A hero is an ordinary individual who finds the strength to persevere and endure in spite of overwhelming obstacles.

A man does what he must—in spite of personal consequences, in spite of obstacles and dangers and pressures—and that is the basis of all human morality.

Adventure isn’t hanging on a rope off the side of a mountain. Adventure is an attitude that we must apply to the day to day obstacles of life - facing new challenges, seizing new opportunities, testing our resources against the unknown and in the process, discovering our own unique potential.

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.

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.

Considerable obstacles generally present themselves to the beginner, in studying the elements of Solid Geometry, from the practice which has hitherto uniformly prevailed in this country, of never submitting to the eye of the student, the figures on whose properties he is reasoning, but of drawing perspective representations of them upon a plane. ...I hope that I shall never be obliged to have recourse to a perspective drawing of any figure whose parts are not in the same plane.

Courage and perseverance have a magical talisman, before which difficulties disappear and obstacles vanish into air.

Creating a new theory is not like destroying an old barn and erecting a skyscraper in its place. It is rather like climbing a mountain, gaining new and wider views, discovering unexpected connections between our starting point and its rich environment. But the point from which we started out still exists and can be seen, although it appears smaller and forms a tiny part of our broad view gained by the mastery of the obstacles on our adventurous way up.

Even mistaken hypotheses and theories are of use in leading to discoveries. This remark is true in all the sciences. The alchemists founded chemistry by pursuing chimerical problems and theories which are false. In physical science, which is more advanced than biology, we might still cite men of science who make great discoveries by relying on false theories. It seems, indeed, a necessary weakness of our mind to be able to reach truth only across a multitude of errors and obstacles.

Evolution is an obstacle course not a freeway; the correct analogue for long-term success is a distant punt receiver evading legions of would-be tacklers in an oddly zigzagged path toward a goal, not a horse thundering down the flat.

Gifford Pinchot points out that in colonial and pioneer days the forest was a foe and an obstacle to the settler. It had to be cleared away... But [now] as a nation we have not yet come to have a proper respect for the forest and to regard it as an indispensable part of our resources—one which is easily destroyed but difficult to replace; one which confers great benefits while it endures, but whose disappearance is accompanied by a train of evil consequences not readily foreseen and positively irreparable.

I think that science would never have achieved much progress if it had always imagined unknown obstacles hidden round every corner. At least we may peer gingerly round the corner, and perhaps we shall find there is nothing very formidable after all.

I took him [Lawrence Bragg] to a young zoologist working on pattern formation in insect cuticles. The zoologist explained how disturbances introduced into these regular patterns pointed to their formation being governed by some kind of gradient. Bragg listened attentively and then exclaimed: “Your disturbed gradient behaves like a stream of sand running downhill and encountering an obstacle.” “Good heavens,” replied the zoologist, “I had been working on this problem for years before this simple analogy occurred to me and you think of it after twenty minutes.”

I was unable to devote myself to the learning of this al-jabr [algebra] and the continued concentration upon it, because of obstacles in the vagaries of Time which hindered me; for we have been deprived of all the people of knowledge save for a group, small in number, with many troubles, whose concern in life is to snatch the opportunity, when Time is asleep, to devote themselves meanwhile to the investigation and perfection of a science; for the majority of people who imitate philosophers confuse the true with the false, and they do nothing but deceive and pretend knowledge, and they do not use what they know of the sciences except for base and material purposes; and if they see a certain person seeking for the right and preferring the truth, doing his best to refute the false and untrue and leaving aside hypocrisy and deceit, they make a fool of him and mock him.

I would like to emphasize strongly my belief that the era of computing chemists, when hundreds if not thousands of chemists will go to the computing machine instead of the laboratory for increasingly many facets of chemical information, is already at hand. There is only one obstacle, namely that someone must pay for the computing time.

If it were always necessary to reduce everything to intuitive knowledge, demonstration would often be insufferably prolix. This is why mathematicians have had the cleverness to divide the difficulties and to demonstrate separately the intervening propositions. And there is art also in this; for as the mediate truths (which are called lemmas, since they appear to be a digression) may be assigned in many ways, it is well, in order to aid the understanding and memory, to choose of them those which greatly shorten the process, and appear memorable and worthy in themselves of being demonstrated. But there is another obstacle, viz.: that it is not easy to demonstrate all the axioms, and to reduce demonstrations wholly to intuitive knowledge. And if we had chosen to wait for that, perhaps we should not yet have the science of geometry.

