…nature seems very conversant with the rules of pure mathematics, as our own mathematicians have formulated them in their studies, out of their own inner consciousness and without drawing to any appreciable extent on their experience of the outer world.

...the study of butterflies—creatures selected as the types of airiness and frivolity—instead of being despised, will some day be valued as one of the most important branches of Biological science.

…this discussion would be unprofitable if it did not lead us to appreciate the wisdom of our Creator, and the wondrous knowledge of the Author of the world, Who in the beginning created the world out of nothing, and set everything in number, measure and weight, and then, in time and the age of man, formulated a science which reveals fresh wonders the more we study it.

“Going fishing!” How often the question has been asked by acquaintances, as they have met me, with rod and basket, on an excursion after materials for microscopic study. “Yes!” has been the invariable answer, for it saved much detention and explanation; and now, behold! I offer them the results of that fishing. No fish for the stomach, but, as the old French microscopist Joblet observed, “some of the most remarkable fishes that have ever been seen”; and food-fishes for the intellect.

“Science studies everything,” say the scientists. But, really, everything is too much. Everything is an infinite quantity of objects; it is impossible at one and the same time to study all. As a lantern cannot light up everything, but only lights up the place on which it is turned or the direction in which the man carrying it is walking, so also science cannot study everything, but inevitably only studies that to which its attention is directed. And as a lantern lights up most strongly the place nearest to it, and less and less strongly objects that are more and more remote from it, and does not at all light up those things its light does not reach, so also human science, of whatever kind, has always studied and still studies most carefully what seems most important to the investigators, less carefully what seems to them less important, and quite neglects the whole remaining infinite quantity of objects. ... But men of science to-day ... have formed for themselves a theory of “science for science's sake,” according to which science is to study not what mankind needs, but everything.

[A contemporary study] predicted the loss of two-thirds of all tropical forests by the turn of the century. Hundreds of thousands of species will perish, and this reduction of 10 to 20 percent of the earth’s biota will occur in about half a human life span. … This reduction of the biological diversity of the planet is the most basic issue of our time.

[About the mechanical properties of the molecules of a chemical substance being studied:] They could be measured, but that would have taken several months. So someone said, ‘Let’s get Teller in and make him guess the data.’ We got him into a room and locked the door, so no one else could get at him, and he asked questions and did some figuring at the blackboard. He got the answers in about two hours, not entirely accurately, of course, but—as we found out when we got around to verifying them—close enough for the purpose.

[After the flash of the atomic bomb test explosion] Fermi got up and dropped small pieces of paper … a simple experiment to measure the energy liberated by the explosion … [W]hen the front of the shock wave arrived (some seconds after the flash) the pieces of paper were displaced a few centimeters in the direction of propagation of the shock wave. From the distance of the source and from the displacement of the air due to the shock wave, he could calculate the energy of the explosion. This Fermi had done in advance having prepared himself a table of numbers, so that he could tell immediately the energy liberated from this crude but simple measurement. … It is also typical that his answer closely approximated that of the elaborate official measurements. The latter, however, were available only after several days’ study of the records, whereas Fermi had his within seconds.

[Beyond natural history] Other biological sciences take up the study at other levels of organization: dissecting the individual into organs and tissues and seeing how these work together, as in physiology; reaching down still further to the level of cells, as in cytology; and reaching the final biological level with the study of living molecules and their interactions, as in biochemistry. No one of these levels can be considered as more important than any other.

[Florence Nightingale] was a great administrator, and to reach excellence here is impossible without being an ardent student of statistics. Florence Nightingale has been rightly termed the “Passionate Statistician.” Her statistics were more than a study, they were indeed her religion. For her, Quetelet was the hero as scientist, and the presentation copy of his Physique Sociale is annotated by her on every page. Florence Nightingale believed—and in all the actions of her life acted upon that belief—that the administrator could only be successful if he were guided by statistical knowledge. The legislator—to say nothing of the politician—too often failed for want of this knowledge. Nay, she went further: she held that the universe—including human communities—was evolving in accordance with a divine plan; that it was man's business to endeavour to understand this plan and guide his actions in sympathy with it. But to understand God's thoughts, she held we must study statistics, for these are the measure of his purpose. Thus the study of statistics was for her a religious duty.

[Henry Cavendish] fixed the weight of the earth; he established the proportions of the constituents of the air; he occupied himself with the quantitative study of the laws of heat; and lastly, he demonstrated the nature of water and determined its volumetric composition. Earth, air, fire, and water—each and all came within the range of his observations.

