[Regarding mathematics,] there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy. This may be true; indeed it is probable, since the sensational triumphs of Einstein, that stellar astronomy and atomic physics are the only sciences which stand higher in popular estimation.

[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.

Eine neue wissenschaftliche Wahrheit pflegt sich nicht in der Weise durchzusetzen, daß ihre Gegner überzeugt werden und sich als belehrt erklären, sondern vielmehr dadurch, daß ihre Gegner allmählich aussterben und daß die heranwachsende Generation von vornherein mit der Wahrheit vertraut gemacht ist.
A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather its opponents eventually die, and a new generation grows up that is familiar with it.

Engineering, too, owes its most useful materials to the achievements of chemists in identifying, separating, and transforming materials: structural steel for the framework of bridges and buildings, portland cement for roadways and aqueducts, pure copper for the electrical industries, aluminum alloys for automobiles and airplanes, porcelain for spark plugs and electrical insulators. The triumphs of engineering skill rest on a chemical foundation.

A great discovery solves a great problem, but there is a grain of discovery in the solution of any problem. Your problem may be modest, but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.

A single tree by itself is dependent upon all the adverse chances of shifting circumstances. The wind stunts it: the variations in temperature check its foliage: the rains denude its soil: its leaves are blown away and are lost for the purpose of fertilisation. You may obtain individual specimens of line trees either in exceptional circumstances, or where human cultivation had intervened. But in nature the normal way in which trees flourish is by their association in a forest. Each tree may lose something of its individual perfection of growth, but they mutually assist each other in preserving the conditions of survival. The soil is preserved and shaded; and the microbes necessary for its fertility are neither scorched, nor frozen, nor washed away. A forest is the triumph of the organisation of mutually dependent species.

A typical triumph of modern science to find the only part of Randolph [Churchill] that was not malignant and remove it.

All of us who are concerned for peace and triumph of reason and justice must be keenly aware how small an influence reason and honest good will exert upon events in the political field.

Almost everything that distinguishes the modern world from earlier centuries is attributable to science, which achieved its most spectacular triumphs in the seventeenth century.

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 for me ... I would much rather be a perfected ape than a degraded Adam. Yes, if it is shown to me that my humble ancestors were quadrupedal animals, arboreal herbivores, brothers or cousins of those who were also the ancestors of monkeys and apes, far from blushing in shame for my species because of its genealogy and parentage, I will be proud of all that evolution has accomplished, of the continuous improvement which takes us up to the highest order, of the successive triumphs that have made us superior to all of the other species ... the splendid work of progress.
I will conclude in saying: the fixity of species is almost impossible, it contradicts the mode of succession and of the distribution of species in the sequence of extant and extinct creatures. It is therefore extremely likely that species are variable and are subject to evolution. But the causes, the mechanisms of this evolution are still unknown.

As soon … as it was observed that the stars retained their relative places, that the times of their rising and setting varied with the seasons, that sun, moon, and planets moved among them in a plane, … then a new order of things began.… Science had begun, and the first triumph of it was the power of foretelling the future; eclipses were perceived to recur in cycles of nineteen years, and philosophers were able to say when an eclipse was to be looked for. The periods of the planets were determined. Theories were invented to account for their eccentricities; and, false as those theories might be, the position of the planets could be calculated with moderate certainty by them.

At the bidding of a Peter the Hermit many millions of men swarmed to the East; the words of an hallucinated person … have created the force necessary to triumph over the Graeco-Roman world; an obscure monk like Luther set Europe ablaze and bathed in blood. The voice of a Galileo or a Newton will never have the least echo among the masses. The inventors of genius transform a civilization. The fanatics and the hallucinated create history.

Evolution triumphs because it turns to natural selection, the plodding accumulation of error.

Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure, than to take rank with those poor spirits who neither enjoy much or suffer much, because they live in the gray twilight that knows not victory nor defeat.

For my own part I would as soon be descended from that heroic little monkey, who braved his dreaded enemy in order to save the life of his keeper; or from that old baboon, who, descending from the mountains, carried away in triumph his young comrade from a crowd of astonished dogs—as from a savage who delights to torture his enemies, offers up bloody sacrifices, practices infanticide without remorse, treats his wives like slaves, knows no decency, and is haunted by the grossest superstitions.

Great triumphs of engineering genius—the locomotive, the truss bridge, the steel rail— ... are rather invention than engineering proper.

