Greatest Quotes (330 quotes)
… the icy layers of the upper atmosphere contain conundrums enough to be worthy of humanity's greatest efforts.
[1665-07-31] ...Thus we end this month, as I said, after the greatest glut of content that ever I had; only, under some difficulty because of the plague, which grows mightily upon us, the last week being about 1700 or 1800 of the plague. ...
[About mathematicians’ writings] Extreme external elegance, sometimes a somewhat weak skeleton of conclusions characterizes the French; the English, above all Maxwell, are distinguished by the greatest dramatic bulk.
[About the structure of DNA] [T]he whole business was like a child's toy that you could buy at the dime store, all built in this wonderful way that you could explain in Life magazine so that really a five-year-old can understand what's going on...This was the greatest surprise for everyone.
[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.”
[Heisenberg's seminal 1925 paper initiating quantum mechanics marked] one of the great jumps—perhaps the greatest—in the development of twentieth century physics.
[It] is the little causes, long continued, which are considered as bringing about the greatest changes of the earth.
[O]ur own existence once presented the greatest of all mysteries, but … it is a mystery no longer because it is solved. Darwin and Wallace solved it … I was surprised that so many people seemed not only unaware of the elegant and beautiful solution to this deepest of problems but, incredibly, in many cases actually unaware that there was a problem in the first place!
[On the 11th day of November 1572], in the evening, after sunset, when, according to my habit, I was contemplating the stars in a clear sky, I noticed that a new and unusual star, surpassing all others in brilliancy, was shining almost directly over my head; and since I had, almost from boyhood, known all the stars of the heavens perfectly (there is no great difficulty in gaining that knowledge), it was quite evident to me that there had never before been any star in that place in the sky, even the smallest, to say nothing of a star so conspicuously bright as this. I was so astonished at this sight that I was not ashamed to doubt the trustworthiness of my own eyes. But when I observed that others, too, on having the place pointed out to them, could see that there was a star there, I had no further doubts. A miracle indeed, either the greatest of all that have occurred in the whole range of nature since the beginning of the world, or one certainly that is to be classed with those attested by the Holy Oracles.
[The ancient monuments] were all dwarfs in size and pigmies in spirit beside this mighty Statue of Liberty, and its inspiring thought. Higher than the monument in Trafalgar Square which commemorates the victories of Nelson on the sea; higher than the Column Vendome, which perpetuates the triumphs of Napoleon on the land; higher than the towers of the Brooklyn Bridge, which exhibit the latest and greatest results of science, invention, and industrial progress, this structure rises toward the heavens to illustrate an idea ... which inspired the charter in the cabin of the Mayflower and the Declaration of Independence from the Continental Congress.
[The famous attack of Sir William Hamilton on the tendency of mathematical studies] affords the most express evidence of those fatal lacunae in the circle of his knowledge, which unfitted him for taking a comprehensive or even an accurate view of the processes of the human mind in the establishment of truth. If there is any pre-requisite which all must see to be indispensable in one who attempts to give laws to the human intellect, it is a thorough acquaintance with the modes by which human intellect has proceeded, in the case where, by universal acknowledgment, grounded on subsequent direct verification, it has succeeded in ascertaining the greatest number of important and recondite truths. This requisite Sir W. Hamilton had not, in any tolerable degree, fulfilled. Even of pure mathematics he apparently knew little but the rudiments. Of mathematics as applied to investigating the laws of physical nature; of the mode in which the properties of number, extension, and figure, are made instrumental to the ascertainment of truths other than arithmetical or geometrical—it is too much to say that he had even a superficial knowledge: there is not a line in his works which shows him to have had any knowledge at all.
[The] humanization of mathematical teaching, the bringing of the matter and the spirit of mathematics to bear not merely upon certain fragmentary faculties of the mind, but upon the whole mind, that this is the greatest desideratum is. I assume, beyond dispute.
[Thomas Henry] Huxley, I believe, was the greatest Englishman of the Nineteenth Century—perhaps the greatest Englishman of all time. When one thinks of him, one thinks inevitably of such men as Goethe and Aristotle. For in him there was that rich, incomparable blend of intelligence and character, of colossal knowledge and high adventurousness, of instinctive honesty and indomitable courage which appears in mankind only once in a blue moon. There have been far greater scientists, even in England, but there has never been a scientist who was a greater man.
[Werhner von Braun] is a human leader whose eyes and thoughts have always been turned toward the stars. It would be foolish to assign rocketry success to one person totally. Components must necessarily be the work of many minds; so must successive stages of development. But because Wernher von Braun joins technical ability, passionate optimism, immense experience and uncanny organizing ability in the elusive power to create a team, he is the greatest human element behind today’s rocketry success
The Redwoods
Here, sown by the Creator's hand,
In serried ranks, the Redwoods stand;
No other clime is honored so,
No other lands their glory know.
The greatest of Earth's living forms,
Tall conquerors that laugh at storms;
Their challenge still unanswered rings,
Through fifty centuries of kings.
The nations that with them were young,
Rich empires, with their forts far-flung,
Lie buried now—their splendor gone;
But these proud monarchs still live on.
So shall they live, when ends our day,
When our crude citadels decay;
For brief the years allotted man,
But infinite perennials' span.
This is their temple, vaulted high,
And here we pause with reverent eye,
With silent tongue and awe-struck soul;
For here we sense life's proper goal;
To be like these, straight, true and fine,
To make our world, like theirs, a shrine;
Sink down, oh traveler, on your knees,
God stands before you in these trees.
Here, sown by the Creator's hand,
In serried ranks, the Redwoods stand;
No other clime is honored so,
No other lands their glory know.
The greatest of Earth's living forms,
Tall conquerors that laugh at storms;
Their challenge still unanswered rings,
Through fifty centuries of kings.
The nations that with them were young,
Rich empires, with their forts far-flung,
Lie buried now—their splendor gone;
But these proud monarchs still live on.
So shall they live, when ends our day,
When our crude citadels decay;
For brief the years allotted man,
But infinite perennials' span.
This is their temple, vaulted high,
And here we pause with reverent eye,
With silent tongue and awe-struck soul;
For here we sense life's proper goal;
To be like these, straight, true and fine,
To make our world, like theirs, a shrine;
Sink down, oh traveler, on your knees,
God stands before you in these trees.
Amicus Plato amicus Aristoteles magis amica verita.
Plato is my friend, Aristotle is my friend, but my greatest friend is truth.
Plato is my friend, Aristotle is my friend, but my greatest friend is truth.
He who doth with the greatest exactness imaginable, weigh every individual thing that shall or hath hapned to his Patient, and may be known from the Observations of his own, or of others, and who afterwards compareth all these with one another, and puts them in an opposite view to such Things as happen in a healthy State; and lastly, from all this with the nicest and severest bridle upon his reasoning faculty riseth to the knowledge of the very first Cause of the Disease, and of the Remedies fit to remove them; He, and only He deserveth the Name of a true Physician.
La théorie est l’hypothèse vérifiée, après qu’elle a été soumise au contrôle du raisonnement et de la critique expérimentale. La meilleure théorie est celle qui a été vérifiée par le plus grand nombre de faits. Mais une théorie, pour rester bonne, doit toujours se modifier avec les progrès de la science et demeurer constamment soumise à la vérification et à la critique des faits nouveaux qui apparaissent.
A theory is a verified hypothesis, after it has been submitted to the control of reason and experimental criticism. The soundest theory is one that has been verified by the greatest number of facts. But to remain valid, a theory must be continually altered to keep pace with the progress of science and must be constantly resubmitted to verification and criticism as new facts appear.
A theory is a verified hypothesis, after it has been submitted to the control of reason and experimental criticism. The soundest theory is one that has been verified by the greatest number of facts. But to remain valid, a theory must be continually altered to keep pace with the progress of science and must be constantly resubmitted to verification and criticism as new facts appear.
~~[Misattributed]~~ The greatest enemy of progress is the illusion of knowledge.
230(231-1) ... is the greatest perfect number known at present, and probably the greatest that ever will be discovered; for; as they are merely curious without being useful, it is not likely that any person will attempt to find a number beyond it.
A hundred years ago … an engineer, Herbert Spencer, was willing to expound every aspect of life, with an effect on his admiring readers which has not worn off today.
Things do not happen quite in this way nowadays. This, we are told, is an age of specialists. The pursuit of knowledge has become a profession. The time when a man could master several sciences is past. He must now, they say, put all his efforts into one subject. And presumably, he must get all his ideas from this one subject. The world, to be sure, needs men who will follow such a rule with enthusiasm. It needs the greatest numbers of the ablest technicians. But apart from them it also needs men who will converse and think and even work in more than one science and know how to combine or connect them. Such men, I believe, are still to be found today. They are still as glad to exchange ideas as they have been in the past. But we cannot say that our way of life is well-fitted to help them. Why is this?
Things do not happen quite in this way nowadays. This, we are told, is an age of specialists. The pursuit of knowledge has become a profession. The time when a man could master several sciences is past. He must now, they say, put all his efforts into one subject. And presumably, he must get all his ideas from this one subject. The world, to be sure, needs men who will follow such a rule with enthusiasm. It needs the greatest numbers of the ablest technicians. But apart from them it also needs men who will converse and think and even work in more than one science and know how to combine or connect them. Such men, I believe, are still to be found today. They are still as glad to exchange ideas as they have been in the past. But we cannot say that our way of life is well-fitted to help them. Why is this?
A sense of the unknown has always lured mankind and the greatest of the unknowns of today is outer space. The terrors, the joys and the sense of accomplishment are epitomized in the space program.
After a certain high level of technical skill is achieved, science and art tend to coalesce in esthetics, plasticity, and form. The greatest scientists are always artists as well.
Alfred Nobel - pitiable half-creature, should have been stifled by humane doctor when he made his entry yelling into life. Greatest merits: Keeps his nails clean and is never a burden to anyone. Greatest fault: Lacks family, cheerful spirits, and strong stomach. Greatest and only petition: Not to be buried alive. Greatest sin: Does not worship Mammon. Important events in his life: None.