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

In the tropical and subtropical regions, endemic malaria takes first place almost everywhere among the causes of morbidity and mortality and it constitutes the principal obstacle to the acclimatization of Europeans in these regions.

Incompetency is a greater obstacle to perfection than one would think.

Intellectual work is an act of creation. It is as if the mental image that is studied over a period of time were to sprout appendages like an ameba—outgrowths that extend in all directions while avoiding one obstacle after another—before interdigitating with related ideas.

It was shortly after midday on December 12, 1901, [in a hut on the cliffs at St. John’s, Newfoundland] that I placed a single earphone to my ear and started listening. The receiver on the table before me was very crude—a few coils and condensers and a coherer—no valves [vacuum tubes], no amplifiers, not even a crystal. I was at last on the point of putting the correctness of all my beliefs to test. … [The] answer came at 12:30. … Suddenly, about half past twelve there sounded the sharp click of the “tapper” … Unmistakably, the three sharp clicks corresponding to three dots sounded in my ear. “Can you hear anything, Mr. Kemp?” I asked, handing the telephone to my assistant. Kemp heard the same thing as I. … I knew then that I had been absolutely right in my calculations. The electric waves which were being sent out from Poldhu [Cornwall, England] had travelled the Atlantic, serenely ignoring the curvature of the earth which so many doubters considered a fatal obstacle. … I knew that the day on which I should be able to send full messages without wires or cables across the Atlantic was not far distant.

Logic teaches us that on such and such a road we are sure of not meeting an obstacle; it does not tell us which is the road that leads to the desired end. For this, it is necessary to see the end from afar, and the faculty which teaches us to see is intuition. Without it, the geometrician would be like a writer well up in grammar but destitute of ideas.

No matter how we twist and turn we shall always come back to the cell. The eternal merit of Schwann does not lie in his cell theory that has occupied the foreground for so long, and perhaps will soon be given up, but in his description of the development of the various tissues, and in his demonstration that this development (hence all physiological activity) is in the end traceable back to the cell. Now if pathology is nothing but physiology with obstacles, and diseased life nothing but healthy life interfered with by all manner of external and internal influences then pathology too must be referred back to the cell.

Now, I must tell you of a strange experience which bore fruit in my later life. … We had a cold [snap] drier that ever observed before. People walking in the snow left a luminous trail behind them and a snowball thrown against an obstacle gave a flare of light like a loaf of sugar hit with a knife. [As I stroked] Mačak’s back, [it became] a sheet of light and my hand produced a shower of sparks. … My father … remarked, this is nothing but electricity, the same thing you see on the trees in a storm. My mother seemed alarmed. Stop playing with the cat, she said, he might start a fire. I was thinking abstractly. Is nature a cat? If so, who strokes its back? It can only be God, I concluded. …
I cannot exaggerate the effect of this marvelous sight on my childish imagination. Day after day I asked myself what is electricity and found no answer. Eighty years have gone by since and I still ask the same question, unable to answer it.

Obstacles are those frightful things you see when you take your eyes off your goal.

Obstacles cannot crush me. Every obstacle yields to stern resolve. He who is fixed to a star does not change his mind.

Of all obstacles to a thoroughly penetrating account of existence, none looms up more dismayingly than “time.” Explain time? Not without explaining existence. Explain existence? Not without explaining time. To uncover the deep and hidden connection between time and existence, to close on itself our quartet of questions, is a task for the future.

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

Religious creeds are a great obstacle to any full sympathy between the outlook of the scientist and the outlook which religion is so often supposed to require … The spirit of seeking which animates us refuses to regard any kind of creed as its goal. It would be a shock to come across a university where it was the practice of the students to recite adherence to Newton's laws of motion, to Maxwell's equations and to the electromagnetic theory of light. We should not deplore it the less if our own pet theory happened to be included, or if the list were brought up to date every few years. We should say that the students cannot possibly realise the intention of scientific training if they are taught to look on these results as things to be recited and subscribed to. Science may fall short of its ideal, and although the peril scarcely takes this extreme form, it is not always easy, particularly in popular science, to maintain our stand against creed and dogma.

