as though he had reached the conclusions by pure thought, unaided, without listening to the opinions of others. To a surprisingly large extent, that is precisely what he had done.

Eternity is a terrible thought. I mean, where's it going to end?

Fear of something is at the root of hate for others and hate within will eventually destroy the hater. Keep your thoughts free from hate, and you will have no fear from those who hate you. ...
David, though small, was filled with truth, right thinking and good will for others. Goliath represents one who let fear into his heart, and it stayed there long enough to grow into hate for others.

For my confirmation, I didn't get a watch and my first pair of long pants, like most Lutheran boys. I got a telescope. My mother thought it would make the best gift.

For the rest of my life I will reflect on what light is.

Had you or I been born at the Bay of Soldania, possibly our Thoughts, and Notions, had not exceeded those brutish ones of the Hotentots that inhabit there: And had the Virginia King Apochancana, been educated in England, he had, perhaps been as knowing a Divine, and as good a Mathematician as any in it. The difference between him, and a more improved English-man, lying barely in this, That the exercise of his Facilities was bounded within the Ways, Modes, and Notions of his own Country, and never directed to any other or farther Enquiries.

History, as it lies at the root of all science, is also the first distinct product of man's spiritual nature, his earliest expression of what may be called thought

I am convinced that an important stage of human thought will have been reached when the physiological and the psychological, the objective and the subjective, are actually united, when the tormenting conflicts or contradictions between my consciousness and my body will have been factually resolved or discarded.

I do not think that G. H. Hardy was talking nonsense when he insisted that the mathematician was discovering rather than creating, nor was it wholly nonsense for Kepler to exult that he was thinking God's thoughts after him. The world for me is a necessary system, and in the degree to which the thinker can surrender his thought to that system and follow it, he is in a sense participating in that which is timeless or eternal.

I started studying law, but this I could stand just for one semester. I couldn't stand more. Then I studied languages and literature for two years. After two years I passed an examination with the result I have a teaching certificate for Latin and Hungarian for the lower classes of the gymnasium, for kids from 10 to 14. I never made use of this teaching certificate. And then I came to philosophy, physics, and mathematics. In fact, I came to mathematics indirectly. I was really more interested in physics and philosophy and thought about those. It is a little shortened but not quite wrong to say: I thought I am not good enough for physics and I am too good for philosophy. Mathematics is in between.

I thank you for your Expt on the Hedge Hog; but why do you ask me such a question, by way of solving it. I think your solution is just; but why think, why not try the Expt.
[Often seen, without context, briefly as: But why think, why not try the experiment?']

I was sitting in a chair in the patent office at Bern when all of a sudden a thought occurred to me: “If a person falls freely he will not feel his own weight.” I was startled. This simple thought made a deep impression on me. It impelled me toward a theory of gravitation.

If human thought is a growth, like all other growths, its logic is without foundation of its own, and is only the adjusting constructiveness of all other growing things. A tree cannot find out, as it were, how to blossom, until comes blossom-time. A social growth cannot find out the use of steam engines, until comes steam-engine-time.

If it is a terrifying thought that life is at the mercy of the multiplication of these minute bodies [microbes], it is a consoling hope that Science will not always remain powerless before such enemies...

If mankind is to profit freely from the small and sporadic crop of the heroically gifted it produces, it will have to cultivate the delicate art of handling ideas. Psychology is now able to tell us with reasonable assurance that the most influential obstacle to freedom of thought and to new ideas is fear; and fear which can with inimitable art disguise itself as caution, or sanity, or reasoned skepticism, or on occasion even as courage.

If there is no God, we are just molecules in motion, and we have no sense and no mind; we are just random firings of chemical in the brain. If our minds are composed only of physical matter, then our thoughts are, as Doug Wilson wittily quipped in his debate with atheist Dan Barker, just “brain gas.”

If we put together all that we have learned from anthropology and ethnography about primitive men and primitive society, we perceive that the first task of life is to live. Men begin with acts, not with thoughts.

If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.

