...great difficulties are felt at first and these cannot be overcome except by starting from experiments .. and then be conceiving certain hypotheses ... But even so, very much hard work remains to be done and one needs not only great perspicacity but often a degree of good fortune.

...learning chiefly in mathematical sciences can so swallow up and fix one's thought, as to possess it entirely for some time; but when that amusement is over, nature will return, and be where it was, being rather diverted than overcome by such speculations.

[In childhood, to overcome fear, the] need took me back again and again to a sycamore tree rising from the earth at the edge of a ravine. It was a big, old tree that had grown out over the ravine, so that when you climbed it, you looked straight down fifty feet or more. Every time I climbed that tree, I forced myself to climb to the last possible safe limb and then look down. Every time I did it, I told myself I’d never do it again. But I kept going back because it scared me and I had to know I could overcome that.

[Mercurial medicines] affect the human constitution in a peculiar manner, taking, so to speak, an iron grasp of all its systems, and penetrating even to the bones, by which they not only change the healthy action of its vessels, and general structure, but greatly impair and destroy its energies; so that their abuse is rarely overcome. When the tone of the stomach, intestines, or nervous system generally, has been once injured by this mineral ... it could seldom be restored.

Question: A hollow indiarubber ball full of air is suspended on one arm of a balance and weighed in air. The whole is then covered by the receiver of an air pump. Explain what will happen as the air in the receiver is exhausted.
Answer: The ball would expand and entirely fill the vessell, driving out all before it. The balance being of greater density than the rest would be the last to go, but in the end its inertia would be overcome and all would be expelled, and there would be a perfect vacuum. The ball would then burst, but you would not be aware of the fact on account of the loudness of a sound varying with the density of the place in which it is generated, and not on that in which it is heard.

A strange feeling of complete, almost solemn contentment suddenly overcame me when the descent module landed, rocked, and stilled. The weather was foul, but I smelled Earth, unspeakably sweet and intoxicating. And wind. Now utterly delightful; wind after long days in space.

Be of good cheer. Do not think of today’s failures, but of the success that may come tomorrow. You have set yourself a difficult task, but you will succeed if you persevere; and you will find a joy in overcoming obstacles.

Borel makes the amusing supposition of a million monkeys allowed to play upon the keys of a million typewriters. What is the chance that this wanton activity should reproduce exactly all of the volumes which are contained in the library of the British Museum? It certainly is not a large chance, but it may be roughly calculated, and proves in fact to be considerably larger than the chance that a mixture of oxygen and nitrogen will separate into the two pure constituents. After we have learned to estimate such minute chances, and after we have overcome our fear of numbers which are very much larger or very much smaller than those ordinarily employed, we might proceed to calculate the chance of still more extraordinary occurrences, and even have the boldness to regard the living cell as a result of random arrangement and rearrangement of its atoms. However, we cannot but feel that this would be carrying extrapolation too far. This feeling is due not merely to a recognition of the enormous complexity of living tissue but to the conviction that the whole trend of life, the whole process of building up more and more diverse and complex structures, which we call evolution, is the very opposite of that which we might expect from the laws of chance.

By 1999, over 880 studies suggested that some mutations might … be genetic alterations “custom tailored” to overcome emergencies.

Darwin's theory was received in Russia with profound sympathy. While in Western Europe it met firmly established old traditions which it had first to overcome, in Russia its appearance coincided with the awakening of our society after the Crimean War and here it immediately received the status of full citizenship and ever since has enjoyed widespread popularity.

Everest for me, and I believe for the world, is the physical and symbolic manifestation of overcoming odds to achieve a dream.

I still take failure very seriously, but I've found that the only way I could overcome the feeling is to keep on working, and trying to benefit from failures or disappointments. There are always some lessons to be learned. So I keep on working.

If the resident zoologist of Galaxy X had visited the earth 5 million years ago while making his inventory of inhabited planets in the universe, he would surely have corrected his earlier report that apes showed more promise than Old World monkeys and noted that monkeys had overcome an original disadvantage to gain domination among primates. (He will confirm this statement after his visit next year–but also add a footnote that one species from the ape bush has enjoyed an unusual and unexpected flowering, thus demanding closer monitoring.)

In the first papers concerning the aetiology of tuberculosis I have already indicated the dangers arising from the spread of the bacilli-containing excretions of consumptives, and have urged moreover that prophylactic measures should be taken against the contagious disease. But my words have been unheeded. It was still too early, and because of this they still could not meet with full understanding. It shared the fate of so many similar cases in medicine, where a long time has also been necessary before old prejudices were overcome and the new facts were acknowledged to be correct by the physicians.