[I] learnt, for the first time, the joys of substituting hard, disciplined study for the indulgence of day-dreaming.
[Comment on his successful undergraduate studies at the University of St. Andrews.]

[In addition to classical, literary and philosophical studies,] I devoured without much appetite the Elements of Algebra and Geometry…. From these serious and scientific pursuits I derived a maturity of judgement, a philosophic spirit, of more value than the sciences themselves…. I could extract and digest the nutritive particles of every species of litterary food.

[Mathematics is] the study of ideal constructions (often applicable to real problems), and the discovery thereby of relations between the parts of these constructions, before unknown.

[Mathematics is] the study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols.

[Microscopic] evidence cannot be presented ad populum. What is seen with the microscope depends not only upon the instrument and the rock-section, but also upon the brain behind the eye of the observer. Each of us looks at a section with the accumulated experience of his past study. Hence the veteran cannot make the novice see with his eyes; so that what carries conviction to the one may make no appeal to the other. This fact does not always seem to be sufficiently recognized by geologists at large.

[My friends and I studied science to get away from] the stench of Fascist truths which tainted the sky. ... [T]he chemistry and physics on which we fed, besides being nourishment vital in themselves, were an antidote to Fascism. ... [T]hey were clear and distinct and verifiable at every step, and not a tissue of lies and emptiness like the radio and the newspapers.

[My study of the universe] leaves little doubt that life has occurred on other planets. I doubt if the human race is the most intelligent form of life.

[Niels Bohr] is a national pride to his fellow Danes. In Denmark, Bohr’s standing is only slightly less than that of the royal family and Hans Christian Anderson. When the wife of an American physicist casually told a gentleman seated next to her on a Copenhagen streetcar that her husband was studying under Professor Bohr, the old man jumped to his feet, swept off his hat with a flourish and bowed deeply.

[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 object of education is] to train the mind to ascertain the sequence of a particular conclusion from certain premises, to detect a fallacy, to correct undue generalisation, to prevent the growth of mistakes in reasoning. Everything in these must depend on the spirit and the manner in which the instruction itself is conveyed and honoured. If you teach scientific knowledge without honouring scientific knowledge as it is applied, you do more harm than good. I do think that the study of natural science is so glorious a school for the mind, that with the laws impressed on all these things by the Creator, and the wonderful unity and stability of matter, and the forces of matter, there cannot be a better school for the education of the mind.

[The] subjective [historical] element in geologic studies accounts for two characteristic types that can be distinguished among geologists: one considering geology as a creative art, the other regarding geology as an exact science.

[The] weakness of biological balance studies has aptly been illustrated by comparison with the working of a slot machine. A penny brings forth one package of chewing gum; two pennies bring forth two. Interpreted according to the reasoning of balance physiology, the first observation is an indication of the conversion of copper into gum; the second constitutes proof.
[Co-author with David Rittenberg (1906-70).]

[Urbain Jean Joseph] Le Verrier—without leaving his study, without even looking at the sky—had found the unknown planet [Neptune] solely by mathematical calculation, and, as it were, touched it with the tip of his pen!

[William Gull] endeavoured, above all things, to study the natural history of disease, uncomplicated by the action of unnecessary drugs, and he resented all useless interference with the course of nature. He would say of meddlesome poly-pharmacy—“Fools rush in, where angels fear to tread.”

“The Universe repeats itself, with the possible exception of history.” Of all earthly studies history is the only one that does not repeat itself. ... Astronomy repeats itself; botany repeats itself; trigonometry repeats itself; mechanics repeats itself; compound long division repeats itself. Every sum if worked out in the same way at any time will bring out the same answer. ... A great many moderns say that history is a science; if so it occupies a solitary and splendid elevation among the sciences; it is the only science the conclusions of which are always wrong.

[Almost certainly not by Einstein.] The more I study science, the more I believe in God.

[In reply to a question about how he got his expertise:]
By studying the masters and not their pupils.

[Recalling Professor Ira Remsen's remarks (1895) to a group of his graduate students about to go out with their degrees into the world beyond the university:]
He talked to us for an hour on what was ahead of us; cautioned us against giving up the desire to push ahead by continued study and work. He warned us against allowing our present accomplishments to be the high spot in our lives. He urged us not to wait for a brilliant idea before beginning independent research, and emphasized the fact the Lavoisier's first contribution to chemistry was the analysis of a sample of gypsum. He told us that the fields in which the great masters had worked were still fruitful; the ground had only been scratched and the gleaner could be sure of ample reward.