If you want to find out anything from the theoretical physicists about the methods they use, I advise you to stick closely to one principle: don't listen to their words, fix your attention on their deeds. To him who is a discoverer in this field the products of his imagination appear so necessary and natural that he regards them, and would like to have them regarded by others, not as creations of thought but as given realities.

In America we can say what we think, and even if we can't think, we can say it anyhow.

In England, more than in any other country, science is felt rather than thought. … A defect of the English is their almost complete lack of systematic thinking. Science to them consists of a number of successful raids into the unknown.

In modern thought, (if not in fact)
Nothing is that doesn't act, So that is reckoned wisdom which
Describes the scratch but not the itch.

In our search after the Knowledge of Substances, our want of Ideas, that are suitable to such a way of proceeding, obliges us to a quite different method. We advance not here, as in the other (where our abstract Ideas are real as well as nominal Essences) by contemplating our Ideas, and considering their Relations and Correspondencies; that helps us very little, for the Reasons, and in another place we have at large set down. By which, I think it is evident, that Substances afford Matter of very little general Knowledge; and the bare Contemplation of their abstract Ideas, will carry us but a very little way in the search of Truth and Certainty. What then are we to do for the improvement of our Knowledge in Substantial beings? Here we are to take a quite contrary Course, the want of Ideas of their real essences sends us from our own Thoughts, to the Things themselves, as they exist.

In the new era, thought itself will be transmitted by radio.

In the world of human thought generally, and in physical science particularly, the most important and fruitful concepts are those to which it is impossible to attach a well-defined meaning.

Interestingly, according to modern astronomers, space is finite. This is a very comforting thought—particularly for people who can never remember where they have left things.

Invention is an Heroic thing, and plac'd above the reach of a low, and vulgar Genius. It requires an active, a bold, a nimble, a restless mind: a thousand difficulties must be contemn'd with which a mean heart would be broken: many attempts must be made to no purpose: much Treasure must sometimes be scatter'd without any return: much violence, and vigour of thoughts must attend it: some irregularities, and excesses must be granted it, that would hardly be pardon'd by the severe Rules of Prudence.

Is evolution a theory, a system or a hypothesis? It is much more: it is a general condition to which all theories, all hypotheses, all systems must bow and which they must satisfy henceforth if they are to be thinkable and true. Evolution is a light illuminating all facts, a curve that all lines must follow. ... The consciousness of each of us is evolution looking at itself and reflecting upon itself....Man is not the center of the universe as once we thought in our simplicity, but something much more wonderful—the arrow pointing the way to the final unification of the world in terms of life. Man alone constitutes the last-born, the freshest, the most complicated, the most subtle of all the successive layers of life. ... The universe has always been in motion and at this moment continues to be in motion. But will it still be in motion tomorrow? ... What makes the world in which we live specifically modern is our discovery in it and around it of evolution. ... Thus in all probability, between our modern earth and the ultimate earth, there stretches an immense period, characterized not by a slowing-down but a speeding up and by the definitive florescence of the forces of evolution along the line of the human shoot.

It is impossible not to feel stirred at the thought of the emotions of man at certain historic moments of adventure and discovery—Columbus when he first saw the Western shore, Pizarro when he stared at the Pacific Ocean, Franklin when the electric spark came from the string of his kite, Galileo when he first turned his telescope to the heavens. Such moments are also granted to students in the abstract regions of thought, and high among them must be placed the morning when Descartes lay in bed and invented the method of co-ordinate geometry.

It is rigid dogma that destroys truth; and, please notice, my emphasis is not on the dogma, but on the rigidity. When men say of any question, 'This is all there is to be known or said of the subject; investigation ends here,' that is death. It may be that the mischief comes not from the thinker but for the use made of his thinking by late-comers. Aristotle, for example, gave us out scientific technique ... yet his logical propositions, his instruction in sound reasoning which was bequeathed to Europe, are valid only within the limited framework of formal logic, and, as used in Europe, they stultified the minds of whole generations of mediaeval Schoolmen. Aristotle invented science, but destroyed philosophy.