All admit that the mountains of the globe are situated mostly along the border regions of the continents (taking these regions as 300 to 1000 miles or more in width), and that over these same areas the sedimentary deposits have, as a general thing, their greatest thickness. At first thought, it would seem almost incredible that the upliftings of mountains, whatever their mode of origin, should have taken place just where the earth’s crust, through these sedimentary accumulations, was the thickest, and where, therefore, there was the greatest weight to be lifted. … Earthquakes show that even now, in this last of the geological ages, the same border regions of the continents, although daily thickening from the sediments borne to the ocean by rivers, are the areas of the greatest and most frequent movements of the earth’s crust. (1866)
[Thus, the facts were known long ago; the explanation by tectonic activity came many decades later.]
[Thus, the facts were known long ago; the explanation by tectonic activity came many decades later.]
All those who think it paradoxical that so great a weight as the earth should not waver or move anywhere seem to me to go astray by making their judgment with an eye to their own affects and not to the property of the whole. For it would not still appear so extraordinary to them, I believe, if they stopped to think that the earth’s magnitude compared to the whole body surrounding it is in the ratio of a point to it. For thus it seems possible for that which is relatively least to be supported and pressed against from all sides equally and at the same angle by that which is absolutely greatest and homogeneous.
— Ptolemy
Almost all the greatest discoveries in astronomy have resulted from what we have elsewhere termed Residual Phenomena, of a qualitative or numerical kind, of such portions of the numerical or quantitative results of observation as remain outstanding and unaccounted for, after subducting and allowing for all that would result from the strict application of known principles.
America has always been greatest when we dared to be great. We can reach for greatness again. We can follow our dreams to distant stars, living and working in space for peaceful, economic, and scientific gain. Tonight, I am directing NASA to develop a permanently manned space station and to do it within a decade.
And men ought to know that from nothing else but thence [from the brain] come joys, delights, laughter and sports, and sorrows, griefs, despondency, and lamentations. And by this, in an especial manner, we acquire wisdom and knowledge, and see and hear, and know what are foul and hat are fair, what are bad and what are good, what are sweet, and what unsavory... And by the same organ we become mad and delirious, and fears and terrors assail us... All these things we endure from the brain, when it is not healthy... In these ways I am of the opinion that the brain exercises the greatest power in the man. This is the interpreter to us of those things which emanate from the air, when it [the brain] happens to be in a sound state.
Arguably the greatest technological triumph of the century has been the public-health system, which is sophisticated preventive and investigative medicine organized around mostly low- and medium-tech equipment; ... fully half of us are alive today because of the improvements.
As an investigator [Robert Bunsen] was great, as a teacher he was greater, as a man and friend he was greatest.
As every circumstance relating to so capital a discovery as this (the greatest, perhaps, that has been made in the whole compass of philosophy, since the time of Sir Isaac Newton) cannot but give pleasure to all my readers, I shall endeavour to gratify them with the communication of a few particulars which I have from the best authority. The Doctor [Benjamin Franklin], after having published his method of verifying his hypothesis concerning the sameness of electricity with the matter lightning, was waiting for the erection of a spire in Philadelphia to carry his views into execution; not imagining that a pointed rod, of a moderate height, could answer the purpose; when it occurred to him, that, by means of a common kite, he could have a readier and better access to the regions of thunder than by any spire whatever. Preparing, therefore, a large silk handkerchief, and two cross sticks, of a proper length, on which to extend it, he took the opportunity of the first approaching thunder storm to take a walk into a field, in which there was a shed convenient for his purpose. But dreading the ridicule which too commonly attends unsuccessful attempts in science, he communicated his intended experiment to no body but his son, who assisted him in raising the kite.
The kite being raised, a considerable time elapsed before there was any appearance of its being electrified. One very promising cloud passed over it without any effect; when, at length, just as he was beginning to despair of his contrivance, he observed some loose threads of the hempen string to stand erect, and to avoid one another, just as if they had been suspended on a common conductor. Struck with this promising appearance, he inmmediately presented his knuckle to the key, and (let the reader judge of the exquisite pleasure he must have felt at that moment) the discovery was complete. He perceived a very evident electric spark. Others succeeded, even before the string was wet, so as to put the matter past all dispute, and when the rain had wetted the string, he collected electric fire very copiously. This happened in June 1752, a month after the electricians in France had verified the same theory, but before he had heard of any thing that they had done.
The kite being raised, a considerable time elapsed before there was any appearance of its being electrified. One very promising cloud passed over it without any effect; when, at length, just as he was beginning to despair of his contrivance, he observed some loose threads of the hempen string to stand erect, and to avoid one another, just as if they had been suspended on a common conductor. Struck with this promising appearance, he inmmediately presented his knuckle to the key, and (let the reader judge of the exquisite pleasure he must have felt at that moment) the discovery was complete. He perceived a very evident electric spark. Others succeeded, even before the string was wet, so as to put the matter past all dispute, and when the rain had wetted the string, he collected electric fire very copiously. This happened in June 1752, a month after the electricians in France had verified the same theory, but before he had heard of any thing that they had done.
As scientists the two men were contrasting types—Einstein all calculation, Rutherford all experiment ... There was no doubt that as an experimenter Rutherford was a genius, one of the greatest. He worked by intuition and everything he touched turned to gold. He had a sixth sense.
(Reminiscence comparing his friend, Ernest Rutherford, with Albert Einstein, whom he also knew.)
(Reminiscence comparing his friend, Ernest Rutherford, with Albert Einstein, whom he also knew.)
Atoms for peace. Man is still the greatest miracle and the greatest problem on earth. [Message tapped out by Sarnoff using a telegraph key in a tabletop circuit demonstrating an RCA atomic battery as a power source.]
Bacteria represent the world’s greatest success story. They are today and have always been the modal organisms on earth; they cannot be nuked to oblivion and will outlive us all. This time is their time, not the ‘age of mammals’ as our textbooks chauvinistically proclaim. But their price for such success is permanent relegation to a microworld, and they cannot know the joy and pain of consciousness. We live in a universe of trade-offs; complexity and persistence do not work well as partners.
Books are fatal: they are the curse of the human race. Nine-tenths of existing books are nonsense, and the clever books are the refutation of that nonsense. The greatest misfortune that ever befell man was the invention of printing.
Break the chains of your prejudices and take up the torch of experience, and you will honour nature in the way she deserves, instead of drawing derogatory conclusions from the ignorance in which she has left you. Simply open your eyes and ignore what you cannot understand, and you will see that a labourer whose mind and knowledge extend no further than the edges of his furrow is no different essentially from the greatest genius, as would have been proved by dissecting the brains of Descartes and Newton; you will be convinced that the imbecile or the idiot are animals in human form, in the same way as the clever ape is a little man in another form; and that, since everything depends absolutely on differences in organisation, a well-constructed animal who has learnt astronomy can predict an eclipse, as he can predict recovery or death when his genius and good eyesight have benefited from some time at the school of Hippocrates and at patients' bedsides.
But among all these many departments of research, these many branches of industry, new and old, which are being rapidly expanded, there is one dominating all others in importance—one which is of the greatest significance for the comfort and welfare, not to say for the existence, of mankind, and that is the electrical transmission of power.
But by far the greatest hindrance and aberration of the human understanding proceeds from the dullness, incompetency, and deceptions of the senses; in that things which strike the sense outweigh things which do not immediately strike it, though they be more important. Hence it is that speculation commonly ceases where sight ceases; insomuch that of things invisible there is little or no observation.
But by far the greatest obstacle to the progress of science and to the undertaking of new tasks and provinces therein is found in this—that men despair and think things impossible.
But how to raise a sum in the different States has been my greatest difficulty.
But it is precisely mathematics, and the pure science generally, from which the general educated public and independent students have been debarred, and into which they have only rarely attained more than a very meagre insight. The reason of this is twofold. In the first place, the ascendant and consecutive character of mathematical knowledge renders its results absolutely insusceptible of presentation to persons who are unacquainted with what has gone before, and so necessitates on the part of its devotees a thorough and patient exploration of the field from the very beginning, as distinguished from those sciences which may, so to speak, be begun at the end, and which are consequently cultivated with the greatest zeal. The second reason is that, partly through the exigencies of academic instruction, but mainly through the martinet traditions of antiquity and the influence of mediaeval logic-mongers, the great bulk of the elementary text-books of mathematics have unconsciously assumed a very repellant form,—something similar to what is termed in the theory of protective mimicry in biology “the terrifying form.” And it is mainly to this formidableness and touch-me-not character of exterior, concealing withal a harmless body, that the undue neglect of typical mathematical studies is to be attributed.
But that which will excite the greatest astonishment by far, and which indeed especially moved me to call the attention of all astronomers and philosophers, is this: namely, that I have observed four planets, neither known nor observed by any one of the astronomers before my time, which have their orbits round a certain bright star [Jupiter], one of those previously known, like Venus or Mercury round the sun, and are sometimes in front of it, sometimes behind it, though they never depart from it beyond certain limits. All of which facts were discovered and observed a few days ago by the help of a telescope devised by me, through God’s grace first enlightening my mind.
But the greatest error of all the rest is the mistaking or misplacing of the last or farthest end of knowledge: for men have entered into a desire of learning and knowledge, sometimes upon a natural curiosity and inquisitive appetite; sometimes to entertain their minds with variety and delight; sometimes for ornament and reputation; and sometimes to enable them to victory of wit and contradiction; and most times for lucre and profession; and seldom sincerely to give a true account of their gift of reason, to the benefit and use of men...
But when you come right down to it, the reason that we did this job is because it was an organic necessity. If you are a scientist you cannot stop such a thing. If you are a scientist you believe that it is good to find out how the world works; that it is good to find out what the realities are; that it is good to turn over to mankind at large the greatest possible power to control the world and to deal with it according to its lights and values.
Regarding the atomic bomb project.
Regarding the atomic bomb project.
Clarity about the aims and problems of socialism is of greatest significance in our age of transition. Since, under present circumstances, free and unhindered discussion of these problems has come under a powerful taboo, I consider the foundation of this magazine to be an important public service.
Climbing is not a competition, and you cannot talk in terms of “greatest”, it means nothing,
Commenting on Archimedes, for whom he also had a boundless admiration, Gauss remarked that he could not understand how Archimedes failed to invent the decimal system of numeration or its equivalent (with some base other than 10). … This oversight Gauss regarded as the greatest calamity in the history of science.
Confucius once said: “our greatest glory is not in never falling, but in getting up every time we do”. Scholars believe he was referring to roller coasters.
Conservation is the foresighted utilization, preservation. And/or renewal of forest, waters, lands and minerals, for the greatest good of the greatest number for the longest time.