[Responding to a student whose friend asked about studying Agricultural Chemistry at Johns Hopkins:]
We would be glad to have your friend come here to study, but tell him that we teach Chemistry here and not Agricultural Chemistry, nor any other special kind of chemistry. ... We teach Chemistry.

Ac astronomye is an hard thyng,
And yvel for to knowe;
Geometrie and geomesie,
So gynful of speche,
Who so thynketh werche with tho two
Thryveth ful late,
For sorcerie is the sovereyn book
That to tho sciences bilongeth.
Now, astronomy is a difficult discipline, and the devil to learn;
And geometry and geomancy have confusing terminology:
If you wish to work in these two, you will not succeed quickly.
For sorcery is the chief study that these sciences entail.

Ath. There still remain three studies suitable for freemen. Calculation in arithmetic is one of them; the measurement of length, surface, and depth is the second; and the third has to do with the revolutions of the stars in reference to one another … there is in them something that is necessary and cannot be set aside, … if I am not mistaken, [something of] divine necessity; for as to the human necessities of which men often speak when they talk in this manner, nothing can be more ridiculous than such an application of the words.
Cle. And what necessities of knowledge are there, Stranger, which are divine and not human?
Ath. I conceive them to be those of which he who has no use nor any knowledge at all cannot be a god, or demi-god, or hero to mankind, or able to take any serious thought or charge of them.

Dans l’étude de la nature, comme dans la pratique de l’art, il n’est pas donné a l’homme d’arriver au but sans laisser des traces des fausses routes qu’il a tenues.
In the study of nature, as in the practice of art, it is not given to man to achieve the goal without leaving a trail of dead ends he had pursued.

L’analyse mathématique … dans l’étude de tous les phénomènes; elle les interprète par le même langage, comme pour attester l’unité et la simplicité du plan de l’univers, et rendre encore plus manifeste cet ordre immuable qui préside à toutes les causes naturelles.
Mathematical analysis … in the study of all phenomena, interprets them by the same language, as if to attest the unity and simplicity of the plan of the universe, and to make still more evident that unchangeable order which presides over all natural causes.

La vraye science et le vray étude de l'homme c'est l'homme.
The true science and study of mankind is man.

Le savant n’étudie pas la nature parce que cela est utile; il l’étudie parce qu’il y prend plaisir et il y prend plaisir parce qu’elle est belle. Si la nature n’était pas belle, elle ne vaudrait pas la peine d’être connue, la vie ne vaudrait pas la peine d’être vécue.
The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and life would not be worth living. I am not speaking, of course, of the beauty which strikes the senses, of the beauty of qualities and appearances. I am far from despising this, but it has nothing to do with science. What I mean is that more intimate beauty which comes from the harmonious order of its parts, and which a pure intelligence can grasp.

Les causes primordiales ne nous sont point connues; mais elles sont assujetties à des lois simples et constantes, que l’on peut découvrir par l’observation, et dont l’étude est l’objet de la philosophie naturelle.
Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy.

Les mathématique sont un triple. Elles doivent fournir un instrument pour l'étude de la nature. Mais ce n'est pas tout: elles ont un but philosophique et, j'ose le dire, un but esthétique.
Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.

Mi è impossibile cingere i fianchi di una ragazza con il mio braccio destro e serrare il suo sorriso nella mia mano sinistra, per poi tentare di studiare i due oggetti separatamente. Allo stesso modo, non ci è possibile separare la vita dalla materia vivente, allo scopo di studiare la sola materia vivente e le sue reazioni. Inevitabilmente, studiando la materia vivente e le sue reazioni, studiamo la vita stessa.
It is impossible to encircle the hips of a girl with my right arm and hold her smile in my left hand, then proceed to study the two items separately. Similarly, we can not separate life from living matter, in order to study only living matter and its reactions. Inevitably, studying living matter and its reactions, we study life itself

Question: Explain why pipes burst in cold weather.
Answer: People who have not studied acoustics think that Thor bursts the pipes, but we know that is nothing of the kind for Professor Tyndall has burst the mythologies and has taught us that it is the natural behaviour of water (and bismuth) without which all fish would die and the earth be held in an iron grip. (1881)

Socrates: Shall we set down astronomy among the objects of study? Glaucon: I think so, to know something about the seasons, the months and the years is of use for military purposes, as well as for agriculture and for navigation. Socrates: It amuses me to see how afraid you are, lest the common herd of people should accuse you of recommending useless studies.