It certainly strikes the beholder with astonishment, to perceive what vast difficulties can be overcome by the pigmy arms of little mortal man, aided by science and directed by superior skill.

It is perhaps a law of nature that when a species (or group) fits itself to a place not previously occupied, and in which it is subject to no opposition from beings of its own class, or where it attains so great a perfection as to be able easily to overcome all opposition, the character eventually loses its original plasticity, or tendency to vary, since improvement in such a case would be superfluous, and becomes, so to speak, crystallized in that form which continues thereafter unaltered. … [Such as] the humming-bird.

It stands to the everlasting credit of science that by acting on the human mind it has overcome man's insecurity before himself and before nature.

Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty (of the parallel axiom). He went so far as to write a paper, which he took with him to the Institute, and began to read it. But in the first paragraph something struck him that he had not observed: he muttered: 'Il faut que j'y songe encore', and put the paper in his pocket.' [I must think about it again]

MAGNITUDE, n. Size. Magnitude being purely relative, nothing is large and nothing small. If everything in the universe were increased in bulk one thousand diameters nothing would be any larger than it was before, but if one thing remained unchanged all the others would be larger than they had been. To an understanding familiar with the relativity of magnitude and distance the spaces and masses of the astronomer would be no more impressive than those of the microscopist. For anything we know to the contrary, the visible universe may be a small part of an atom, with its component ions, floating in the life-fluid (luminiferous ether) of some animal. Possibly the wee creatures peopling the corpuscles of our own blood are overcome with the proper emotion when contemplating the unthinkable distance from one of these to another.

Man must at all costs overcome the Earth’s gravity and have, in reserve, the space at least of the Solar System. All kinds of danger wait for him on the Earth… We are talking of disaster that can destroy the whole of mankind or a large part of it… For instance, a cloud of bolides [meteors] or a small planet a few dozen kilometers in diameter could fall on the Earth, with such an impact that the solid, liquid or gaseous blast produced by it could wipe off the face of the Earth all traces of man and his buildings. The rise of temperature accompanying it could alone scorch or kill all living beings… We are further compelled to take up the struggle against gravity, and for the utilization of celestial space and all its wealth, because of the overpopulation of our planet. Numerous other terrible dangers await mankind on the Earth, all of which suggest that man should look for a way into the Cosmos. We have said a great deal about the advantages of migration into space, but not all can be said or even imagined.

Man tries to make for himself in the fashion that suits him best a simplified and intelligible picture of the world; he then tries to some extent to substitute this cosmos of his for the world of experience, and thus to overcome it. This is what the painter, the poet, the speculative philosopher, and the natural scientist do, each in his own fashion. Each makes this cosmos and its construction the pivot of his emotional life, in order to find in this way the peace and security which he cannot find in the narrow whirlpool of personal experience.

Nature does not consist entirely, or even largely, of problems designed by a Grand Examiner to come out neatly in finite terms, and whatever subject we tackle the first need is to overcome timidity about approximating.

Nature is often hidden, sometimes overcome, seldom extinguished.

That alone is worthy to be called Natural History, which investigates and records the condition of living things, of things in a state of nature; if animals, of living animals:— which tells of their 'sayings and doings,' their varied notes and utterances, songs and cries; their actions, in ease and under the pressure of circumstances; their affections and passions, towards their young, towards each other, towards other animals, towards man: their various arts and devices, to protect their progeny, to procure food, to escape from their enemies, to defend themselves from attacks; their ingenious resources for concealment; their stratagems to overcome their victims; their modes of bringing forth, of feeding, and of training, their offspring; the relations of their structure to their wants and habits; the countries in which they dwell; their connexion with the intimate world around them, mountain or plain, forest or field, barren heath or bushy dell, open savanna or wild hidden glen, river, lake, or sea:— this would be indeed zoology, i.e. the science of living creatures.

The first successes were such that one might suppose all the difficulties of science overcome in advance, and believe that the mathematician, without being longer occupied in the elaboration of pure mathematics, could turn his thoughts exclusively to the study of natural laws.

The inertia hardest to overcome is that of perfectly good seconds.

The Mathematics, I say, which effectually exercises, not vainly deludes or vexatiously torments studious Minds with obscure Subtilties, perplexed Difficulties, or contentious Disquisitions; which overcomes without Opposition, triumphs without Pomp, compels without Force, and rules absolutely without Loss of Liberty; which does not privately over-reach a weak Faith, but openly assaults an armed Reason, obtains a total Victory, and puts on inevitable Chains; whose Words are so many Oracles, and Works as many Miracles; which blabs out nothing rashly, nor designs anything from the Purpose, but plainly demonstrates and readily performs all Things within its Verge; which obtrudes no false Shadow of Science, but the very Science itself, the Mind firmly adhering to it, as soon as possessed of it, and can never after desert it of its own Accord, or be deprived of it by any Force of others: Lastly the Mathematics, which depends upon Principles clear to the Mind, and agreeable to Experience; which draws certain Conclusions, instructs by profitable Rules, unfolds pleasant Questions; and produces wonderful Effects; which is the fruitful Parent of, I had almost said all, Arts, the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human Affairs.