Considering the difficulties represented by the lack of water, by extremes of temperature, by the full force of gravity unmitigated by the buoyancy of water, it must be understood that the spread to land of life forms that evolved to meet the conditions of the ocean represented the greatest single victory won by life over the inanimate environment.
Defenders of the short-sighted men who in their greed and selfishness will, if permitted, rob our country of half its charm by their reckless extermination of all useful and beautiful wild things sometimes seek to champion them by saying the “the game belongs to the people.” So it does; and not merely to the people now alive, but to the unborn people. The “greatest good for the greatest number” applies to the number within the womb of time, compared to which those now alive form but an insignificant fraction. Our duty to the whole, including the unborn generations, bids us restrain an unprincipled present-day minority from wasting the heritage of these unborn generations. The movement for the conservation of wild life and the larger movement for the conservation of all our natural resources are essentially democratic in spirit, purpose, and method.
During seasons of great pestilence men have often believed the prophecies of crazed fanatics, that the end of the world was come. Credulity is always greatest in times of calamity. Prophecies of all sorts are rife on such occasions, and are readily believed, whether for good or evil.
During the time of the Deluge, whilst the Water was out upon, and covered the Terrestrial Globe, … all Fossils whatever that had before obtained any Solidity, were totally dissolved, and their constituent Corpuscles all disjoyned, their Cohesion perfectly ceasing … [A]nd, to be short, all Bodies whatsoever that were either upon the Earth, or that constituted the Mass of it, if not quite down to the Abyss, yet at least to the greatest depth we ever dig: I say all these were assumed up promiscuously into the Water, and sustained in it, in such a manner that the Water, and Bodies in it, together made up one common confused Mass. That at length all the Mass that was thus borne up in the Water, was again precipitated and subsided towards the bottom. That this subsidence happened generally, and as near as possibly could be expected in so great a Confusion, according to the laws of Gravity.
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 theory 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.
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.
Everything that the greatest minds of all times have accomplished toward the comprehension of forms by means of concepts is gathered into one great science, mathematics.
Exact science and its practical movements are no checks on the greatest poet, but always his encouragement and support … The sailor and traveller, the anatomist, chemist, astronomer, geologist, phrenologist, spiritualist, mathematician, historian and lexicographer are not poets, but they are the lawgivers of poets and their construction underlies the structure of every perfect poem.
Examinations are formidable even to the best prepared, for the greatest fool may ask more than the wisest man can answer.
Exercises in being obedient can not begin too early, and I have, during an almost daily observation of six years, discovered no harm from an early, consistent guiding of the germinating will, provided only this guiding be done with the greatest mildness and justice, as if the infant had already an insight into the benefits of obedience.
Facts are to the mind the same thing as food to the body. On the due digestion of facts depends the strength and wisdom of the one, just as vigor and health depend on the other. The wisest in council, the ablest in debate, and the most agreeable in the commerce of life is that man who has assimilated to his understanding the greatest number of facts.
For man being the minister and interpreter of nature, acts and understands so far as he has observed of the order, the works and mind of nature, and can proceed no further; for no power is able to loose or break the chain of causes, nor is nature to be conquered but by submission: whence those twin intentions, human knowledge and human power, are really coincident; and the greatest hindrance to works is the ignorance of causes.
For the Members of the Assembly having before their eyes so many fatal Instances of the errors and falshoods, in which the greatest part of mankind has so long wandred, because they rely'd upon the strength of humane Reason alone, have begun anew to correct all Hypotheses by sense, as Seamen do their dead Reckonings by Cœlestial Observations; and to this purpose it has been their principal indeavour to enlarge and strengthen the Senses by Medicine, and by such outward Instruments as are proper for their particular works.
For those [observations] that I made in Leipzig in my youth and up to my 21st year, I usually call childish and of doubtful value. Those that I took later until my 28th year [i.e., until 1574] I call juvenile and fairly serviceable. The third group, however, which I made at Uraniborg during approximately the last 21 years with the greatest care and with very accurate instruments at a more mature age, until I was fifty years of age, those I call the observations of my manhood, completely valid and absolutely certain, and this is my opinion of them.
Fragments of the natural method must be sought with the greatest care. This is the first and last desideratum among botanists.
Nature makes no jumps.
[Natura non facit saltus]
All taxa show relationships on all sides like the countries on a map of the world.
Nature makes no jumps.
[Natura non facit saltus]
All taxa show relationships on all sides like the countries on a map of the world.
Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings which compose it—an intelligence sufficiently vast to submit these data to analysis, it would embrace in the same formula the movements of the greatest bodies in the universe and those of the lightest atom; to it nothing would be uncertain, and the future as the past would be present to its eyes.
He [Robert Boyle] is very tall (about six foot high) and straight, very temperate, and vertuouse, and frugall: a batcheler; keepes a Coach; sojournes with his sister, the Lady Ranulagh. His greatest delight is Chymistrey. He has at his sister’s a noble laboratory, and severall servants (Prentices to him) to look to it. He is charitable to ingeniose men that are in want, and foreigne Chymists have had large proofe of his bountie, for he will not spare for cost to get any rare Secret.
He [Robert Hooke] is but of midling stature, something crooked, pale faced, and his face but little belowe, but his head is lardge; his eie full and popping, and not quick; a grey eie. He haz a delicate head of haire, browne, and of an excellent moist curle. He is and ever was very temperate, and moderate in dyet, etc. As he is of prodigious inventive head, so is a person of great vertue and goodnes. Now when I have sayd his Inventive faculty is so great, you cannot imagine his Memory to be excellent, for they are like two Bucketts, as one goes up, the other goes downe. He is certainly the greatest Mechanick this day in the World.
He is the best Physician in whom the Patient has the greatest Confidence.
He should avail himself of their resources in such ways as to advance the expression of the spirit in the life of mankind. He should use them so as to afford to every human being the greatest possible opportunity for developing and expressing his distinctively human capacity as an instrument of the spirit, as a centre of sensitive and intelligent awareness of the objective universe, as a centre of love of all lovely things, and of creative action for the spirit.
He that knows the secrets of nature with Albertus Magnus, or the motions of the heavens with Galileo, or the cosmography of the moon with Hevelius, or the body of man with Galen, or the nature of diseases with Hippocrates, or the harmonies in melody with Orpheus, or of poesy with Homer, or of grammar with Lilly, or of whatever else with the greatest artist; he is nothing if he knows them merely for talk or idle speculation, or transient and external use. But he that knows them for value, and knows them his own, shall profit infinitely.
His [Edison’s] greatest invention was that of the industrial research laboratory, turning out inventions as a business.
His work was so great that it cannot be compassed in a few words. His death is one of the greatest losses ever to occur to British science.
Describing Ernest Rutherford upon his death at age 66. Thomson, then 80 years old, was once his teacher.
Describing Ernest Rutherford upon his death at age 66. Thomson, then 80 years old, was once his teacher.
Hubris is the greatest danger that accompanies formal data analysis, including formalized statistical analysis. The feeling of “Give me (or more likely even, give my assistant) the data, and I will tell you what the real answer is!” is one we must all fight against again and again, and yet again.
Hudson is at his best about the greatest living English stylist ... Besides this he is the finest living observer, and the greatest living lover of bird and animal life, and of Nature in her moods.
I believe sustainable use is the greatest propaganda in wildlife conservation at the moment.
I came to biochemistry through chemistry; I came to chemistry, partly by the labyrinthine routes that I have related, and partly through the youthful romantic notion that the natural sciences had something to do with nature. What I liked about chemistry was its clarity surrounded by darkness; what attracted me, slowly and hesitatingly, to biology was its darkness surrounded by the brightness of the givenness of nature, the holiness of life. And so I have always oscillated between the brightness of reality and the darkness of the unknowable. When Pascal speaks of God in hiding, Deus absconditus, we hear not only the profound existential thinker, but also the great searcher for the reality of the world. I consider this unquenchable resonance as the greatest gift that can be bestowed on a naturalist.
I had a dislike for [mathematics], and ... was hopelessly short in algebra. ... [One extraordinary teacher of mathematics] got the whole year's course into me in exactly six [after-school] lessons of half an hour each. And how? More accurately, why? Simply because he was an algebra fanatic—because he believed that algebra was not only a science of the utmost importance, but also one of the greatest fascination. ... [H]e convinced me in twenty minutes that ignorance of algebra was as calamitous, socially and intellectually, as ignorance of table manners—That acquiring its elements was as necessary as washing behind the ears. So I fell upon the book and gulped it voraciously. ... To this day I comprehend the binomial theorem.
I have been able to solve a few problems of mathematical physics on which the greatest mathematicians since Euler have struggled in vain … But the pride I might have held in my conclusions was perceptibly lessened by the fact that I knew that the solution of these problems had almost always come to me as the gradual generalization of favorable examples, by a series of fortunate conjectures, after many errors. I am fain to compare myself with a wanderer on the mountains who, not knowing the path, climbs slowly and painfully upwards and often has to retrace his steps because he can go no further—then, whether by taking thought or from luck, discovers a new track that leads him on a little till at length when he reaches the summit he finds to his shame that there is a royal road by which he might have ascended, had he only the wits to find the right approach to it. In my works, I naturally said nothing about my mistake to the reader, but only described the made track by which he may now reach the same heights without difficulty.
I have learned to use the word “impossible” with the greatest caution.
I have seen many phases of life; I have moved in imperial circles, I have been a Minister of State; but if I had to live my life again, I would always remain in my laboratory, for the greatest joy of my life has been to accomplish original scientific work, and, next to that, to lecture to a set of intelligent students.
I know that most men, including those at ease with problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives.
I ran into the gigantic and gigantically wasteful lumbering of great Sequoias, many of whose trunks were so huge they had to be blown apart before they could be handled. I resented then, and I still resent, the practice of making vine stakes hardly bigger than walking sticks out of these greatest of living things.
I remember my first look at the great treatise of Maxwell’s when I was a young man… I saw that it was great, greater and greatest, with prodigious possibilities in its power… I was determined to master the book and set to work. I was very ignorant. I had no knowledge of mathematical analysis (having learned only school algebra and trigonometry which I had largely forgotten) and thus my work was laid out for me. It took me several years before I could understand as much as I possibly could. Then I set Maxwell aside and followed my own course. And I progressed much more quickly… It will be understood that I preach the gospel according to my interpretation of Maxwell.