To Wheeler's comment, If you haven't found something strange during the day, it hasn't been much of a day, a student responded, I can't believe that space is that crummy. Wheeler replied: To disagree leads to study, to study leads to understanding, to understand is to appreciate, to appreciate is to love. So maybe I'll end up loving your theory.

~~[Unverified]~~ The strongest affection and utmost zeal should, I think, promote the studies concerned with the most beautiful objects. This is the discipline that deals with the universe’s divine revolutions, the stars’ motions, sizes, distances, risings and settings . . . for what is more beautiful than heaven?

A century ago astronomers, geologists, chemists, physicists, each had an island of his own, separate and distinct from that of every other student of Nature; the whole field of research was then an archipelago of unconnected units. To-day all the provinces of study have risen together to form a continent without either a ferry or a bridge.

A first step in the study of civilization is to dissect it into details, and to classify these in their proper groups. Thus, in examining weapons, they are to be classed under spear, club, sling, bow and arrow, and so forth; among textile arts are to be ranged matting, netting, and several grades of making and weaving threads; myths are divided under such headings as myths of sunrise and sunset, eclipse-myths, earthquake-myths, local myths which account for the names of places by some fanciful tale, eponymic myths which account for the parentage of a tribe by turning its name into the name of an imaginary ancestor; under rites and ceremonies occur such practices as the various kinds of sacrifice to the ghosts of the dead and to other spiritual beings, the turning to the east in worship, the purification of ceremonial or moral uncleanness by means of water or fire. Such are a few miscellaneous examples from a list of hundreds … To the ethnographer, the bow and arrow is the species, the habit of flattening children’s skulls is a species, the practice of reckoning numbers by tens is a species. The geographical distribution of these things, and their transmission from region to region, have to be studied as the naturalist studies the geography of his botanical and zoological species.

A free soul ought not to pursue any study slavishly; for while bodily labors performed under constraint do not harm the body, nothing that is learned under compulsion stays with the mind.

A great surgeon performs operations for stone by a single method; later he makes a statistical summary of deaths and recoveries, and he concludes from these statistics that the mortality law for this operation is two out of five. Well, I say that this ratio means literally nothing scientifically and gives us no certainty in performing the next operation; for we do not know whether the next case will be among the recoveries or the deaths. What really should be done, instead of gathering facts empirically, is to study them more accurately, each in its special determinism. We must study cases of death with great care and try to discover in them the cause of mortal accidents so as to master the cause and avoid the accidents.

A hundred years ago the study of life was often pursued, and also presented to the public, in a highly unified way. Darwin, as everyone knows, in addressing the world at large began his story with the history of pigeons and ended it with the breeding of primroses, having made excursions on the way into the origins of coral reefs and of the races of Man.

A large part of the training of the engineer, civil and military, as far as preparatory studies are concerned; of the builder of every fabric of wood or stone or metal designed to stand upon the earth, or bridge the stream, or resist or float upon the wave; of the surveyor who lays out a building lot in a city, or runs a boundary line between powerful governments across a continent; of the geographer, navigator, hydrographer, and astronomer,—must be derived from the mathematics.

A learned man is an idler who kills time with study. Beware of his false knowledge: it is more dangerous than ignorance.

A multidisciplinary study group ... estimated that it would be 1980 before developments in artificial intelligence make it possible for machines alone to do much thinking or problem solving of military significance. That would leave, say, five years to develop man-computer symbiosis and 15 years to use it. The 15 may be 10 or 500, but those years should be intellectually the most creative and exciting in the history of mankind.

A noteworthy and often-remarked similarity exists between the facts and methods of geology and those of linguistic study. The science of language is, as it were, the geology of the most modern period, the Age of the Man, having for its task to construct the history of development of the earth and its inhabitants from the time when the proper geological record remains silent … The remains of ancient speech are like strata deposited in bygone ages, telling of the forms of life then existing, and of the circumstances which determined or affected them; while words are as rolled pebbles, relics of yet more ancient formations, or as fossils, whose grade indicates the progress of organic life, and whose resemblances and relations show the correspondence or sequence of the different strata; while, everywhere, extensive denudation has marred the completeness of the record, and rendered impossible a detailed exhibition of the whole course of development.