The privilege is not allowed even to genius in this world to inspect its own elements, and read its own destiny, and it is perhaps well for mankid that it is so. Could we lift the curtain which hides our future lives, and glance hastily at the misfortunes, the vexations, and the disappointments which await us, we should be discouraged from attempting the performance of even of such deeds as are destined eventually to crown us with honor.
In a book of his reminiscenses, Oliver Hampton Smith, years after his first meeting with Morse, described the inventor - who had by then overcome the initial scepticism over his invention, but instead needed to vigorously defend his exclusive right of property in the magnetic telegraph.

The traditional mathematics professor of the popular legend is absentminded. He usually appears in public with a lost umbrella in each hand. He prefers to face a blackboard and to turn his back on the class. He writes a, he says b, he means c, but it should be d. Some of his sayings are handed down from generation to generation:
“In order to solve this differential equation you look at it till a solution occurs to you.”
“This principle is so perfectly general that no particular application of it is possible.”
“Geometry is the science of correct reasoning on incorrect figures.”
“My method to overcome a difficulty is to go round it.”
“What is the difference between method and device? A method is a device which you used twice.”

There is another ground of hope that must not be omitted. Let men but think over their infinite expenditure of understanding, time, and means on matters and pursuits of far less use and value; whereof, if but a small part were directed to sound and solid studies, there is no difficulty that might not be overcome.

This man, one of the chief architects of the atomic bomb, so the story runs, was out wandering in the woods one day with a friend when he came upon a small tortoise. Overcome with pleasurable excitement, he took up the tortoise and started home, thinking to surprise his children with it. After a few steps he paused and surveyed the tortoise doubtfully.
“What's the matter?” asked his friend.
Without responding, the great scientist slowly retraced his steps as precisely as possible, and gently set the turtle down on the exact spot from which he had taken him.
Then he turned solemnly to his friend. “It just struck me,” he said, “that, perhaps for one man, I have tampered enough with the universe.” He turned, and left the turtle to wander on its way.

Tranquilizers to overcome angst, pep pills to wake us up, life pills to ensure blissful sterility. I will lift up my ears unto the pills whence cometh my help.

True majorities, in a TV-dominated and anti-intellectual age, may need sound bites and flashing lights–and I am not against supplying such lures if they draw children into even a transient concern with science. But every classroom has one [Oliver] Sacks, one [Eric] Korn, or one [Jonathan] Miller, usually a lonely child with a passionate curiosity about nature, and a zeal that overcomes pressures for conformity. Do not the one in fifty deserve their institutions as well–magic places, like cabinet museums, that can spark the rare flames of genius?

We have overcome the notion that mathematical truths have an existence independent and apart from our own minds. It is even strange to us that such a notion could ever have existed.

We have overcome the notion that mathematical truths have an existence independent and apart from our own minds. It is even strange to us that such a notion could ever have existed. [Coauthor with James R. Newman]

When Allah created his creatures Fie wrote above His throne: “Verily, my Compassion overcomes my wrath

When Death lurks at the door, the physician is considered as a God. When danger has been overcome, the physician is looked upon as an angel. When the patient begins to convalesce, the physician becomes a mere human. When the physician asks for his fees, he is considered as the devil himself.

Who … is not familiar with Maxwell’s memoirs on his dynamical theory of gases? … from one side enter the equations of state; from the other side, the equations of motion in a central field. Ever higher soars the chaos of formulae. Suddenly we hear, as from kettle drums, the four beats “put n=5.” The evil spirit v vanishes; and … that which had seemed insuperable has been overcome as if by a stroke of magic … One result after another follows in quick succession till at last … we arrive at the conditions for thermal equilibrium together with expressions for the transport coefficients.

With or without us, the wild will return. … … It seems that, however grave our mistakes, nature will be able to overcome them, given the chance. The living world has survived mass extinctions several times before. But we humans cannot assume that we will do the same.

Without tracing back to the Tower of Babel, one can observe that the very idea of building a very tall tower has long haunted human imagination. That kind of victory over the formidable law of gravity that tethers man to the ground has always appeared to him a symbol of the force and the challenges overcome.