Heroes and scholars represent the opposite extremes... The scholar struggles for the benefit of all humanity, sometimes to reduce physical effort, sometimes to reduce pain, and sometimes to postpone death, or at least render it more bearable. In contrast, the patriot sacrifices a rather substantial part of humanity for the sake of his own prestige. His statue is always erected on a pedestal of ruins and corpses... In contrast, all humanity crowns a scholar, love forms the pedestal of his statues, and his triumphs defy the desecration of time and the judgment of history.

I attained a triumph so complete that it is now rare to meet an American with marks of small pox on his face... Benefits are valuable according to their duration and extent, like the showers from heaven, but the benign remedy Vaccination saves millions of lives every century, like the blessing of the sun, universal and everlasting.
(Remark made near the end of his life.)

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 the Weismann idea triumphs, it will be in a sense a triumph of fatalism; for, according to it, while we may indefinitely improve the forces of our education and surroundings, and this civilizing nurture will improve the individuals of each generation, its actual effects will not be cumulative as regards the race itself, but only as regards the environment of the race; each new generation must start de novo, receiving no increment of the moral and intellectual advance made during the lifetime of its predecessors. It would follow that one deep, almost instinctive motive for a higher life would be removed if the race were only superficially benefited by its nurture, and the only possible channel of actual improvement were in the selection of the fittest chains of race plasma.

If we do discover a complete unified theory, it should be in time understandable in broad principle by everyone, not just a few scientists. Then we shall all, philosophers, scientists and just ordinary people, be able to take part in the discussion of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason—for then we would know the mind of God.

In 1810, the Triumph man-of-war and Phipps schooner received on board several tons of quicksilver, saved from the wreck of a vessel near Cadiz. In consequence of the rolling of the bags the mercury escaped, and the whole of the crews became more or less affected. In the space of three weeks, two hundred men were salivated, two died, and all the animals—cats, dogs, sheep, fowls, a canary bird, nay, even the rats, mice and cockroaches were destroyed.
[The leather bags of mercury had been salvaged and stored without the original wooden cases. Some were stowed in sleeping quarters, and the in same hold as spirit rations.]

In the true triumph, however, there are no losers.

In vertebrate paleontology, increasing knowledge leads to triumphant loss of clarity.

Is this your triumph—this your proud applause,
Children of Truth, and champions of her cause?
For this has Science search’d, on weary wing,
By shore and sea—each mute and living thing!

It can happen to but few philosophers, and but at distant intervals, to snatch a science, like Dalton, from the chaos of indefinite combination, and binding it in the chains of number, to exalt it to rank amongst the exact. Triumphs like these are necessarily 'few and far between.'

It is not failure but success that is forcing man off this earth. It is not sickness but the triumph of health... Our capacity to survive has expanded beyond the capacity of Earth to support us. The pains we are feeling are growing pains. We can solve growth problems in direct proportion to our capacity to find new worlds... If man stays on Earth, his extinction is sure even if he lasts till the sun expands and destroys him... It is no longer reasonable to assume that the meaning of life lies on this earth alone. If Earth is all there is for man, we are reaching the foreseeable end of man.

It is one of the triumphs of human wit ... to conquer by humility and submissiveness ... to make oneself small in order to appear great ... such ... are often the expedients of the neurotic.

It is the triumph of civilization that at last communities have obtained such a mastery over natural laws that they drive and control them. The winds, the water, electricity, all aliens that in their wild form were dangerous, are now controlled by human will, and are made useful servants.

It is worthy the observing, that there is no passion in the mind of man, so weak, but it mates, and masters, the fear of death; and therefore, death is no such terrible enemy, when a man hath so many attendants about him, that can win the combat of him. Revenge triumphs over death; love slights it; honor aspireth to it; grief flieth to it; fear preoccupieth it.

It might be going too far to say that the modern scientific movement was tainted from its birth; but I think it would be true to say that it was born in an unhealthy neighborhood and at an inauspicious hour. Its triumphs may have been too rapid and purchased at too high a price: reconsideration, and something like repentance, may be required.