A person by study must try to disengage the subject from useless matter, and to seize on points capable of improvement. ... When subjects are viewed through the mists of prejudice, useful truths may escape.

A physician’s subject of study is necessarily the patient, and his first field for observation is the hospital. But if clinical observation teaches him to know the form and course of diseases, it cannot suffice to make him understand their nature; to this end he must penetrate into the body to find which of the internal parts are injured in their functions. That is why dissection of cadavers and microscopic study of diseases were soon added to clinical observation. But to-day these various methods no longer suffice; we must push investigation further and, in analyzing the elementary phenomena of organic bodies, must compare normal with abnormal states. We showed elsewhere how incapable is anatomy alone to take account of vital phenenoma, and we saw that we must add study of all physico-chemical conditions which contribute necessary elements to normal or pathological manifestations of life. This simple suggestion already makes us feel that the laboratory of a physiologist-physician must be the most complicated of all laboratories, because he has to experiment with phenomena of life which are the most complex of all natural phenomena.

A plain, reasonable working man supposes, in the old way which is also the common-sense way, that if there are people who spend their lives in study, whom he feeds and keeps while they think for him—then no doubt these men are engaged in studying things men need to know; and he expects of science that it will solve for him the questions on which his welfare, and that of all men, depends. He expects science to tell him how he ought to live: how to treat his family, his neighbours and the men of other tribes, how to restrain his passions, what to believe in and what not to believe in, and much else. And what does our science say to him on these matters?
It triumphantly tells him: how many million miles it is from the earth to the sun; at what rate light travels through space; how many million vibrations of ether per second are caused by light, and how many vibrations of air by sound; it tells of the chemical components of the Milky Way, of a new element—helium—of micro-organisms and their excrements, of the points on the hand at which electricity collects, of X rays, and similar things.
“But I don't want any of those things,” says a plain and reasonable man—“I want to know how to live.”

A recognized fact which goes back to the earliest times is that every living organism is not the sum of a multitude of unitary processes, but is, by virtue of interrelationships and of higher and lower levels of control, an unbroken unity. When research, in the efforts of bringing understanding, as a rule examines isolated processes and studies them, these must of necessity be removed from their context. In general, viewed biologically, this experimental separation involves a sacrifice. In fact, quantitative findings of any material and energy changes preserve their full context only through their being seen and understood as parts of a natural order.

A rock or stone is not a subject that, of itself, may interest a philosopher to study; but, when he comes to see the necessity of those hard bodies, in the constitution of this earth, or for the permanency of the land on which we dwell, and when he finds that there are means wisely provided for the renovation of this necessary decaying part, as well as that of every other, he then, with pleasure, contemplates this manifestation of design, and thus connects the mineral system of this earth with that by which the heavenly bodies are made to move perpetually in their orbits.

A scientific or technical study always consists of the following three steps:
1. One decides the objective.
2. One considers the method.
3. One evaluates the method in relation to the objective.

A student who wishes now-a-days to study geometry by dividing it sharply from analysis, without taking account of the progress which the latter has made and is making, that student no matter how great his genius, will never be a whole geometer. He will not possess those powerful instruments of research which modern analysis puts into the hands of modern geometry. He will remain ignorant of many geometrical results which are to be found, perhaps implicitly, in the writings of the analyst. And not only will he be unable to use them in his own researches, but he will probably toil to discover them himself, and, as happens very often, he will publish them as new, when really he has only rediscovered them.

A study of Disease—of Pestilences methodically prepared and deliberately launched upon man and beast—is certainly being pursued in the laboratories of more than one great country. Blight to destroy crops, Anthrax to slay horses and cattle, Plague to poison not armies but whole districts—such are the lines along which military science is remorselessly advancing.

A study of history shows that civilizations that abandon the quest for knowledge are doomed to disintegration.

A superficial knowledge of mathematics may lead to the belief that this subject can be taught incidentally, and that exercises akin to counting the petals of flowers or the legs of a grasshopper are mathematical. Such work ignores the fundamental idea out of which quantitative reasoning grows—the equality of magnitudes. It leaves the pupil unaware of that relativity which is the essence of mathematical science. Numerical statements are frequently required in the study of natural history, but to repeat these as a drill upon numbers will scarcely lend charm to these studies, and certainly will not result in mathematical knowledge.

