...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.

[Shawn Lawrence Otto describes the damaging] strategy used to undermine science in the interest of those industries where science has pointed out the dangers of their products to individuals and human life in general … [It was] used a generation ago by the tobacco industry… First they manufacture uncertainty by raising doubts about even the most indisputable scientific evidence. Then they launder information by using seemingly independent front organizations to promote their desired message and thereby confuse the public. And finally they recruit unscrupulous scientific spokespeople to misrepresent peer-reviewed scientific findings and cherry-pick facts in an attempt to persuade the media and the public that there is still serious debate among scientists on the issue at hand.

A cosmic mystery of immense proportions, once seemingly on the verge of solution, has deepened and left astronomers and astrophysicists more baffled than ever. The crux ... is that the vast majority of the mass of the universe seems to be missing.
[Reporting a Nature article discrediting explanation of invisible mass being due to neutrinos]

At the beginning of its existence as a science, biology was forced to take cognizance of the seemingly boundless variety of living things, for no exact study of life phenomena was possible until the apparent chaos of the distinct kinds of organisms had been reduced to a rational system. Systematics and morphology, two predominantly descriptive and observational disciplines, took precedence among biological sciences during the eighteenth and nineteenth centuries. More recently physiology has come to the foreground, accompanied by the introduction of quantitative methods and by a shift from the observationalism of the past to a predominance of experimentation.

At the heart of science is an essential balance between two seemingly contradictory attitudes—an openness to new ideas, no matter how bizarre or counterintuitive they may be, and the most ruthless skeptical scrutiny of all ideas, old and new. This is how deep truths are winnowed from deep nonsense.

Confucius once said that a bear could not fart at the North Pole without causing a big wind in Chicago.
By this he meant that all events, therefore, all men, are interconnected in an unbreakable web. What man does, no matter how seemingly insignificant, vibrates through the strands and affects every man.

Divers of Hermetic Books have such involv’d Obscuritys that they may justly be compar’d to Riddles written in Cyphers. For after a Man has surmounted the difficulty of decyphering the Words & Terms, he finds a new & greater difficulty to discover ye meaning of the seemingly plain Expression.

For the most part we humans live with the false impression of security and a feeling of being at home in a seemingly trustworthy physical and human environment. But when the expected course of everyday life is interrupted, we are like shipwrecked people on a miserable plank in the open sea, having forgotten where they came from and not knowing whither they are drifting. But once we fully accept this, life becomes easier and there is no longer any disappointment.

Had there not been in zoology men who devoted themselves to such seemingly unimportant studies as the differentiation of the species of mosquitoes, we should not have been able to place on a firm foundation the aetiology of malaria and yellow fever.

If we knew all the laws of Nature, we should need only one fact or the description of one actual phenomenon to infer all the particular results at that point. Now we know only a few laws, and our result is vitiated, not, of course, by any confusion or irregularity in Nature, but by our ignorance of essential elements in the calculation. Our notions of law and harmony are commonly confined to those instances which we detect, but the harmony which results from a far greater number of seemingly conflicting, but really concurring, laws which we have not detected, is still more wonderful. The particular laws are as our points of view, as to the traveler, a mountain outline varies with every step, and it has an infinite number of profiles, though absolutely but one form. Even when cleft or bored through, it is not comprehended in its entireness.

In scientific study, or, as I prefer to phrase it, in creative scholarship, the truth is the single end sought; all yields to that. The truth is supreme, not only in the vague mystical sense in which that expression has come to be a platitude, but in a special, definite, concrete sense. Facts and the immediate and necessary inductions from facts displace all pre-conceptions, all deductions from general principles, all favourite theories. Previous mental constructions are bowled over as childish play-structures by facts as they come rolling into the mind. The dearest doctrines, the most fascinating hypotheses, the most cherished creations of the reason and of the imagination perish from a mind thoroughly inspired with the scientific spirit in the presence of incompatible facts. Previous intellectual affections are crushed without hesitation and without remorse. Facts are placed before reasonings and before ideals, even though the reasonings and the ideals be more beautiful, be seemingly more lofty, be seemingly better, be seemingly truer. The seemingly absurd and the seemingly impossible are sometimes true. The scientific disposition is to accept facts upon evidence, however absurd they may appear to our pre-conceptions.

It is as if Cleopatra fell off her barge in 40 BC and hasn't hit the water yet.
[Illustrating how strange the behaviour of kaon particles, when first found in cosmic rays, which lived without predicted decay for a surprisingly long time—seemingly postponed a million billion times longer than early theory expected.]

It is clear that in maize, seemingly blending is really segregating inheritance, but with entire absence of dominance, and it seems probably that the same will be found to be true among rabbits and other mammals; failure to observe it hitherto is probably due to the fact that the factors concerned are numerous. For the greater the number of factors concerned, the more nearly will the result obtained approximate a complete and permanent blend. As the number of factors approaches infinity, the result will become identical with a permanent blend.

It’s impossible to move, to live, to operate at any level without leaving traces, bits, seemingly meaningless fragments of personal information.