I saw [Linus Pauling] as a brilliant lecturer and a man with a fantastic memory, and a great, great showman. I think he was the century’s greatest chemist. No doubt about it.
I see no good reason why the views given this volume [The Origin of Species] should shock the religious feelings of any one. It is satisfactory, as showing how transient such impressions are, to remember that the greatest discovery ever made by man, namely, the law of attraction of gravity, was also attacked by Leibnitz, “as subversive of natural, and inferentially of revealed, religion.”
I think that the formation of [DNA's] structure by Watson and Crick may turn out to be the greatest developments in the field of molecular genetics in recent years.
I will not now discuss the Controversie betwixt some of the Modern Atomists, and the Cartesians; the former of whom think, that betwixt the Earth and the Stars, and betwixt these themselves there are vast Tracts of Space that are empty, save where the beams of Light do pass through them; and the later of whom tell us, that the Intervals betwixt the Stars and Planets (among which the Earth may perhaps be reckon'd) are perfectly fill'd, but by a Matter far subtiler than our Air, which some call Celestial, and others Æther. I shall not, I say, engage in this controversie, but thus much seems evident, That If there be such a Celestial Matter, it must ' make up far the Greatest part of the Universe known to us. For the Interstellar part of the world (If I may so stile it) bears so very great a proportion to the Globes, and their Atmospheres too, (If other Stars have any as well as the Earth,) that It Is almost incomparably Greater in respect of them, than all our Atmosphere is in respect of the Clouds, not to make the comparison between the Sea and the Fishes that swim in it.
I wish the lecturers to treat their subject as a strictly natural science, the greatest of all possible sciences, indeed, in one sense, the only science, that of Infinite Being, without reference to or reliance upon any supposed special exception or so-called miraculous revelation. I wish it considered just as astronomy or chemistry is.
Statement in deed of foundation of the Gifford Lectures on natural theology (1885).
Statement in deed of foundation of the Gifford Lectures on natural theology (1885).
I would be the last to deny that the greatest scientific pioneers belonged to an aristocracy of the spirit and were exceptionally intelligent, something that we as modest investigators will never attain, no matter how much we exert ourselves. Nevertheless … I continue to believe that there is always room for anyone with average intelligence … to utilize his energy and … any man could, if he were so inclined, be the sculptor of his own brain, and that even the least gifted may, like the poorest land that has been well-cultivated and fertilized, produce an abundant harvest..
If basketball was going to enable Bradley to make friends, to prove that a banker’s son is as good as the next fellow, to prove that he could do without being the greatest-end-ever at Missouri, to prove that he was not chicken, and to live up to his mother’s championship standards, and if he was going to have some moments left over to savor his delight in the game, he obviously needed considerable practice, so he borrowed keys to the gym and set a schedule for himself that he adhereded to for four full years—in the school year, three and a half hours every day after school, nine to five on Saturday, one-thirty to five on Sunday, and, in the summer, about three hours a day.
If I dared to say just what I think, I should add that it is chiefly in the service where the medication is the most active and heroic that the mortality is the greatest. Gentlemen, medicine is charlatanism.
If it is true as Whewell says, that the essence of the triumphs of Science and its progress consists in that it enables us to consider evident and necessary, views which our ancestors held to be unintelligible and were unable to comprehend, then the extension of the number concept to include the irrational, and we will at once add, the imaginary, is the greatest forward step which pure mathematics has ever taken.
If Melancholy increases so far, that from the great motion of the Liquid of the Brain the Patient be thrown into a wild Fury, it is call’d Madness.… The greatest Remedy for it is to throw the Patient unwarily into the Sea, and to keep him under Water as long as he can possibly bear without being quite stifled.
If the man of science chose to follow the example of historians and pulpit-orators, and to obscure strange and peculiar phenomena by employing a hollow pomp of big and sounding words, this would be his opportunity; for we have approached one of the greatest mysteries which surround the problem of animated nature and distinguish it above all other problems of science. To discover the relations of man and woman to the egg-cell would be almost equivalent of the egg-cell in the body of the mother, the transfer to it by means of the seed, of the physical and mental characteristics of the father, affect all the questions which the human mind has ever raised in regard to existence.
In acute diseases the physician must conduct his inquiries in the following way. First he must examine the face of the patient, and see whether it is like the faces of healthy people, and especially whether it is like its usual self. Such likeness will be the best sign, and the greatest unlikeness will be the most dangerous sign. The latter will be as follows. Nose sharp, eyes hollow, temples sunken, ears cold and contracted with their lobes turned outwards, the skin about the face hard and tense and parched, the colour of the face as a whole being yellow or black.
In all times and epochs the greatest happiness for man has been to take part in new discoveries.
In attempting to understand the elements out of which mental phenomena are compounded, it is of the greatest importance to remember that from the protozoa to man there is nowhere a very wide gap either in structure or in behaviour. From this fact it is a highly probable inference that there is also nowhere a very wide mental gap.
In diabetes the thirst is greater for the fluid dries the body ... For the thirst there is need of a powerful remedy, for in kind it is the greatest of all sufferings, and when a fluid is drunk, it stimulates the discharge of urine.
In Euclid each proposition stands by itself; its connection with others is never indicated; the leading ideas contained in its proof are not stated; general principles do not exist. In modern methods, on the other hand, the greatest importance is attached to the leading thoughts which pervade the whole; and general principles, which bring whole groups of theorems under one aspect, are given rather than separate propositions. The whole tendency is toward generalization. A straight line is considered as given in its entirety, extending both ways to infinity, while Euclid is very careful never to admit anything but finite quantities. The treatment of the infinite is in fact another fundamental difference between the two methods. Euclid avoids it, in modern mathematics it is systematically introduced, for only thus is generality obtained.
In man, population structure reaches its greatest complexity. Mankind—the human species, Homo sapiens—is the most inclusive Mendelian population, one which inhabits nearly the whole globe.
In my considered opinion the peer review system, in which proposals rather than proposers are reviewed, is the greatest disaster visited upon the scientific community in this century. No group of peers would have approved my building the 72-inch bubble chamber. Even Ernest Lawrence told me he thought I was making a big mistake. He supported me because he knew my track record was good. I believe that U.S. science could recover from the stultifying effects of decades of misguided peer reviewing if we returned to the tried-and-true method of evaluating experimenters rather than experimental proposals. Many people will say that my ideas are elitist, and I certainly agree. The alternative is the egalitarianism that we now practice and I’ve seen nearly kill basic science in the USSR and in the People's Republic of China.
In science as in life the greatest truths are the simplest.
In scientific matters ... the greatest discoverer differs from the most arduous imitator and apprentice only in degree, whereas he differs in kind from someone whom nature has endowed for fine art. But saying this does not disparage those great men to whom the human race owes so much in contrast to those whom nature has endowed for fine art. For the scientists' talent lies in continuing to increase the perfection of our cognitions and on all the dependent benefits, as well as in imparting that same knowledge to others; and in these respects they are far superior to those who merit the honour of being called geniuses. For the latter's art stops at some point, because a boundary is set for it beyond which it cannot go and which has probably long since been reached and cannot be extended further.
In short, the greatest contribution to real security that science can make is through the extension of the scientific method to the social sciences and a solution of the problem of complete avoidance of war.
In symbols one observes an advantage in discovery which is greatest when they express the exact nature of a thing briefly and, as it were, picture it; then indeed the labor of thought is wonderfully diminished.
In the animal world we have seen that the vast majority of species live in societies, and that they find in association the best arms for the struggle for life: understood, of course, in its wide Darwinian sense—not as a struggle for the sheer means of existence, but as a struggle against all natural conditions unfavourable to the species. The animal species, in which individual struggle has been reduced to its narrowest limits, and the practice of mutual aid has attained the greatest development, are invariably the most numerous, the most prosperous, and the most open to further progress. The mutual protection which is obtained in this case, the possibility of attaining old age and of accumulating experience, the higher intellectual development, and the further growth of sociable habits, secure the maintenance of the species, its extension, and its further progressive evolution. The unsociable species, on the contrary, are doomed to decay.
In the celestial spaces above the Earth’s atmosphere; in which spaces, where there is no air to resist their motions, all bodies will move with the greatest freedom; and the Planets and Comets will constantly pursue their revolutions in orbits … by the mere laws of gravity.
In the history of the discovery of zero will always stand out as one of the greatest single achievements of the human race.
In the vestibule of the Manchester Town Hall are placed two life-sized marble statues facing each other. One of these is that of John Dalton … the other that of James Prescott Joule. … Thus honour is done to Manchester’s two greatest sons—to Dalton, the founder of modern Chemistry and of the Atomic Theory, and the laws of chemical-combining proportions; to Joule, the founder of modern Physics and the discoverer of the Law of Conservation of Energy. The one gave to the world the final and satisfactory proof … that in every kind of chemical change no loss of matter occurs; the other proved that in all the varied modes of physical change, no loss of energy takes place.
In the year 2000, the solar water heater behind me, which is being dedicated today, will still be here supplying cheap, efficient energy. A generation from now, this solar heater can either be a curiosity, a museum piece, an example of a road not taken, or it can be just a small part of one of the greatest and most exciting adventures ever undertaken by the American people: harnessing the power of the Sun to enrich our lives as we move away from our crippling dependence on foreign oil.
[The next President, Republican Ronald Reagan, removed the solar panels and gutted renewable energy research budgets. The road was not taken, nationally, in the eight years of his presidency. Several of the panels are, indeed, now in museums. Most were bought as government surplus and put to good use on a college roof.]
[The next President, Republican Ronald Reagan, removed the solar panels and gutted renewable energy research budgets. The road was not taken, nationally, in the eight years of his presidency. Several of the panels are, indeed, now in museums. Most were bought as government surplus and put to good use on a college roof.]
In-depth studies have an influence on general ideas, whereas theories, in turn, in order to maintain themselves, push their spectators to search for new evidence. The mind’s activity that is maintained by the debates about these works, is probably the source of the greatest joys given to man to experience on Earth.
Instead of disbursing her annual millions for these dye stuffs, England will, beyond question, at no distant day become herself the greatest coloring producing country in the world; nay, by the very strangest of revolutions she may ere long send her coal-derived blues to indigo-growing India, her tar-distilled crimson to cochineal-producing Mexico, and her fossil substitutes for quercitron and safflower to China, Japan and the other countries whence these articles are now derived.