It is the lone worker who makes the first advance in a subject: the details may be worked out by a team, but the prime idea is due to the enterprise, thought, and perception of an individual.

It was my Uncle George who discovered that alcohol was a food well in advance of modern medical thought.

It's a good thing to turn your mind upside down now and then, like an hour-glass, to let the particles run the other way.

Just as a physicist has to examine the telescope and galvanometer with which he is working; has to get a clear conception of what he can attain with them, and how they may deceive him; so, too, it seemed to me necessary to investigate likewise the capabilities of our power of thought.

Know then thyself, presume not God to scan;
The proper study of Mankind is Man.
Plac'd on this isthmus of a middle state,
A being darkly wise, and rudely great:
With too much knowledge for the Sceptic side,
With too much weakness for the Stoic's pride,
He hangs between; in doubt to act, or rest;
In doubt to deem himself a God, or Beast;
In doubt his Mind or Body to prefer,
Born but to die, and reas'ning but to err;
Alike in ignorance, his reason such,
Whether he thinks too little, or too much:
Chaos of Thought and Passion, all confus'd;
Still by himself abus'd, or disabus'd;
Created half to rise, and half to fall;
Great lord of all things, yet a prey to all;
Sole judge of Truth, in endless Error hurl'd:
The glory, jest, and riddle of the world!
... Superior beings, when of late they saw
A mortal Man unfold all Nature's law,
Admir'd such wisdom in an earthly shape,
And shew'd a NEWTON as we shew an Ape.

Lecturing after a fashion is easy enough ; teaching is a very different affair. ... The transmission of ideas from one mind to another, in a simple unequivocal form, is not always easy ; but in teaching, the object is not merely to convey the idea, but to give a lively and lasting impression; something that should not merely cause the retention of the image, but in such connection as to excite another process, ' thought.'

Let him look at that dazzling light hung aloft as an eternal lamp to lighten the universe; let him behold the earth, a mere dot compared with the vast circuit which that orb describes, and stand amazed to find that the vast circuit itself is but a very fine point compared with the orbit traced by the stars as they roll their course on high. But if our vision halts there, let imagination pass beyond; it will fail to form a conception long before Nature fails to supply material. The whole visible world is but an imperceptible speck in the ample bosom of Nature. No notion comes near it. Though we may extend our thought beyond imaginable space, yet compared with reality we bring to birth mere atoms. Nature is an infinite sphere whereof the centre is everywhere, the circumference nowhere. In short, imagination is brought to silence at the thought, and that is the most perceptible sign of the all-power of God.
Let man reawake and consider what he is compared with the reality of things; regard himself lost in this remote corner of Nature; and from the tiny cell where he lodges, to wit the Universe, weigh at their true worth earth, kingdoms, towns, himself. What is a man face to face with infinity?

Let him look at that dazzling light hung aloft as an eternal lamp to lighten the universe; let him behold the earth, a mere dot compared with the vast circuit which that orb describes, and stand amazed to find that the vast circuit itself is but a very fine point compared with the orbit traced by the stars as they roll their course on high. But if our vision halts there, let imagination pass beyond; it will fail to form a conception long before Nature fails to supply material. The whole visible world is but an imperceptible speck in the ample bosom of Nature. No notion comes near it. Though we may extend our thought beyond imaginable space, yet compared with reality we bring to birth mere atoms. Nature is an infinite sphere whereof the centre is everywhere, the circumference nowhere. In short, imagination is brought to silence at the thought, and that is the most perceptible sign of the all-power of God.
Let man reawake and consider what he is compared with the reality of things; regard himself lost in this remote corner of Nature; and from the tiny cell where he lodges, to wit the Universe, weigh at their true worth earth, kingdoms, towns, himself. What is a man face to face with infinity?

Let nobody be afraid of true freedom of thought. Let us be free in thought and criticism; but, with freedom, we are bound to come to the conclusion that science is not antagonistic to religion, but a help to it.