A superficial knowledge of mathematics may lead to the belief that this subject can be taught incidentally, and that exercises akin to counting the petals of flowers or the legs of a grasshopper are mathematical. Such work ignores the fundamental idea out of which quantitative reasoning grows—the equality of magnitudes. It leaves the pupil unaware of that relativity which is the essence of mathematical science. Numerical statements are frequently required in the study of natural history, but to repeat these as a drill upon numbers will scarcely lend charm to these studies, and certainly will not result in mathematical knowledge.

A troubling question for those of us committed to the widest application of intelligence in the study and solution of the problems of men is whether a general understanding of the social sciences will be possible much longer. Many significant areas of these disciplines have already been removed by the advances of the past two decades beyond the reach of anyone who does not know mathematics; and the man of letters is increasingly finding, to his dismay, that the study of mankind proper is passing from his hands to those of technicians and specialists. The aesthetic effect is admittedly bad: we have given up the belletristic “essay on man” for the barbarisms of a technical vocabulary, or at best the forbidding elegance of mathematical syntax.

Abraham Maslow, felt … [an] instinctive revolt against the “atmosphere” of Freudian psychology, with its emphasis on sickness and neurosis, and decided that he might obtain some equally interesting results if he studied extremely healthy people.

According to the historian D. B. McIntyre (1963), James Hutton, often known as the father of geology, said in a lecture before the Royal Society of Edinburgh in the 1790s that he thought of the Earth as a superorganism and that its proper study would be by physiology. Hutton went on to make the analogy between the circulation of the blood, discovered by Harvey, and the circulation of the nutrient elements of the Earth and of the way that sunlight distills water from the oceans so that it may later fall as rain and so refresh the earth.

After the birth of printing books became widespread. Hence everyone throughout Europe devoted himself to the study of literature... Every year, especially since 1563, the number of writings published in every field is greater than all those produced in the past thousand years. Through them there has today been created a new theology and a new jurisprudence; the Paracelsians have created medicine anew and the Copernicans have created astronomy anew. I really believe that at last the world is alive, indeed seething, and that the stimuli of these remarkable conjunctions did not act in vain.

All talk about science purely for its practical and wealth-producing results is … idle. … Practical results will follow right enough. No real knowledge is sterile. … With this faith in the ultimate usefulness of all real knowledge a man may proceed to devote himself to a study of first causes without apology, and without hope of immediate return.

Although with the majority of those who study and practice in these capacities [engineers, builders, surveyors, geographers, navigators, hydrographers, astronomers], secondhand acquirements, trite formulas, and appropriate tables are sufficient for ordinary purposes, yet these trite formulas and familiar rules were originally or gradually deduced from the profound investigations of the most gifted minds, from the dawn of science to the present day. … The further developments of the science, with its possible applications to larger purposes of human utility and grander theoretical generalizations, is an achievement reserved for a few of the choicest spirits, touched from time to time by Heaven to these highest issues. The intellectual world is filled with latent and undiscovered truth as the material world is filled with latent electricity.

Among all the liberal arts, the first is logic, and specifically that part of logic which gives initial instruction about words. … [T]he word “logic” has a broad meaning, and is not restricted exclusively to the science of argumentative reasoning. [It includes] Grammar [which] is “the science of speaking and writing correctly—the starting point of all liberal studies.”

Among the current discussions, the impact of new and sophisticated methods in the study of the past occupies an important place. The new 'scientific' or 'cliometric' history—born of the marriage contracted between historical problems and advanced statistical analysis, with economic theory as bridesmaid and the computer as best man—has made tremendous advances in the last generation.

Among the studies to which the [Rockefeller] Foundation is giving support is a series in a relatively new field, which may be called molecular biology, in which delicate modern techniques are being used to investigate ever more minute details of certain life processes.

An astronomer must be the wisest of men; his mind must be duly disciplined in youth; especially is mathematical study necessary; both an acquaintance with the doctrine of number, and also with that other branch of mathematics, which, closely connected as it is with the science of the heavens, we very absurdly call geometry, the measurement of the earth.

An attempt to study the evolution of living organisms without reference to cytology would be as futile as an account of stellar evolution which ignored spectroscopy.

An Experiment, like every other event which takes place, is a natural phenomenon; but in a Scientific Experiment the circumstances are so arranged that the relations between a particular set of phenomena may be studied to the best advantage.