Is not Cuvier the greatest poet of our age? Of course Lord Byron has set down in fine words certain of our souls’ longings; but our immortal naturalist has reconstructed whole worlds out of bleached bones. Like Cadmus, he has rebuilt great cities from teeth, repopulated thousands of forests with all the mysteries of zoology from a few pieces of coal, discovered races of giants in the foot of a mammoth.
It follows from the supreme perfection of God, that in creating the universe has chosen the best possible plan, in which there is the greatest variety together with the greatest order; the best arranged ground, place, time; the most results produced in the most simple ways; the most of power, knowledge, happiness and goodness the creatures that the universe could permit. For since all the possibles in I understanding of God laid claim to existence in proportion to their perfections, the actual world, as the resultant of all these claims, must be the most perfect possible. And without this it would not be possible to give a reason why things have turned out so rather than otherwise.
It is by the aid of iron that we construct houses, cleave rocks, and perform so many other useful offices of life. But it is with iron also that wars, murders, and robberies are effected, and this, not only hand to hand, but from a distance even, by the aid of missiles and winged weapons, now launched from engines, now hurled by the human arm, and now furnished with feathery wings. This last I regard as the most criminal artifice that has been devised by the human mind; for, as if to bring death upon man with still greater rapidity, we have given wings to iron and taught it to fly. ... Nature, in conformity with her usual benevolence, has limited the power of iron, by inflicting upon it the punishment of rust; and has thus displayed her usual foresight in rendering nothing in existence more perishable, than the substance which brings the greatest dangers upon perishable mortality.
It is curious to observe with what different degrees of architectonic skill Providence has endowed birds of the same genus, and so nearly correspondent in their general mode of life! for while the swallow and the house-martin discover the greatest address in raising and securely fixing crusts or shells of loam as cunabula for their young, the bank-martin terebrates a round and regular hole in the sand or earth, which is serpentine, horizontal, and about two feet deep. At the inner end of this burrow does this bird deposit, in a good degree of safety, her rude nest, consisting of fine grasses and feathers, usually goose-feathers, very inartificially laid together.
It is given to but few men to achieve immortality, still less to achieve Olympian rank, during their own lifetime. In a generation that witnesses one of the greatest revolutions in the entire history of science [Ernest Rutherford] was universally acknowledged as the leading explorer of the vast infinitely complex universe within the atom, a universe that he was first to penetrate.
(Rutherford's death was front page news in the New York Times.)
(Rutherford's death was front page news in the New York Times.)
It is good to recall that three centuries ago, around the year 1660, two of the greatest monuments of modern history were erected, one in the West and one in the East; St. Paul’s Cathedral in London and the Taj Mahal in Agra. Between them, the two symbolize, perhaps better than words can describe, the comparative level of architectural technology, the comparative level of craftsmanship and the comparative level of affluence and sophistication the two cultures had attained at that epoch of history. But about the same time there was also created—and this time only in the West—a third monument, a monument still greater in its eventual import for humanity. This was Newton’s Principia, published in 1687. Newton's work had no counterpart in the India of the Mughuls.
It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.
It is interesting thus to follow the intellectual truths of analysis in the phenomena of nature. This correspondence, of which the system of the world will offer us numerous examples, makes one of the greatest charms attached to mathematical speculations.
It is not a disgrace to fail. Failing is one of the greatest arts in the world.
It is not enough that a few brilliant men can create computers to “think” for us; for the greatest thinking machine is inside each of us.
It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again; the never-satisfied man is so strange if he has completed a structure, then it is not in order to dwell in it peacefully,but in order to begin another. I imagine the world conqueror must feel thus, who, after one kingdom is scarcely conquered, stretches out his arms for others.
It is not necessary for all men to be great in action. The greatest and sublimest power is often simple patience.
It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.
It is now necessary to indicate more definitely the reason why mathematics not only carries conviction in itself, but also transmits conviction to the objects to which it is applied. The reason is found, first of all, in the perfect precision with which the elementary mathematical concepts are determined; in this respect each science must look to its own salvation .... But this is not all. As soon as human thought attempts long chains of conclusions, or difficult matters generally, there arises not only the danger of error but also the suspicion of error, because since all details cannot be surveyed with clearness at the same instant one must in the end be satisfied with a belief that nothing has been overlooked from the beginning. Every one knows how much this is the case even in arithmetic, the most elementary use of mathematics. No one would imagine that the higher parts of mathematics fare better in this respect; on the contrary, in more complicated conclusions the uncertainty and suspicion of hidden errors increases in rapid progression. How does mathematics manage to rid itself of this inconvenience which attaches to it in the highest degree? By making proofs more rigorous? By giving new rules according to which the old rules shall be applied? Not in the least. A very great uncertainty continues to attach to the result of each single computation. But there are checks. In the realm of mathematics each point may be reached by a hundred different ways; and if each of a hundred ways leads to the same point, one may be sure that the right point has been reached. A calculation without a check is as good as none. Just so it is with every isolated proof in any speculative science whatever; the proof may be ever so ingenious, and ever so perfectly true and correct, it will still fail to convince permanently. He will therefore be much deceived, who, in metaphysics, or in psychology which depends on metaphysics, hopes to see his greatest care in the precise determination of the concepts and in the logical conclusions rewarded by conviction, much less by success in transmitting conviction to others. Not only must the conclusions support each other, without coercion or suspicion of subreption, but in all matters originating in experience, or judging concerning experience, the results of speculation must be verified by experience, not only superficially, but in countless special cases.
It is the greatest of crimes to depress true art and science.
It is true that physics gives a wonderful training in precise, logical thinking-about physics. It really does depend upon accurate reproducible experiments, and upon framing hypotheses with the greatest possible freedom from dogmatic prejudice. And if these were the really important things in life, physics would be an essential study for everybody.
It is, I find, in zoology as it is in botany: all nature is so full, that that district produces the greatest variety which is the most examined.
It often happens that men, even of the best understandings and greatest circumspection, are guilty of that fault in reasoning which the writers on logick call the insufficient, or imperfect enumeration of parts, or cases: insomuch that I will venture to assert, that this is the chief, and almost the only, source of the vast number of erroneous opinions, and those too very often in matters of great importance, which we are apt to form on all the subjects we reflect upon, whether they relate to the knowledge of nature, or the merits and motives of human actions. It must therefore be acknowledged, that the art which affords a cure to this weakness, or defect, of our understandings, and teaches us to enumerate all the possible ways in which a given number of things may be mixed and combined together, that we may be certain that we have not omitted anyone arrangement of them that can lead to the object of our inquiry, deserves to be considered as most eminently useful and worthy of our highest esteem and attention. And this is the business of the art, or doctrine of combinations ... It proceeds indeed upon mathematical principles in calculating the number of the combinations of the things proposed: but by the conclusions that are obtained by it, the sagacity of the natural philosopher, the exactness of the historian, the skill and judgement of the physician, and the prudence and foresight of the politician, may be assisted; because the business of all these important professions is but to form reasonable conjectures concerning the several objects which engage their attention, and all wise conjectures are the results of a just and careful examination of the several different effects that may possibly arise from the causes that are capable of producing them.
It seems to me that the natural world is the greatest source of excitement; the greatest source of visual beauty, the greatest source of intellectual interest. It is the greatest source of so much in life that makes life worth living.
It was my good fortune to be linked with Mme. Curie through twenty years of sublime and unclouded friendship. I came to admire her human grandeur to an ever growing degree. Her strength, her purity of will, her austerity toward herself, her objectivity, her incorruptible judgement—all these were of a kind seldom found joined in a single individual… The greatest scientific deed of her life—proving the existence of radioactive elements and isolating them—owes its accomplishment not merely to bold intuition but to a devotion and tenacity in execution under the most extreme hardships imaginable, such as the history of experimental science has not often witnessed.
It was not by any accident that the greatest thinkers of all ages were deeply religious souls.
It was their individuality combined with the shyness of their behavior that remained the most captivating impression of this first encounter with the greatest of the great apes.
It wasn’t the finches that put the idea [of natural selection] in Darwin’s head, it was the tortoises. The reason he didn’t use the tortoises [in writing On the Origin of Species] was that, when he got back, he found he didn’t have localities on the tortoise specimens. Here the great god, the greatest naturalist we have records of, made a mistake. His fieldwork wasn’t absolutely perfect.
It would seem at first sight as if the rapid expansion of the region of mathematics must be a source of danger to its future progress. Not only does the area widen but the subjects of study increase rapidly in number, and the work of the mathematician tends to become more and more specialized. It is, of course, merely a brilliant exaggeration to say that no mathematician is able to understand the work of any other mathematician, but it is certainly true that it is daily becoming more and more difficult for a mathematician to keep himself acquainted, even in a general way, with the progress of any of the branches of mathematics except those which form the field of his own labours. I believe, however, that the increasing extent of the territory of mathematics will always be counteracted by increased facilities in the means of communication. Additional knowledge opens to us new principles and methods which may conduct us with the greatest ease to results which previously were most difficult of access; and improvements in notation may exercise the most powerful effects both in the simplification and accessibility of a subject. It rests with the worker in mathematics not only to explore new truths, but to devise the language by which they may be discovered and expressed; and the genius of a great mathematician displays itself no less in the notation he invents for deciphering his subject than in the results attained. … I have great faith in the power of well-chosen notation to simplify complicated theories and to bring remote ones near and I think it is safe to predict that the increased knowledge of principles and the resulting improvements in the symbolic language of mathematics will always enable us to grapple satisfactorily with the difficulties arising from the mere extent of the subject.
Laughter is a most healthful exercise; it is one of the greatest helps to digestion with which I am acquainted; and the custom prevalent among our forefathers, of exciting it at table by jesters and buffoons, was in accordance with true medical principles.
Let us be well assured of the Matter of Fact, before we trouble our selves with enquiring into the Cause. It is true, that this Method is too slow for the greatest part of Mankind, who run naturally to the Cause, and pass over the Truth of the Matter of Fact.
Life is a ticket to the greatest show on earth.
Life’s greatest tragedy is to lose God and not to miss him.
Look at those animals and remember the greatest scientists in the world have never discovered how to make grass into milk.
Looking back over the geological record it would seem that Nature made nearly every possible mistake before she reached her greatest achievement Man—or perhaps some would say her worst mistake of all. ... At last she tried a being of no great size, almost defenseless, defective in at least one of the more important sense organs; one gift she bestowed to save him from threatened extinction—a certain stirring, a restlessness, in the organ called the brain.