Life is order, death is disorder. A fundamental law of Nature states that spontaneous chemical changes in the universe tend toward chaos. But life has, during milliards of years of evolution, seemingly contradicted this law. With the aid of energy derived from the sun it has built up the most complicated systems to be found in the universe—living organisms. Living matter is characterized by a high degree of chemical organisation on all levels, from the organs of large organisms to the smallest constituents of the cell. The beauty we experience when we enjoy the exquisite form of a flower or a bird is a reflection of a microscopic beauty in the architecture of molecules.

No other theory known to science [other than superstring theory] uses such powerful mathematics at such a fundamental level. …because any unified field theory first must absorb the Riemannian geometry of Einstein’s theory and the Lie groups coming from quantum field theory… The new mathematics, which is responsible for the merger of these two theories, is topology, and it is responsible for accomplishing the seemingly impossible task of abolishing the infinities of a quantum theory of gravity.

Occurrences that other men would have noted only with the most casual interest became for Whitney exciting opportunities to experiment. Once he became disturbed by a scientist's seemingly endless pursuit of irrelevant details in the course of an experiment, and criticized this as being as pointless as grabbing beans out of a pot, recording the numbers, and then analyzing the results. Later that day, after he had gone home, his simile began to intrigue him, and he asked himself whether it would really be pointless to count beans gathered in such a random manner. Another man might well have dismissed this as an idle fancy, but to Whitney an opportunity to conduct an experiment was not to be overlooked. Accordingly, he set a pot of beans beside his bed, and for several days each night before retiring he would take as many beans as he could grasp in one hand and make a note of how many were in the handful. After several days had passed he was intrigued to find that the results were not as unrewarding as he had expected. He found that each handful contained more beans than the one before, indicating that with practice he was learning to grasp more and more beans. “This might be called research in morphology, the science of animal structure,” he mused. “My hand was becoming webbed … so I said to myself: never label a real experiment useless, it may reveal something unthought of but worth knowing.”

One wonders whether the rare ability to be completely attentive to, and to profit by, Nature’s slightest deviation from the conduct expected of her is not the secret of the best research minds and one that explains why some men turn to most remarkably good advantage seemingly trivial accidents. Behind such attention lies an unremitting sensitivity.

Over very long time scales, when the perturbing influences of both Jupiter and Saturn are taken into account, the seemingly regular orbits of asteroids that stray into the Kirkwood gaps turn chaotic. For millions of years … such an orbit seems predictable. Then the path grows increasingly eccentric until it begins to cross the orbit of Mars and then the Earth. Collisions or close encounters with those planets are inevitable.

Relativity was a highly technical new theory that gave new meanings to familiar concepts and even to the nature of the theory itself. The general public looked upon relativity as indicative of the seemingly incomprehensible modern era, educated scientists despaired of ever understanding what Einstein had done, and political ideologues used the new theory to exploit public fears and anxieties—all of which opened a rift between science and the broader culture that continues to expand today.

Science has taught us to think the unthinkable. Because when nature is the guide—rather than a priori prejudices, hopes, fears or desires—we are forced out of our comfort zone. One by one, pillars of classical logic have fallen by the wayside as science progressed in the 20th century, from Einstein's realization that measurements of space and time were not absolute but observer-dependent, to quantum mechanics, which not only put fundamental limits on what we can empirically know but also demonstrated that elementary particles and the atoms they form are doing a million seemingly impossible things at once.

The beauty of physics lies in the extent which seemingly complex and unrelated phenomena can be explained and correlated through a high level of abstraction by a set of laws which are amazing in their simplicity.

The greatest gift of the essayistic mind: to extract a momentous truth from the most seemingly trivial event or artifact.

The seemingly useless or trivial observation made by one worker leads on to a useful observation by another: and so science advances, “creeping on from point to point.”

The weeds of a seemingly learned and brilliant but actually trivial and empty philosophy of Nature which, after having been replaced some 50 years ago by the exact sciences, is now once more dug up by pseudo scientists from the lumber room of human fallacies, and like a trollop, newly attired in elegant dress and make-up, is smuggled into respectable company, to which she does not belong.

There is no way to guarantee in advance what pure mathematics will later find application. We can only let the process of curiosity and abstraction take place, let mathematicians obsessively take results to their logical extremes, leaving relevance far behind, and wait to see which topics turn out to be extremely useful. If not, when the challenges of the future arrive, we won’t have the right piece of seemingly pointless mathematics to hand.

We cannot see how the evidence afforded by the unquestioned progressive development of organised existence—crowned as it has been by the recent creation of the earth's greatest wonder, MAN, can be set aside, or its seemingly necessary result withheld for a moment. When Mr. Lyell finds, as a witty friend lately reported that there had been found, a silver-spoon in grauwacke, or a locomotive engine in mica-schist, then, but not sooner, shall we enrol ourselves disciples of the Cyclical Theory of Geological formations.

What to-day is to be believed is to-morrow to be cast aside, certainly has been the law of advancement, and seemingly must continue to be so. With what a babel of discordant voices does it [medicine] celebrate its two thousand years of experience!