Life through many long periods has been manifested in a countless host of varying structures, all circumscribed by one general plan, each appointed to a definite place, and limited to an appointed duration. On the whole the earth has been thus more and more covered by the associated life of plants and animals, filling all habitable space with beings capable of enjoying their own existence or ministering to the enjoyment of others; till finally, after long preparation, a being was created capable of the wonderful power of measuring and weighing all the world of matter and space which surrounds him, of treasuring up the past history of all the forms of life, and considering his own relation to the whole. When he surveys this vast and co-ordinated system, and inquires into its history and origin, can he be at a loss to decide whether it be a work of Divine thought and wisdom, or the fortunate offspring of a few atoms of matter, warmed by the anima mundi, a spark of electricity, or an accidental ray of sunshine?

Logic is a wonderful thing but doesn't always beat actual thought.

Logic is not concerned with human behavior in the same sense that physiology, psychology, and social sciences are concerned with it. These sciences formulate laws or universal statements which have as their subject matter human activities as processes in time. Logic, on the contrary, is concerned with relations between factual sentences (or thoughts). If logic ever discusses the truth of factual sentences it does so only conditionally, somewhat as follows: if such-and-such a sentence is true, then such-and-such another sentence is true. Logic itself does not decide whether the first sentence is true, but surrenders that question to one or the other of the empirical sciences.

Logic issues in tautologies, mathematics in identities, philosophy in definitions; all trivial, but all part of the vital work of clarifying and organising our thought.

Look round the world, contemplate the whole and every part of it: you will find it to be nothing but one great machine, subdivided into an infinite number of lesser machines, which again admit of subdivisions to a degree beyond what human senses and faculties can trace and explain. All these various machines, and even their most minute parts, are adjusted to each other with an accuracy which ravishes into admiration all men who have ever contemplated them. The curious adapting of means to ends, throughout all nature, resembles exactly, though it much exceeds, the productions of human contrivance-of human design, thought, wisdom, and intelligence.

Look wise, say nothing, and grunt. Speech was given to conceal thought.

Man carries the world in his head, the whole astronomy and chemistry suspended in a thought. Because the history of nature is charactered in his brain, therefore he is the prophet and discoverer of her secrets. Every known fact in natural science was divined by the presentiment of somebody, before it was actually verified.

Measure, time and number are nothing but modes of thought or rather of imagination.

Memory is to mind as viscosity is to protoplasm it gives a kind of tenacity to thought—a kind of pied à terre from which it can, and without it could not, advance.

Men give me some credit for genius. All the genius I have lies in this: When I have a subject in hand, I study it profoundly. Day and night it is before me. I explore it in all its bearings. My mind becomes pervaded with it. Then the effort which I have made is what people are pleased to call the fruit of genius. It is the fruit of labor and thought.

My guess is that well over eighty per cent. of the human race goes through life without having a single original thought..

New scientific ideas never spring from a communal body, however organized, but rather from the head of an individually inspired researcher who struggles with his problems in lonely thought and unites all his thought on one single point which is his whole world for the moment.

Newton was not the first of the age of reason. He was the last of the magicians, the last of the Babylonians and Sumerians ... Isaac Newton, a posthumous child born with no father on Christmas Day, 1642, was the last wonder child to whom the Magi could do sincere and appropriate homage... Why do I call him a magician? Because he looked on the whole universe and all that is in it as a riddle, as a secret which could be read by applying pure thought to certain evidence, certain mystic clues which God had laid about the world to allow a sort of philosopher's treasure hunt to the esoteric brotherhood... He regarded the Universe as a cryptogram set by the Almighty—just as he himself wrapt the discovery of the calculus in a cryptogram when he communicated with Leibniz. By pure thought, by concentration of mind, the riddle, he believed, would be revealed to the initiate.

One day we shall certainly 'reduce' thought experimentally to molecular and chemical motions in the brain; but does that exhaust the essence of thought?