It’s not the critic who counts; not the man which points out how the strong man stumbles or where the doer of deeds could have done them better. The credit belongs to the man who is actually in the arena, whose face is marred by dust and sweat and blood; who strives valiantly; who errs, who comes short again and again … who knows great enthusiasms, the great devotions; who spends himself in a worthy cause; who at the best knows in the end the triumph of high achievement, and who at the worst, if he fails, at least fails while daring greatly, so that his place shall never be with those cold and timid souls who neither know victory nor defeat.

Lay down your rails, ye nations, near and far—
Yoke your full trains to Steam’s triumphal car;
Link town to town; unite in iron bands
The long-estranged and oft-embattled lands.

Lord Kelvin was so satisfied with this triumph of science that he declared himself to be as certain of the existence of the ether as a man can be about anything.... “When you can measure what you are speaking about, and express it in numbers, you know something about it....” Thus did Lord Kelvin lay down the law. And though quite wrong, this time he has the support of official modern Science. It is NOT true that when you can measure what you are speaking about, you know something about it. The fact that you can measure something doesn't even prove that that something exists.... Take the ether, for example: didn't they measure the ratio of its elasticity to its density?

Love is the triumph of imagination over intelligence.

Not to destroy but to construct,
I hold the unconquerable belief
that science and peace will triumph over ignorance and war
that nations will come together
not to destroy but to construct
and that the future belongs to those
who accomplish most for humanity.
[His 1956 Christmas card.]

Nothing holds me ... I will indulge in my sacred fury; I will triumph over mankind by the honest confession that I have stolen the golden vases of the Egyptians to build up a tabernacle for my God, far away from the confines of Egypt. If you forgive me, I rejoice ; if you are angry, I can bear it. The die is cast; the book is written, to be read either now or by posterity, I care not which. It may well wait a century for a reader, as God has waited six thousand years for an observer.

One of the chiefest triumphs of modern mathematics consists in having discovered what mathematics really is.

One of the great triumphs of 20th Century astrophysics, was tracing the elements of your body, of all the elements around us, to the actions of stars—that crucible in the centers of stars that cooked basic elements into heavier elements, light elements into heavy elements. (I say “cooked”—I mean thermonuclear fusion.) The heat brings them together, gets you bigger atoms, that then do other interesting chemical things, fleshing out the contents of the Periodic Table.

Only mediocrity can be trusted to be always at its best. Genius must always have lapses proportionate to its triumphs.

Our exploration of the planets represents a triumph of imagination and will for the human race. The events of the last twenty years are perhaps too recent for us to adequately appreciate their proper historical significance.
We can, however, appraise the scientific significance of these voyages of exploration: They have been nothing less than revolutionary both in providing a new picture of the nature of the solar system, its likely origin and evolution, and in giving us a new perspective on our own planet Earth.

Perhaps it is better in this present world of ours that a revolutionary idea or invention instead of being helped and patted be hampered and ill-treated in its adolescence—by want of means, by selfish interest, pedantry, stupidity and ignorance; that it be attacked and stifled; that it pass through bitter trials and tribulations, through the heartless strife of commercial existence. ... So all that was great in the past was ridiculed, condemned, combatted, suppressed—only to emerge all the more powerfully, all the more triumphantly from the struggle.

Psychology marks the triumph of human evolution. How many other species would need a science of the mind?

Science and technology have freed humanity from many burdens and given us this new perspective and great power. This power can be used for the good of all. If wisdom governs our actions; but if the world is mad or foolish, it can destroy itself just when great advances and triumphs are almost without its grasp.

Science is triumphant with far-ranging success, but its triumph is somehow clouded by growing difficulties in providing for the simple necessities of human life on earth.

Science, ships, policies, cities, factories, are not nothing,
Like a grand procession to music of distant bugles pouring, triumphantly moving, and grander heaving in sight,
They stand for realities—all is as it should be.

Some see a clear line between genetic enhancement and other ways that people seek improvement in their children and themselves. Genetic manipulation seems somehow worse—more intrusive, more sinister—than other ways of enhancing performance and seeking success. But, morally speaking, the difference is less significant than it seems. Bioengineering gives us reason to question the low-tech, high-pressure child-rearing practices we commonly accept. The hyperparenting familiar in our time represents an anxious excess of mastery and dominion that misses the sense of life as a gift. This draws it disturbingly close to eugenics... Was the old eugenics objectionable only insofar as it was coercive? Or is there something inherently wrong with the resolve to deliberately design our progeny’s traits... But removing coercion does not vindicate eugenics. The problem with eugenics and genetic engineering is that they represent a one-sided triumph of willfulness over giftedness, of dominion over reverence, of molding over beholding.