Man is the highest product of his own history. The discoverer finds nothing so grand or tall as himself, nothing so valuable to him. The greatest star is at the small end of the telescope, the star that is looking, not looked after nor looked at.
Many years ago the great British explorer George Mallory, who was to die on Mount Everest, was asked why did he want to climb it. He said, “Because it is there.” Well, space is there, and we’re going to climb it, and the moon and the planets are there, and new hopes for knowledge and peace are there. And, therefore, as we set sail we ask God’s blessing on the most hazardous and dangerous and greatest adventure on which man has ever embarked.
Martin Gardner is one of the greatest intellects produced in this country in this century.
Mathematics has beauties of its own—a symmetry and proportion in its results, a lack of superfluity, an exact adaptation of means to ends, which is exceedingly remarkable and to be found only in the works of the greatest beauty. … When this subject is properly and concretely presented, the mental emotion should be that of enjoyment of beauty, not that of repulsion from the ugly and the unpleasant.
Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
Measured objectively, what a man can wrest from Truth by passionate striving is utterly infinitesimal. But the striving frees us from the bonds of the self and makes us comrades of those who are the best and the greatest.
Metals are the great agents by which we can examine the recesses of nature; and their uses are so multiplied, that they have become of the greatest importance in every occupation of life. They are the instruments of all our improvements, of civilization itself, and are even subservient to the progress of the human mind towards perfection. They differ so much from each other, that nature seems to have had in view all the necessities of man, in order that she might suit every possible purpose his ingenuity can invent or his wants require.
Morphological information has provided the greatest single source of data in the formulation and development of the theory of evolution and that even now, when the preponderance of work is experimental, the basis for interpretation in many areas of study remains the form and relationships of structures.
Mr Hooke sent, in his next letter [to Sir Isaac Newton] the whole of his Hypothesis, scil that the gravitation was reciprocall to the square of the distance: ... This is the greatest Discovery in Nature that ever was since the World's Creation. It was never so much as hinted by any man before. I wish he had writt plainer, and afforded a little more paper.
My concern is not whether God is on our side; my greatest concern is to be on God’s side, for God is always right.
My greatest hope for a future without another Deepwater Horizon disaster lies in our schools, living rooms and community centers, not in boardrooms, political chambers and big industry. If this happens again, we won’t have the luxury of the unknown to shield us from answering “Why?”
Name the greatest of all inventors: Accident.
Newton supposed that the case of the planet was similar to that of [a ball spun around on the end of an elastic string]; that it was always pulled in the direction of the sun, and that this attraction or pulling of the sun produced the revolution of the planet, in the same way that the traction or pulling of the elastic string produces the revolution of the ball. What there is between the sun and the planet that makes each of them pull the other, Newton did not know; nobody knows to this day; and all we are now able to assert positively is that the known motion of the planet is precisely what would be produced if it were fastened to the sun by an elastic string, having a certain law of elasticity. Now observe the nature of this discovery, the greatest in its consequences that has ever yet been made in physical science:—
I. It begins with an hypothesis, by supposing that there is an analogy between the motion of a planet and the motion of a ball at the end of a string.
II. Science becomes independent of the hypothesis, for we merely use it to investigate the properties of the motion, and do not trouble ourselves further about the cause of it.
I. It begins with an hypothesis, by supposing that there is an analogy between the motion of a planet and the motion of a ball at the end of a string.
II. Science becomes independent of the hypothesis, for we merely use it to investigate the properties of the motion, and do not trouble ourselves further about the cause of it.
Newton was the greatest creative genius physics has ever seen. None of the other candidates for the superlative (Einstein, Maxwell, Boltzmann, Gibbs, and Feynman) has matched Newton’s combined achievements as theoretician, experimentalist, and mathematician. … If you were to become a time traveler and meet Newton on a trip back to the seventeenth century, you might find him something like the performer who first exasperates everyone in sight and then goes on stage and sings like an angel.
Newton was the greatest creative genius physics has ever seen. None of the other candidates for the superlative (Einstein, Maxwell, Boltzmann, Gibbs, and Feynman) has matched Newton’s combined achievements as theoretician, experimentalist, and mathematician. … If you were to become a time traveler and meet Newton on a trip back to the seventeenth century, you might find him something like the performer who first exasperates everyone in sight and then goes on stage and sings like an angel.
Newton was the greatest genius that ever existed, and the most fortunate, for we cannot find more than once a system of the world to establish.
Next to enjoying ourselves, the next greatest pleasure consists in preventing others from enjoying themselves, or, more generally, in the acquisition of power.
No scientist or student of science, need ever read an original work of the past. As a general rule, he does not think of doing so. Rutherford was one of the greatest experimental physicists, but no nuclear scientist today would study his researches of fifty years ago. Their substance has all been infused into the common agreement, the textbooks, the contemporary papers, the living present.
Nothing could be more admirable than the manner in which for forty years he [Joseph Black] performed this useful and dignified office. His style of lecturing was as nearly perfect as can well be conceived; for it had all the simplicity which is so entirely suited to scientific discourse, while it partook largely of the elegance which characterized all he said or did … I have heard the greatest understandings of the age giving forth their efforts in its most eloquent tongues—have heard the commanding periods of Pitt’s majestic oratory—the vehemence of Fox’s burning declamation—have followed the close-compacted chain of Grant’s pure reasoning—been carried away by the mingled fancy, epigram, and argumentation of Plunket; but I should without hesitation prefer, for mere intellectual gratification (though aware how much of it is derived from association), to be once more allowed the privilege which I in those days enjoyed of being present while the first philosopher of his age was the historian of his own discoveries, and be an eyewitness of those experiments by which he had formerly made them, once more performed with his own hands.
Of all heroes, Spinoza was Einstein’s greatest. No one expressed more strongly than he a belief in the harmony, the beauty, and most of all the ultimate comprehensibility of nature.
Of all investments into the future, the conquest of space demands the greatest efforts and the longest-term commitment… but it also offers the greatest reward: none less than a universe.
Of all man’s works of art, a cathedral is greatest. A vast and majestic tree is greater than that.
Of all many-sided subjects, [education] is the one which has the greatest number of sides.
Of all the forces of nature, I should think the wind contains the largest amount of motive power—that is, power to move things. Take any given space of the earth’s surface— for instance, Illinois; and all the power exerted by all the men, and beasts, and running-water, and steam, over and upon it, shall not equal the one hundredth part of what is exerted by the blowing of the wind over and upon the same space. And yet it has not, so far in the world’s history, become proportionably valuable as a motive power. It is applied extensively, and advantageously, to sail-vessels in navigation. Add to this a few windmills, and pumps, and you have about all. … As yet, the wind is an untamed, and unharnessed force; and quite possibly one of the greatest discoveries hereafter to be made, will be the taming, and harnessing of it.
Of all the frictional resistances, the one that most retards human movement is ignorance, what Buddha called 'the greatest evil in the world.' The friction which results from ignorance ... can be reduced only by the spread of knowledge and the unification of the heterogeneous elements of humanity. No effort could be better spent.
Of all the sciences that pertain to reason, Metaphysics and Geometry are those in which imagination plays the greatest part. … Imagination acts no less in a geometer who creates than in a poet who invents. It is true that they operate differently on their object. The first shears it down and analyzes it, the second puts it together and embellishes it. … Of all the great men of antiquity, Archimedes is perhaps the one who most deserves to be placed beside Homer.
On our planet, all objects are subject to continual and inevitable changes which arise from the essential order of things. These changes take place at a variable rate according to the nature, condition, or situation of the objects involved, but are nevertheless accomplished within a certain period of time. Time is insignificant and never a difficulty for Nature. It is always at her disposal and represents an unlimited power with which she accomplishes her greatest and smallest tasks.
On the whole, I cannot help saying that it appears to me not a little extraordinary, that a theory so new, and of such importance, overturning every thing that was thought to be the best established in chemistry, should rest on so very narrow and precarious a foundation, the experiments adduced in support of it being not only ambiguous or explicable on either hypothesis, but exceedingly few. I think I have recited them all, and that on which the greatest stress is laid, viz. That of the formation of water from the decomposition of the two kinds of air, has not been sufficiently repeated. Indeed it required so difficult and expensive an apparatus, and so many precautions in the use of it, that the frequent repetition of the experiment cannot be expected; and in these circumstances the practised experimenter cannot help suspecting the accuracy of the result and consequently the certainty of the conclusion.
One of the greatest discoveries a man makes, one of his great surprises, is to find he can do what he was afraid he couldn’t do.
One of the greatest experimental scientists of the time who was really doing something, William Harvey, said that what Bacon said science was, was the science that a lord-chancellor would do. He [Bacon] spoke of making observations, but omitted the vital factor of judgment about what to observe and what to pay attention to.
One of the greatest gifts science has brought to the world is continuing elimination of the supernatural, and it was a lesson that my father passed on to me, that knowledge liberates mankind from superstition. We can live our lives without the constant fear that we have offended this or that deity who must be placated by incantation or sacrifice, or that we are at the mercy of devils or the Fates. With increasing knowledge, the intellectual darkness that surrounds us is illuminated and we learn more of the beauty and wonder of the natural world.
One of the greatest pains to human nature is the pain of a new idea.
One of the greatest superstitions of our time is the belief that it has none.
One of the principal objects of theoretical research in my department of knowledge is to find the point of view from which the subject appears in its greatest simplicity.
Our credulity is greatest concerning the things we know least about. And since we know least about ourselves, we are ready to believe all that is said about us. Hence the mysterious power of both flattery and calumny.... It is thus with most of us: we are what other people say we are. We know ourselves chiefly by hearsay.
Our greatest glory is not in never falling, but in rising every time we fall.
Our greatest weariness comes from work not done.
Our two greatest problems are gravity and paperwork. We can lick gravity, but sometimes the paperwork is overwhelming.
Outside the practice of science itself, scientists have sometimes been the greatest offenders in adhering to dogmatic ideas against all the evidence.
People have wracked their brains for an explanation of benzene and how the celebrated man [Kekulé] managed to come up with the concept of the benzene theory. With regard to the last point especially, a friend of mine who is a farmer and has a lively interest in chemistry has asked me a question which I would like to share with you. My “agricultural friend” apparently believes he has traced the origins of the benzene theory. “Has Kekulé,” so ran the question, “once been a bee-keeper? You certainly know that bees too build hexagons; they know well that they can store the greatest amount of honey that way with the least amount of wax. I always liked it,” my agricultural friend went on, “When I received a new issue of the Berichte; admittedly, I don't read the articles, but I like the pictures very much. The patterns of benzene, naphthalene and especially anthracene are indeed wonderful. When I look at the pictures I always have to think of the honeycombs of my bee hives.”