Since 1849 I have studied incessantly, under all its aspects, a question which was already in my mind [since 1832. I confess that my scheme is still a mere dream, and I do not shut my eyes to the fact that so long as I alone believe it to be possible, it is virtually impossible. ... The scheme in question is the cutting of a canal through the Isthmus of Suez. This has been thought of from the earliest historical times, and for that very reason is looked upon as impracticable. Geographical dictionaries inform us indeed that the project would have been executed long ago but for insurmountable obstacles. [On his inspiration for the Suez Canal.]

That the machine of Heaven is not a hard and impervious body full of various real spheres, as up to now has been believed by most people. It will be proved that it extends everywhere, most fluid and simple, and nowhere presents obstacles as was formerly held, the circuits of the Planets being wholly free and without the labour and whirling round of any real spheres at all, being divinely governed under a given law.

The chief obstacle to the progress of the human race is the human race.

The desire to fly after the fashion of the birds is an idea handed down to us by our ancestors who, in their grueling travels across trackless lands in prehistoric times, looked enviously on the birds soaring freely through space, at full speed, above all obstacles, on the infinite highway of the air.

The enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it. But when a woman, who because of her sex and our prejudices encounters infinitely more obstacles that an man in familiarizing herself with complicated problems, succeeds nevertheless in surmounting these obstacles and penetrating the most obscure parts of them, without doubt she must have the noblest courage, quite extraordinary talents and superior genius.

The genius of Laplace was a perfect sledge hammer in bursting purely mathematical obstacles; but, like that useful instrument, it gave neither finish nor beauty to the results. In truth, in truism if the reader please, Laplace was neither Lagrange nor Euler, as every student is made to feel. The second is power and symmetry, the third power and simplicity; the first is power without either symmetry or simplicity. But, nevertheless, Laplace never attempted investigation of a subject without leaving upon it the marks of difficulties conquered: sometimes clumsily, sometimes indirectly, always without minuteness of design or arrangement of detail; but still, his end is obtained and the difficulty is conquered.

The great obstacle to discovering the shape of the earth, the continents, and the oceans was not ignorance, but the illusion of knowledge.

The greatest obstacle to discovery is not ignorance—it is the illusion of knowledge.

The main sources of mathematical invention seem to be within man rather than outside of him: his own inveterate and insatiable curiosity, his constant itching for intellectual adventure; and likewise the main obstacles to mathematical progress seem to be also within himself; his scandalous inertia and laziness, his fear of adventure, his need of conformity to old standards, and his obsession by mathematical ghosts.

Thus identified with astronomy, in proclaiming truths supposed to be hostile to Scripture, Geology has been denounced as the enemy of religion. The twin sisters of terrestrial and celestial physics have thus been joint-heirs of intolerance and persecution—unresisting victims in the crusade which ignorance and fanaticism are ever waging against science. When great truths are driven to make an appeal to reason, knowledge becomes criminal, and philosophers martyrs. Truth, however, like all moral powers, can neither be checked nor extinguished. When compressed, it but reacts the more. It crushes where it cannot expand—it burns where it is not allowed to shine. Human when originally divulged, it becomes divine when finally established. At first, the breath of a rage—at last it is the edict of a god. Endowed with such vital energy, astronomical truth has cut its way through the thick darkness of superstitious times, and, cheered by its conquests, Geology will find the same open path when it has triumphed over the less formidable obstacles of a civilized age.

We do not live in a time when knowledge can be extended along a pathway smooth and free from obstacles, as at the time of the discovery of the infinitesimal calculus, and in a measure also when in the development of projective geometry obstacles were suddenly removed which, having hemmed progress for a long time, permitted a stream of investigators to pour in upon virgin soil. There is no longer any browsing along the beaten paths; and into the primeval forest only those may venture who are equipped with the sharpest tools.

We have now got what seems to be definite proof that an X ray which spreads out in a spherical form from a source as a wave through the aether can when it meets an atom collect up all its energy from all round and concentrate it on the atom. It is as if when a circular wave on water met an obstacle, the wave were all suddenly to travel round the circle and disappear all round and concentrate its energy on attacking the obstacle. Mechanically of course this is absurd, but mechanics have in this direction been for some time a broken reed.

When asked what it was like to set about proving something, the mathematician likened proving a theorem to seeing the peak of a mountain and trying to climb to the top. One establishes a base camp and begins scaling the mountain’s sheer face, encountering obstacles at every turn, often retracing one’s steps and struggling every foot of the journey. Finally when the top is reached, one stands examining the peak, taking in the view of the surrounding countryside and then noting the automobile road up the other side!