Statistics are the triumph of the quantitative method, and the quantitative method is the victory of sterility and death.

The Anglo-Dane appears to possess an aptitude for mathematics which is not shared by the native of any other English district as a whole, and it is in the exact sciences that the Anglo-Dane triumphs.

The beautiful has its place in mathematics as elsewhere. The prose of ordinary intercourse and of business correspondence might be held to be the most practical use to which language is put, but we should be poor indeed without the literature of imagination. Mathematics too has its triumphs of the Creative imagination, its beautiful theorems, its proofs and processes whose perfection of form has made them classic. He must be a “practical” man who can see no poetry in mathematics.

The difference between try and triumph is a little umph.

The dropping of the Atomic Bomb is a very deep problem… Instead of commemorating Hiroshima we should celebrate… man’s triumph over the problem [of transmutation], and not its first misuse by politicians and military authorities.

The Earth is a very small stage in a vast cosmic arena. Think of the rivers of blood spilled by all those generals and emperors, so that, in glory and triumph, they could become the momentary masters of a fraction of a dot. Think of the endless cruelties visited by the inhabitants of one corner of this pixel on the scarcely distinguishable inhabitants of some other corner, how frequent their misunderstandings, how eager they are to kill one another, how fervent their hatreds.

The economic and technological triumphs of the past few years have not solved as many problems as we thought they would, and, in fact, have brought us new problems we did not foresee.

The frost continuing more and more severe, the Thames before London was still planted with booths in formal streets … so that it see’d to be a bacchanalian triumph or carnival on the water, whilst it was a severe judgement on the land, the trees not only splitting as if lightning-struck, but men and cattle perishing in diverse places, and the very seas so lock’d up with ice, that no vessels could stir out or come in. London, by reason of the smoke, was so filled with the fuliginous steame of the sea-coale, that hardly could one see crosse the streets, and this filling the breast, so as one could hardly breath. Here was no water to be had from the pipes and engines, nor could the brewers and divers other tradesmen worke, and every moment was full of disastrous accidents.

The ingenuity and effective logic that enabled chemists to determine complex molecular structures from the number of isomers, the reactivity of the molecule and of its fragments, the freezing point, the empirical formula, the molecular weight, etc., is one of the outstanding triumphs of the human mind.

The Lincoln Highway is to be something more than a road. It will be a road with a personality, a distinctive work of which the Americans of future generations can point with pride - an economic but also artistic triumph. (1914)

The line separating investment and speculation, which is never bright and clear, becomes blurred still further when most market participants have recently enjoyed triumphs. Nothing sedates rationality like large doses of effortless money. After a heady experience of that kind, normally sensible people drift into behavior akin to that of Cinderella at the ball. They know that overstaying the festivities—that is, continuing to speculate in companies that have gigantic valuations relative to the cash they are likely to generate in the future—will eventually bring on pumpkins and mice. But they nevertheless hate to miss a single minute of what is one helluva party. Therefore, the giddy participants all plan to leave just seconds before midnight. There’s a problem, though: They are dancing in a room in which the clocks have no hands.

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 principles which constituted the triumph of the preceding stages of the science, may appear to be subverted and ejected by the later discoveries, but in fact they are, (so far as they were true), taken up into the subsequent doctrines and included in them. They continue to be an essential part of the science. The earlier truths are not expelled but absorbed, not contradicted but extended; and the history of each science, which may thus appear like a succession of revolutions, is, in reality, a series of developments.

The quantum entered physics with a jolt. It didn’t fit anywhere; it made no sense; it contradicted everything we thought we knew about nature. Yet the data seemed to demand it. ... The story of Werner Heisenberg and his science is the story of the desperate failures and ultimate triumphs of the small band of brilliant physicists who—during an incredibly intense period of struggle with the data, the theories, and each other during the 1920s—brought about a revolutionary new understanding of the atomic world known as quantum mechanics.

The requirement for great success is great ambition ... for triumph over other men, not merely over nature.

The trouble with triumph is that you may be on the other side.

The true purpose of education is to teach a man to carry himself triumphant to the sunset.