One of the principal obstacles to the rapid diffusion of a new idea lies in the difficulty of finding suitable expression to convey its essential point to other minds. Words may have to be strained into a new sense, and scientific controversies constantly resolve themselves into differences about the meaning of words. On the other hand, a happy nomenclature has sometimes been more powerful than rigorous logic in allowing a new train of thought to be quickly and generally accepted.

Our fathers thought the world was flat, and we think it is round, not because the earth has changed its shape, but because men have revised their thoughts.

Physiological response to thinking and to pain is the same; and man is not given to hurting himself.

Profundity of thought belongs to youth, clarity of thought to old age.

Regardless of communication between man and man, speech is a necessary condition for the thinking of the individual in solitary seclusion. In appearance, however, language develops only socially, and man understands himself only once he has tested the intelligibility of his words by trial upon others.

Research is to see what everybody has seen and think what nobody has thought.

Science itself, therefore, may be regarded as a minimal problem, consisting of the completest possible presentment of facts with the least possible expenditure of thought.

Science knows no country because knowledge belongs to humanity, and is the torch which illuminates the world. Science is the highest personification of the nation because that nation will remain the first which carries the furthest the works of thought and intelligence.

Science moves, but slowly, slowly, creeping on from point to point. ...
Yet I doubt not through the ages one increasing purpose runs,
And the thoughts of men are widened with the process of the suns. ...
Knowledge comes, but wisdom lingers.

Sin is commitable in thought, word or deed; so is virtue.

Society exists through a process of transmission quite as much as biological life. This transmission occurs by means of communication of habits of doing, thinking, and feeling from the older to the younger.

Solitude in the presence of natural beauty and grandeur is the cradle of thought and aspirations which are not only good for the individual, but which society can ill do without.

Some experience of popular lecturing had convinced me that the necessity of making things plain to uninstructed people, was one of the very best means of clearing up the obscure corners in one's own mind.

Some things mankind can finish and be done with, but not ... science, that persists, and changes from ancient Chaldeans studying the stars to a new telescope with a 200-inch reflector and beyond; not religion, that persists, and changes from old credulities and world views to new thoughts of God and larger apprehensions of his meaning.

The advancement of science is slow; it is effected only by virtue of hard work and perseverance. And when a result is attained, should we not in recognition connect it with the efforts of those who have preceded us, who have struggled and suffered in advance? Is it not truly a duty to recall the difficulties which they vanquished, the thoughts which guided them; and how men of different nations, ideas, positions, and characters, moved solely by the love of science, have bequeathed to us the unsolved problem? Should not the last comer recall the researches of his predecessors while adding in his turn his contribution of intelligence and of labor? Here is an intellectual collaboration consecrated entirely to the search for truth, and which continues from century to century.
[Respecting how the work of prior researchers had enabled his isolation of fluorine.]

The brain seems a thoroughfare for nerve-action passing its way to the motor animal. It has been remarked that Life's aim is an act not a thought. To-day the dictum must be modified to admit that, often, to refrain from an act is no less an act than to commit one, because inhibition is coequally with excitation a nervous activity.

The discovery of an interaction among the four hemes made it obvious that they must be touching, but in science what is obvious is not necessarily true. When the structure of hemoglobin was finally solved, the hemes were found to lie in isolated pockets on the surface of the subunits. Without contact between them how could one of them sense whether the others had combined with oxygen? And how could as heterogeneous a collection of chemical agents as protons, chloride ions, carbon dioxide, and diphosphoglycerate influence the oxygen equilibrium curve in a similar way? It did not seem plausible that any of them could bind directly to the hemes or that all of them could bind at any other common site, although there again it turned out we were wrong. To add to the mystery, none of these agents affected the oxygen equilibrium of myoglobin or of isolated subunits of hemoglobin. We now know that all the cooperative effects disappear if the hemoglobin molecule is merely split in half, but this vital clue was missed. Like Agatha Christie, Nature kept it to the last to make the story more exciting. There are two ways out of an impasse in science: to experiment or to think. By temperament, perhaps, I experimented, whereas Jacques Monod thought.

The fact that astronomies change while the stars abide is a true analogy of every realm of human life and thought, religion not least of all.