Perhaps the greatest paradox of all is that there are paradoxes in mathematics.
Perseus and St. George. These dragon-slayers did not take lessons in dragon-slaying, nor do leaders of forlorn hopes generally rehearse their parts beforehand. Small things may be rehearsed, but the greatest are always do-or-die, neck-or-nothing matters.
Persons possessing great intellect and a capacity for excelling in the creative arts and also in the sciences are generally likely to have heavier brains than the ordinary individual. Arguing from this we might expect to find a corresponding lightness in the brain of the criminal, but this is not always the case ... Many criminals show not a single anomaly in their physical or mental make-up, while many persons with marked evidences of morphological aberration have never exhibited the criminal tendency.
Every attempt to prove crime to be due to a constitution peculiar only to criminals has failed signally. It is because most criminals are drawn from the ranks of the low, the degraded, the outcast, that investigators were ever deceived into attempting to set up a 'type' of criminal. The social conditions which foster the great majority of crimes are more needful of study and improvement.
From study of known normal brains we have learned that there is a certain range of variation. No two brains are exactly alike, and the greatest source of error in the assertions of Benedict and Lombroso has been the finding of this or that variation in a criminal’s brains, and maintaining such to be characteristic of the 'criminal constitution,' unmindful of the fact that like variations of structure may and do exist in the brains of normal, moral persons.
Every attempt to prove crime to be due to a constitution peculiar only to criminals has failed signally. It is because most criminals are drawn from the ranks of the low, the degraded, the outcast, that investigators were ever deceived into attempting to set up a 'type' of criminal. The social conditions which foster the great majority of crimes are more needful of study and improvement.
From study of known normal brains we have learned that there is a certain range of variation. No two brains are exactly alike, and the greatest source of error in the assertions of Benedict and Lombroso has been the finding of this or that variation in a criminal’s brains, and maintaining such to be characteristic of the 'criminal constitution,' unmindful of the fact that like variations of structure may and do exist in the brains of normal, moral persons.
Physiology is the experimental science par excellence of all sciences; that in which there is least to be learnt by mere observation, and that which affords the greatest field for the exercise of those faculties which characterize the experimental philosopher.
Preconceived ideas are like searchlights which illumine the path of experimenter and serve him as a guide to interrogate nature. They become a danger only if he transforms them into fixed ideas – this is why I should like to see these profound words inscribed on the threshold of all the temples of science: “The greatest derangement of the mind is to believe in something because one wishes it to be so.”
Published papers may omit important steps and the memory of men of science, even the greatest, is sadly fallible.
Said M. Waldman, “…Chemistry is that branch of natural philosophy in which the greatest improvements have been and may be made; it is on that account that I have made it my peculiar study; but at the same time, I have not neglected the other branches of science. A man would make but a very sorry chemist if he attended to that department of human knowledge alone. If your wish is to become really a man of science and not merely a petty experimentalist, I should advise you to apply to every branch of natural philosophy, including mathematics.”
Science … has no consideration for ultimate purposes, any more than Nature has, but just as the latter occasionally achieves things of the greatest suitableness without intending to do so, so also true science, as the imitator of nature in ideas, will occasionally and in many ways further the usefulness and welfare of man,—but also without intending to do so.
Science is the Differential Calculus of the mind. Art the Integral Calculus; they may be beautiful when apart, but are greatest only when combined.
Scientific truth, like puristic truth, must come about by controversy. Personally this view is abhorrent to me. It seems to mean that scientific truth must transcend the individual, that the best hope of science lies in its greatest minds being often brilliantly and determinedly wrong, but in opposition, with some third, eclectically minded, middle-of-the-road nonentity seizing the prize while the great fight for it, running off with it, and sticking it into a textbook for sophomores written from no point of view and in defense of nothing whatsoever. I hate this view, for it is not dramatic and it is not fair; and yet I believe that it is the verdict of the history of science.
Sir H. Davy's greatest discovery was Michael Faraday.
Sir Mortimer Wheeler is perhaps the most distinguished archaeologist in Europe. But he owes the greatest of his achievements to the rare combination of two qualities: namely a scientific expertise in the technique of excavation which has always been marked by a meticulous attention to minute detail, and a gift of imaginative vision.
So why fret and care that the actual version of the destined deed was done by an upper class English gentleman who had circumnavigated the globe as a vigorous youth, lost his dearest daughter and his waning faith at the same time, wrote the greatest treatise ever composed on the taxonomy of barnacles, and eventually grew a white beard, lived as a country squire just south of London, and never again traveled far enough even to cross the English Channel? We care for the same reason that we love okapis, delight in the fossil evidence of trilobites, and mourn the passage of the dodo. We care because the broad events that had to happen, happened to happen in a certain particular way. And something unspeakably holy –I don’t know how else to say this–underlies our discovery and confirmation of the actual details that made our world and also, in realms of contingency, assured the minutiae of its construction in the manner we know, and not in any one of a trillion other ways, nearly all of which would not have included the evolution of a scribe to record the beauty, the cruelty, the fascination, and the mystery.
Sociology is the science with the greatest number of methods and the least results.
Some few, & I am one, even wish to God, though at the loss of millions of lives, that the North would proclaim a crusade against Slavery. In the long run, a million horrid deaths would be amply repaid in the cause of humanity. ... Great God how I shd like to see that greatest curse on Earth Slavery abolished.
Speculations apparently the most unprofitable have almost invariably been those from which the greatest practical applications have emanated.
Stone, wood and iron are wrought and put together by mechanical methods, but the greatest work is to keep right the animal part of the machinery.
Surely every medicine is an innovation, and he that will not apply new remedies must expect new evils for time is the greatest innovator.
Taking him for all and all, I think it will be conceded that Michael Faraday was the greatest experimental philosopher the world has ever seen; and I will add the opinion, that the progress of future research will tend, not to dim or to diminish, but to enhance and glorify the labours of this mighty investigator.
Technology is a gift of God. After the gift of life it is perhaps the greatest of God's gifts. It is the mother of civilizations, of arts and of sciences.
That a woman should at present be almost driven from society, for an offence [illegitimate childbearing], which men commit nearly with impunity, seems to be undoubtedly a breach of natural justice… . What at first might be dictated by state necessity, is now supported by female delicacy; and operates with the greatest force on that part of society, where, if the original intention of the custom were preserved, there is the least real occasion for it.
The advances of biology during the past 20 years have been breathtaking, particularly in cracking the mystery of heredity. Nevertheless, the greatest and most difficult problems still lie ahead. The discoveries of the 1970‘s about the chemical roots of memory in nerve cells or the basis of learning, about the complex behavior of man and animals, the nature of growth, development, disease and aging will be at least as fundamental and spectacular as those of the recent past.
The application of algebra to geometry…, far more than any of his metaphysical speculations, immortalized the name of Descartes, and constitutes the greatest single step ever made in the progress of the exact sciences.
The calculus is the greatest aid we have to the appreciation of physical truth in the broadest sense of the word.
The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.
The conservative has but little to fear from the man whose reason is the servant of his passions, but let him beware of him in whom reason has become the greatest and most terrible of the passions.
The discovery of the conic sections, attributed to Plato, first threw open the higher species of form to the contemplation of geometers. But for this discovery, which was probably regarded in Plato’s tune and long after him, as the unprofitable amusement of a speculative brain, the whole course of practical philosophy of the present day, of the science of astronomy, of the theory of projectiles, of the art of navigation, might have run in a different channel; and the greatest discovery that has ever been made in the history of the world, the law of universal gravitation, with its innumerable direct and indirect consequences and applications to every department of human research and industry, might never to this hour have been elicited.
The equation of evolution with progress represents our strongest cultural impediment to a proper understanding of this greatest biological revolution in the history of human thought.
The Europeans and the Americans are not throwing $10 billion down this gigantic tube for nothing. We're exploring the very forefront of physics and cosmology with the Large Hadron Collider because we want to have a window on creation, we want to recreate a tiny piece of Genesis to unlock some of the greatest secrets of the universe.
The external world of physics has … become a world of shadows. In removing our illusions we have removed the substance, for indeed we have seen that substance is one of the greatest of our illusions. Later perhaps we may inquire whether in our zeal to cut out all that is unreal we may not have used the knife too ruthlessly. Perhaps, indeed, reality is a child which cannot survive without its nurse illusion. But if so, that is of little concern to the scientist, who has good and sufficient reasons for pursuing his investigations in the world of shadows and is content to leave to the philosopher the determination of its exact status in regard to reality.
The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself.
The fact that stares one in the face is that people of the greatest sincerity and of all levels of intelligence differ and have always differed in their religious beliefs. Since at most one faith can be true, it follows that human beings are extremely liable to believe firmly and honestly in something untrue in the field of revealed religion. One would have expected this obvious fact to lead to some humility, to some thought that however deep one's faith, one may conceivably be mistaken. Nothing is further from the believer, any believer, than this elementary humility. All in his power … must have his faith rammed down their throats. In many cases children are indeed indoctrinated with the disgraceful thought that they belong to the one group with superior knowledge who alone have a private wire to the office of the Almighty, all others being less fortunate than they themselves.
The first [quality] to be named must always be the power of attention, of giving one's whole mind to the patient without the interposition of anything of oneself. It sounds simple but only the very greatest doctors ever fully attain it. … The second thing to be striven for is intuition. This sounds an impossibility, for who can control that small quiet monitor? But intuition is only interference from experience stored and not actively recalled. … The last aptitude I shall mention that must be attained by the good physician is that of handling the sick man's mind.
The first observation of cancer cells in the smear of the uterine cervix gave me one of the greatest thrills I ever experienced during my scientific career.
The grand aim of all science is to cover the greatest number of empirical facts by logical deduction from the smallest possible number of hypotheses or axioms.
The greatest achievements in the science of this [twentieth] century are themselves the sources of more puzzlement than human beings have ever experienced. Indeed, it is likely that the twentieth century will be looked back at as the time when science provided the first close glimpse of the profundity of human ignorance. We have not reached solutions; we have only begun to discover how to ask questions.