There is romance, the genuine glinting stuff, in typewriters, and not merely in their development from clumsy giants into agile dwarfs, but in the history of their manufacture, which is filled with raids, battles, lonely pioneers, great gambles, hope, fear, despair, triumph. If some of our novels could be written by the typewriters instead of on them, how much better they would be.

This leads us to ask for the reasons which call for this new theory of transmutation. The beginning of things must needs lie in obscurity, beyond the bounds of proof, though within those of conjecture or of analogical inference. Why not hold fast to the customary view, that all species were directly, instead of indirectly, created after their respective kinds, as we now behold them,--and that in a manner which, passing our comprehension, we intuitively refer to the supernatural? Why this continual striving after “the unattained and dim,”—these anxious endeavors, especially of late years, by naturalists and philosophers of various schools and different tendencies, to penetrate what one of them calls “the mystery of mysteries,” the origin of species? To this, in general, sufficient answer may be found in the activity of the human intellect, “the delirious yet divine desire to know,” stimulated as it has been by its own success in unveiling the laws and processes of inorganic Nature,—in the fact that the principal triumphs of our age in physical science have consisted in tracing connections where none were known before, in reducing heterogeneous phenomena to a common cause or origin, in a manner quite analogous to that of the reduction of supposed independently originated species to a common ultimate origin,—thus, and in various other ways, largely and legitimately extending the domain of secondary causes. Surely the scientific mind of an age which contemplates the solar system as evolved from a common, revolving, fluid mass,— which, through experimental research, has come to regard light, heat, electricity, magnetism, chemical affinity, and mechanical power as varieties or derivative and convertible forms of one force, instead of independent species,—which has brought the so-called elementary kinds of matter, such as the metals, into kindred groups, and raised the question, whether the members of each group may not be mere varieties of one species,—and which speculates steadily in the direction of the ultimate unity of matter, of a sort of prototype or simple element which may be to the ordinary species of matter what the protozoa or component cells of an organism are to the higher sorts of animals and plants,—the mind of such an age cannot be expected to let the old belief about species pass unquestioned.

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.

Truth is a naked and open daylight, that doth not shew the masks and mummeries and triumphs of the world, half so stately and daintily as candlelights.

Vaccination was discovered, and, like all new discoveries, had at the first to maintain a vigorous battle for existence. It was condemned by the church as a cunning device of the devil to defeat the judgments of God. Nevertheless, it has triumphed, and is now adopted by the best instructed of all nations.

We reverence ancient Greece as the cradle of western science. Here for the first time the world witnessed the miracle of a logical system which proceeded from step to step with such precision that every single one of its propositions was absolutely indubitable—I refer to Euclid’s geometry. This admirable triumph of reasoning gave the human intellect the necessary confidence in itself for its subsequent achievements. If Euclid failed to kindle your youthful enthusiasm, then you were not born to be a scientific thinker.

We think of Euclid as of fine ice; we admire Newton as we admire the peak of Teneriffe. Even the intensest labors, the most remote triumphs of the abstract intellect, seem to carry us into a region different from our own—to be in a terra incognita of pure reasoning, to cast a chill on human glory.

Well the first War of the Machines seems to be drawing to its final inconclusive chapter—leaving, alas, everyone the poorer, many bereaved or maimed and millions dead, and only one thing triumphant: the Machines. As the servants of the Machines are becoming a privileged class, the Machines are going to be enormously more powerful. What’s their next move?

When a conjecture inspires new hopes or creates new fears, action is indicated. There is an important asymmetry between hope, which leads to actions that will test its basis, and fear, which leads to restriction of options frequently restricting testing of the basis for the fear. As we know only too well, many of our hopes do not survive their tests. However, fears accumulate untested. Our inventory of untested fears has always made humanity disastrously vulnerable to thought control. While science was independent of politics, its greatest triumph was the reduction of that vulnerability.

When Richard Dawkins first published his idea of a meme, he made it clear he was speaking of “a unit of imitation” … Memes were supposed to be exclusive triumphs of humanity. But memes come in two different kinds—behavioral and verbal. … behavioral memes began brain-hopping long before there were such things as human minds.

You bring me the deepest joy that can be felt by a man [Pasteur himself] whose invincible belief is that Science and Peace will triumph over Ignorance and War, that nations will unite, not to destroy, but to build, and that the future will belong to those who will have done most for suffering humanity. But whether our efforts are or are not favored by life, let us be able to say, when we come near to the great goal, “I have done what I could.”