The fear of meeting the opposition of envy, or the illiberality of ignorance is, no doubt, the frequent cause of preventing many ingenious men from ushering opinions into the world which deviate from common practice. Hence for want of energy, the young idea is shackled with timidity and a useful thought is buried in the impenetrable gloom of eternal oblivion.

The first effect of the mind growing cultivated is that processes once multiple get to be performed in a single act. Lazarus has called this the progressive “condensation” of thought. ... Steps really sink from sight. An advanced thinker sees the relations of his topics is such masses and so instantaneously that when he comes to explain to younger minds it is often hard ... Bowditch, who translated and annotated Laplace's Méchanique Céleste, said that whenever his author prefaced a proposition by the words “it is evident,” he knew that many hours of hard study lay before him.

The genius of Man in our time has gone into jet-propulsion, atom-splitting, penicillin-curing, etc. There is left none over for works of imagination; of spiritual insight or mystical enlightenment. I asked for bread and was given a tranquilizer. It is important to recognize that in our time man has not written one word, thought one thought, put two notes or two bricks together, splashed color on to canvas or concrete into space, in a manner which will be of any conceivable imaginative interest to posterity.

The highest possible stage in moral culture is when we recognize that we ought to control our thoughts.

The important thing in science is not so much to obtain new facts as to discover new ways of thinking about them.

The influence (for good or ill) of Plato's work is immeasurable. Western thought, one might say, has been Platonic or anti-Platonic, but hardly ever non-Platonic.

The influence of modern physics goes beyond technology. It extends to the realm of thought and culture where it has led to a deep revision in man's conception of the universe and his relation to it

The most noble and profitable invention of all other, was that of SPEECH, consisting of Names or Appellations, and their Connexion; whereby men register their Thoughts; recall them when they are past; and also declare them one to another for mutuall utility and conversation; without which, there had been amongst men, neither Commonwealth, nor Society, nor Contract, nor Peace, no more than amongst Lyons, Bears, and Wolves.

The new mathematics is a sort of supplement to language, affording a means of thought about form and quantity and a means of expression, more exact, compact, and ready than ordinary language. The great body of physical science, a great deal of the essential facts of financial science, and endless social and political problems are only accessible and only thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood that for complete initiation as an efficient citizen of the great complex world-wide States that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and write.

The object of geometry in all its measuring and computing, is to ascertain with exactness the plan of the great Geometer, to penetrate the veil of material forms, and disclose the thoughts which lie beneath them? When our researches are successful, and when a generous and heaven-eyed inspiration has elevated us above humanity, and raised us triumphantly into the very presence, as it were, of the divine intellect, how instantly and entirely are human pride and vanity repressed, and, by a single glance at the glories of the infinite mind, are we humbled to the dust.

The old metaphysical prejudice that man 'always thinks' has not yet entirely disappeared. I am myself inclined to hold that man really thinks very little and very seldom.

The only reason some people get lost in thought is because it's unfamiliar territory.

The power of mathematics rests on its evasion of all unnecessary thought and on its wonderful saving of mental operations.

The progress of science depends less than is usually believed on the efforts and performance of the individual genius ... many important discoveries have been made by men of ordinary talents, simply because chance had made them, at the proper time and in the proper place and circumstances, recipients of a body of doctrines, facts and techniques that rendered almost inevitable the recognition of an important phenomenon. It is surprising that some historian has not taken malicious pleasure in writing an anthology of 'one discovery' scientists. Many exciting facts have been discovered as a result of loose thinking and unimaginative experimentation, and described in wrappings of empty words. One great discovery does not betoken a great scientist; science now and then selects insignificant standard bearers to display its banners.

The publication in 1859 of the Origin of Species by Charles Darwin made a marked epoch in my own mental development, as it did in that of human thought generally. Its effect was to demolish a multitude of dogmatic barriers by a single stroke, and to arouse a spirit of rebellion against all ancient authorities whose positive and unauthenticated statements were contradicted by modern science.