The greatest advantage to be derived from the study of geometry of more than three dimensions is a real understanding of the great science of geometry. Our plane and solid geometries are but the beginning of this science. The four-dimensional geometry is far more extensive than the three-dimensional, and all the higher geometries are more extensive than the lower.
The greatest and noblest pleasure which we can have in this world is to discover new truths; and the next is to shake off old prejudices.
The greatest challenge facing mankind is the challenge of distinguishing reality from fantasy, truth from propaganda. We must daily decide whether the threats we face are real, whether the solutions we are offered will do any good, whether the problems we’re told exist are in fact real problems, or non-problems.
The greatest difficulty comes at the start. It’s called "getting ready."
The greatest discoveries of surgery are anaesthesia, asepsis, and roentgenology—and none was made by a surgeon.
The greatest enemy, however, to true arithmetic work is found in so-called practical or illustrative problems, which are freely given to our pupils, of a degree of difficulty and complexity altogether unsuited to their age and mental development. … I am, myself, no bad mathematician, and all the reasoning powers with which nature endowed me have long been as fully developed as they are ever likely to be; but I have, not infrequently, been puzzled, and at times foiled, by the subtle logical difficulty running through one of these problems, given to my own children. The head-master of one of our Boston high schools confessed to me that he had sometimes been unable to unravel one of these tangled skeins, in trying to help his own daughter through her evening’s work. During this summer, Dr. Fairbairn, the distinguished head of one of the colleges of Oxford, England, told me that not only had he himself encountered a similar difficulty, in the case of his own children, but that, on one occasion, having as his guest one of the first mathematicians of England, the two together had been completely puzzled by one of these arithmetical conundrums.
The greatest evil is physical pain.
The greatest gift of the essayistic mind: to extract a momentous truth from the most seemingly trivial event or artifact.
The greatest good you can do for another is not just share your riches, but reveal to them their own.
The greatest human evils are not those that individuals perform in private, the tiny transgressions against some arbitrary social standard we call sins. The ultimate evils are the mass murders that occur in revolution and war, the large-scale savageries that arise when one agglomeration of humans tries to dominate another: the deeds of the social group. … only group efforts can save us from the sporadic insanities of the group.
The greatest invention of the nineteenth century was the invention of the method of invention.
The greatest inventions are those inquiries which tend to increase the power of man over matter.
The greatest Inventions were produced in Times of Ignorance; as the Use of the Compass, Gunpowder, and Printing; and by the dullest Nation, as the Germans.
The greatest inventors are unknown to us. Someone invented the wheel—but who?
The greatest joy in life is to accomplish. It is the getting, not the having. It is the giving, not the keeping.
The greatest marvel is not in the individual. It is in the succession, in the renewal and in the duration of the species that Nature would seem quite inconceivable. This power of producing its likeness that resides in animals and plants, this form of unity, always subsisting and appearing eternal, this procreative virtue which is perpetually expressed without ever being destroyed, is for us a mystery which, it seems, we will never be able to fathom.
The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure.
The greatest men I have ever known have written their own papers.
The greatest mystery is why there is something instead of nothing, and the greatest something is this thing we call life.
The greatest obstacle to discovery is not ignorance—it is the illusion of knowledge.
The greatest of all spectral classifiers, Antonia Maury had two strikes on her: the biggest one was, she was a woman. A woman had no chance at anything in astronomy except at Harvard in the 1880’s and 1890’s. And even there, things were rough. It now turns out that her director, E.C. Pickering, did not like the way she classified; she then refused to change to suit him; and after her great publication in Harvard Annals 28 (1897), she left Harvard—and in a sense, astronomy. ... I would say the most remarkable phenomenological investigation in modern astronomy is Miss Maury’s work in Harvard Annals 28. She didn’t have anything astrophysical to go on. Investigations between 1890 and 1900 were the origin of astrophysics. But these were solar, mostly. And there Miss Maury was on the periphery. I’ve seen pictures of groups, where she’d be standing away a little bit to one side of the other people, a little bit in the background. It was a very sad thing. When Hertzsprung wrote Pickering to congratulate him on Miss Maury’s work that had led to Hertzsprung’s discovery of super giants, Pickering is supposed to have replied that Miss Maury’s work was wrong — could not possibly be correct.
The greatest pleasure in life is doing what people say you cannot do.
The greatest possibility of evil in self-medication [with penicillin] is the use of too-small doses, so that, instead of clearing up the infection, the microbes are educated to resist penicillin and a host of penicillin-fast organisms is bred out which can be passed on to other individuals and perhaps from there to others until they reach someone who gets a septicemia or a pneumonia which penicillin cannot save. In such a case the thoughtless person playing with penicillin treatment is morally responsible for the death of the man who finally succumbs to infection with the penicillin-resistant organism. I hope this evil can be averted.
The greatest problem of communication is the illusion that it has been achieved.
The greatest productive force is human selfishness.
The greatest reward lies in making the discovery; recognition can add little or nothing to that.
The greatest scandal of the century in American psychiatry … is the growing mania among thousands of inept therapists, family counselors, and social workers for arousing false memories of childhood sexual abuse.
The greatest scientists have always looked on scientific materialism as a kind of religion, as a mythology. They are impelled by a great desire to explore mystery, to celebrate mystery in the universe, to open it up, to read the stars, to find the deeper meaning.
The greatest service which can be rendered any country is to add an useful plant to its culture; especially, a bread grain; next in value to bread is oil.
The greatest single achievement of nature to date was surely the invention of the molecule DNA.
The greatest slave is not he who is ruled by a despot, great though that evil be, but he who is in the thrall of his own moral ignorance, selfishness, and vice.
The greatest spiritual revolutionary Western history, Saint Francis, proposed what he thought was an alternative Christian view of nature and man’s relation to it: he tried to substitute the idea of the equality of creatures, including man, for the idea of man’s limitless rule of creation. He failed. Both our present science and our present technology are so tinctured with orthodox Christian arrogance toward nature that no solution for our ecologic crisis can be expected from them alone. Since the roots of our trouble are so largely religious, the remedy must also be essentially religious, whether we call it that or not. We must rethink and refeel our nature and destiny. The profoundly religious, but heretical, sense of the primitive Franciscans for the spiritual autonomy of all parts of nature may point a direction. I propose Francis as a patron saint for ecologists.
The greatest unsolved theorem in mathematics is why some people are better at it than others.
The greatest value of a picture is when it forces us to notice what we never expected to see.
The Greeks in the first vigour of their pursuit of mathematical truth, at the time of Plato and soon after, had by no means confined themselves to those propositions which had a visible bearing on the phenomena of nature; but had followed out many beautiful trains of research concerning various kinds of figures, for the sake of their beauty alone; as for instance in their doctrine of Conic Sections, of which curves they had discovered all the principal properties. But it is curious to remark, that these investigations, thus pursued at first as mere matters of curiosity and intellectual gratification, were destined, two thousand years later, to play a very important part in establishing that system of celestial motions which succeeded the Platonic scheme of cycles and epicycles. If the properties of conic sections had not been demonstrated by the Greeks and thus rendered familiar to the mathematicians of succeeding ages, Kepler would probably not have been able to discover those laws respecting the orbits and motions of planets which were the occasion of the greatest revolution that ever happened in the history of science.
The influence of electricity in producing decompositions, although of inestimable value as an instrument of discovery in chemical inquiries, can hardly be said to have been applied to the practical purposes of life, until the same powerful genius [Davy] which detected the principle, applied it, by a singular felicity of reasoning, to arrest the corrosion of the copper-sheathing of vessels. … this was regarded as by Laplace as the greatest of Sir Humphry's discoveries.
The law of gravitation is indisputably and incomparably the greatest scientific discovery ever made, whether we look at the advance which it involved, the extent of truth disclosed, or the fundamental and satisfactory nature of this truth.
The laws of nature, as we understand them, are the foundation of our knowledge in natural things. So much as we know of them has been developed by the successive energies of the highest intellects, exerted through many ages. After a most rigid and scrutinizing examination upon principle and trial, a definite expression has been given to them; they have become, as it were, our belief or trust. From day to day we still examine and test our expressions of them. We have no interest in their retention if erroneous. On the contrary, the greatest discovery a man could make would be to prove that one of these accepted laws was erroneous, and his greatest honour would be the discovery.
The life and soul of science is its practical application, and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in the earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind.
The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful.
The more I think of it, I find this conclusion more impressed upon me—that the greatest thing a human soul ever does in this world is to see something, and tell what it saw in a plain way.
The most part of leaves pour out the greatest quantity of this dephlogisticated air [oxygen] from their under surface, principally those of lofty trees.
The most remarkable thing was his [Clifford’s] great strength as compared with his weight, as shown in some exercises. At one time he could pull up on the bar with either hand, which is well known to be one of the greatest feats of strength. His nerve at dangerous heights was extraordinary. I am appalled now to think that he climbed up and sat on the cross bars of the weathercock on a church tower, and when by way of doing something worse I went up and hung by my toes to the bars he did the same.
The most successful men in the end are those whose success is the result of steady accretion. That intellectuality is more vigorous that has attained its strength gradually. It is the man who carefully advances step by step, with his mind becoming wider and wider—and progressively better able to grasp any theme or situation—persevering in what he knows to be practical, and concentrating his thought upon it, who is bound to succeed in the greatest degree.
The necessary has never been man’s top priority. The passionate pursuit of the nonessential and the extravagant is one of the chief traits of human uniqueness. Unlike other forms of life, man’s greatest exertions are made in the pursuit not of necessities but of superfluities. Man is the only creature that strives to surpass himself, and yearns for the impossible.
The overwhelming astonishment, the queerest structure we know about so far in the whole universe, the greatest of all cosmological scientific puzzles, confounding all our efforts to comprehend it, is the earth.
The overwhelming astonishment, the queerest structure we know about so far in the whole universe, the greatest of all cosmological scientific puzzles, confounding all our efforts to comprehend it, is the earth. We are only now beginning to appreciate how strange and splendid it is, how it catches the breath, the loveliest object afloat around the sun, enclosed in its own blue bubble of atmosphere, manufacturing and breathing its own oxygen, fixing its own nitrogen from the air into its own soil, generating its own weather at the surface of its rain forests, constructing its own carapace from living parts: chalk cliffs, coral reefs, old fossils from earlier forms of life now covered by layers of new life meshed together around the globe, Troy upon Troy.