The rudest numerical scales, such as that by which the mineralogists distinguish different degrees of hardness, are found useful. The mere counting of pistils and stamens sufficed to bring botany out of total chaos into some kind of form. It is not, however, so much from counting as from measuring, not so much from the conception of number as from that of continuous quantity, that the advantage of mathematical treatment comes. Number, after all, only serves to pin us down to a precision in our thoughts which, however beneficial, can seldom lead to lofty conceptions, and frequently descend to pettiness.

The task is ... not so much to see what no one has yet seen; but to think what nobody has yet thought, about that which everybody sees.

The universe is one at God's thoughts.

The velocity of light occupies an extraordinary place in modern physics. It is lèse-majesté to make any criticism of the velocity of light. It is a sacred cow within a sacred cow, and it is just about the Absolutest Absolute in the history of human thought.

There are some men who are counted great because they represent the actuality of their own age, and mirror it as it is. Such an one was Voltaire, of whom it was epigrammatically said: 'he expressed everybody's thoughts better than anyone.' But there are other men who attain greatness because they embody the potentiality of their own day and magically reflect the future. They express the thoughts which will be everybody's two or three centuries after them. Such as one was Descartes.

There are wavelengths that people cannot see, there are sounds that people cannot hear, and maybe computers have thoughts that people cannot think.

There can be no thought of finishing, for aiming at the stars, both literally and figuratively, is the work of generations, but no matter how much progress one makes there is always the thrill of just beginning.

There is in the chemist a form of thought by which all ideas become visible in the mind as strains of an imagined piece of music. This form of thought is developed in Faraday in the highest degree, whence it arises that to one who is not acquainted with this method of thinking, his scientific works seem barren and dry, and merely a series of researches strung together, while his oral discourse when he teaches or explains is intellectual, elegant, and of wonderful clearness.

There is, however, no genius so gifted as not to need control and verification. ... [T]he brightest flashes in the world of thought are incomplete until they have been proved to have their counterparts in the world of fact. Thus the vocation of the true experimentalist may be defined as the continued exercise of spiritual insight, and its incessant correction and realisation. His experiments constitute a body, of which his purified intuitions are, as it were, the soul.

Thinking is one thing no one has ever been able to tax.

Those who take refuge behind theological barbed wire fences, quite often wish they could have more freedom of thought, but fear the change to the great ocean of truth as they would a cold bath.

Those [scientists] who dislike entertaining contradictory thoughts are unlikely to enrich their science with new ideas.

Thought and science follow their own law of development; they are slowly elaborated in the growth and forward pressure of humanity, in what Shakespeare calls
...The prophetic soul,
Of the wide world dreaming on things to come.

Thought experiment is in any case a necessary precondition for physical experiment. Every experimenter and inventor must have the planned arrangement in his head before translating it into fact.

Thought isn't a form of energy. So how on Earth can it change material processes? That question has still not been answered.

Thought once awakened does not again slumber; unfolds itself into a System of Thought; grows, in man after man, generation after generation,—till its full stature is reached, and such System of Thought can grow no farther, and must give place to another.

Thoughts without content are empty, intuitions without concepts are blind... The understanding can intuit nothing, the senses can think nothing. Only through their union can knowledge arise.

We must also teach science not as the bare body of fact, but more as human endeavor in its historic context—in the context of the effects of scientific thought on every kind of thought. We must teach it as an intellectual pursuit rather than as a body of tricks.

We see not only thought as participating in evolution as an anomaly or as an epiphenomenon; but evolution as so reducible to and identifiable with a progress towards thought that the movement of our souls expresses and measures the very stages of progress of evolution itself. Man discovers that he is nothing else than evolution become conscious of itself.

We [may] answer the question: “Why is snow white?” by saying, “For the same reason that soap-suds or whipped eggs are white”—in other words, instead of giving the reason for a fact, we give another example of the same fact. This offering a similar instance, instead of a reason, has often been criticised as one of the forms of logical depravity in men. But manifestly it is not a perverse act of thought, but only an incomplete one. Furnishing parallel cases is the necessary first step towards abstracting the reason imbedded in them all.

What is a scientist?… We give the name scientist to the type of man who has felt experiment to be a means guiding him to search out the deep truth of life, to lift a veil from its fascinating secrets, and who, in this pursuit, has felt arising within him a love for the mysteries of nature, so passionate as to annihilate the thought of himself.

What is best in mathematics deserves not merely to be learnt as a task, but to assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement.

When ever we turn in these days of iron, steam and electricity we find that Mathematics has been the pioneer. Were its back bone removed, our material civilization would inevitably collapse. Modern thought and belief would have been altogether different, had Mathematics not made the various sciences exact.

When I saw the alpha-helix and saw what a beautiful, elegant structure it was, I was thunderstruck and was furious with myself for not having built this, but on the other hand, I wondered, was it really right?
So I cycled home for lunch and was so preoccupied with the turmoil in my mind that didn’t respond to anything. Then I had an idea, so I cycled back to the lab. I realized that I had a horse hair in a drawer. I set it up on the X-ray camera and gave it a two hour exposure, then took the film to the dark room with my heart in my mouth, wondering what it showed, and when I developed it, there was the 1.5 angstrom reflection which I had predicted and which excluded all structures other than the alpha-helix.
So on Monday morning I stormed into my professor’s office, into Bragg’s office and showed him this, and Bragg said, 'Whatever made you think of that?' And I said, 'Because I was so furious with myself for having missed that beautiful structure.' To which Bragg replied coldly, 'I wish I had made you angry earlier.'

When our thoughts—which bring actions—are filled with hate against anyone, Negro or white, we are in a living hell. That is as real as hell will ever be.
While hate for our fellow man puts us in a living hell, holding good thoughts for them brings us an opposite state of living, one of happiness, success, peace. We are then in heaven.

Whether one show one's self a man of genius in science or compose a song, the only point is, whether the thought, the discovery, the deed, is living and can live on.

Will fluorine ever have practical applications?
It is very difficult to answer this question. I may, however, say in all sincerity that I gave this subject little thought when I undertook my researches, and I believe that all the chemists whose attempts preceded mine gave it no more consideration.
A scientific research is a search after truth, and it is only after discovery that the question of applicability can be usefully considered.

With thought comprising a non-computational element, computers can never do what we human beings can.

With time, I attempt to develop hypotheses that are more risky. I agree with [Karl] Popper that scientists need to be interested in risky hypotheses because risky hypotheses advance science by producing interesting thoughts and potential falsifications of theories (of course, personally, we always strive for verification—we love our theories after all; but we should be ready to falsify them as well.

Without the sensuous faculty no object would be given to us, without understanding no object would be thought. Thoughts without content are void, intuitions without conceptions, blind.

Without writing, the literate mind would not and could not think as it does, not only when engaged in writing but normally even when it is composing its thoughts in oral form. More than any other single invention writing has transformed human consciousness.

Words well up freely from the breast, without necessity or intent, and there may well have been no wandering horde in any desert that did not already have its own songs. For man, as a species, is a singing creature, though the notes, in his case, are also coupled with thought.

[An engineer's] invention causes things to come into existence from ideas, makes world conform to thought; whereas science, by deriving ideas from observation, makes thought conform to existence.

[D]iscovery should come as an adventure rather than as the result of a logical process of thought. Sharp, prolonged thinking is necessary that we may keep on the chosen road but it does not itself necessarily lead to discovery. The investigator must be ready and on the spot when the light comes from whatever direction.

[Man] ... his origin, his growth, his hopes and fears, his loves and his beliefs are but the outcome of accidental collocations of atoms; that no fire, no heroism, no intensity of thought and feeling can preserve an individual life beyond the grave; that all the labour of the ages, all the devotion, all the inspiration, all the noonday brightness of human genius are destined to extinction in the vast death of the solar system, and that the whole temple of Man's achievement must inevitably be buried beneath the debris of a universe in ruins...