An extremely healthy dose of skepticism about the reliability of science is an absolutely inevitable consequence of any scientific study of its track record.

An infinity of these tiny animals defoliate our plants, our trees, our fruits... they attack our houses, our fabrics, our furniture, our clothing, our furs ... He who in studying all the different species of insects that are injurious to us, would seek means of preventing them from harming us, would seek to cause them to perish, proposes for his goal important tasks indeed.

And if you want the exact moment in time, it was conceived mentally on 8th March in this year one thousand six hundred and eighteen, but submitted to calculation in an unlucky way, and therefore rejected as false, and finally returning on the 15th of May and adopting a new line of attack, stormed the darkness of my mind. So strong was the support from the combination of my labour of seventeen years on the observations of Brahe and the present study, which conspired together, that at first I believed I was dreaming, and assuming my conclusion among my basic premises. But it is absolutely certain and exact that the proportion between the periodic times of any two planets is precisely the sesquialterate proportion of their mean distances.

And when with excellent Microscopes I discern in otherwise invisible Objects the Inimitable Subtlety of Nature’s Curious Workmanship; And when, in a word, by the help of Anatomicall Knives, and the light of Chymicall Furnaces, I study the Book of Nature, and consult the Glosses of Aristotle, Epicurus, Paracelsus, Harvey, Helmont, and other learn'd Expositors of that instructive Volumne; I find my self oftentimes reduc’d to exclaim with the Psalmist, How manifold are thy works, O Lord? In wisdom hast thou made them all.

Anthropology is the study of human beings as creatures of society. It fastens its attention upon those physical characteristics and industrial techniques, those conventions and values, which distinguish one community from all others that belong to a different tradition.

Antoine Magnan, a French zoologist, in 1934 made some very careful studies of bumblebee flight and came to the conclusion that bumblebees cannot fly at all! Fortunately, the bumblebees never heard this bit of news and so went on flying as usual.

Any one who has studied the history of science knows that almost every great step therein has been made by the “anticipation of Nature,” that is, by the invention of hypotheses, which, though verifiable, often had very little foundation to start with; and, not unfrequently, in spite of a long career of usefulness, turned out to be wholly erroneous in the long run.

Any scientist of any age who wants to make important discoveries must study important problems. Dull or piffling problems yield dull or piffling answers. It is not not enough that a problem should be “interesting.” … The problem must be such that it matters what the answer is—whether to science generally or to mankind.

Archimedes had discovered the truth about several important natural laws, but more significant—at least from Galileo’s standpoint—was Archimedes’s discovery of a way for a scientist to solve problems: first separating what he truly wants to solve from irrelevant externals and then attacking the core of the problem with boldness and imagination. Galileo realized that this approach was suitable for his own studies.

Archimedes possessed so high a spirit, so profound a soul, and such treasures of highly scientific knowledge, that though these inventions [used to defend Syracuse against the Romans] had now obtained him the renown of more than human sagacity, he yet would not deign to leave behind him any commentary or writing on such subjects; but, repudiating as sordid and ignoble the whole trade of engineering, and every sort of art that lends itself to mere use and profit, he placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life; studies, the superiority of which to all others is unquestioned, and in which the only doubt can be whether the beauty and grandeur of the subjects examined, or the precision and cogency of the methods and means of proof, most deserve our admiration.

Arts and sciences in one and the same century have arrived at great perfection; and no wonder, since every age has a kind of universal genius, which inclines those that live in it to some particular studies; the work then, being pushed on by many hands, must go forward.

As a man who has devoted his whole life to the most clear headed science, to the study of matter, I can tell you as a result of my research about atoms this much: There is no matter as such. All matter originates and exists only by virtue of a force which brings the particle of an atom to vibration and holds this most minute solar system of the atom together. … We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter.

As a second year high school chemistry student, I still have a vivid memory of my excitement when I first saw a chart of the periodic table of elements. The order in the universe seemed miraculous, and I wanted to study and learn as much as possible about the natural sciences.

As a teenage fisherman, I watched and followed terns to find fish. Later I studied terns for my Ph.D. During those studies I came to see and love other seabirds. Albatrosses are the biggest, so they get your attention.

As Crystallography was born of a chance observation by Haüy of the cleavage-planes of a single fortunately fragile specimen, … so out of the slender study of the Norwich Spiral has sprung the vast and interminable Calculus of Cyclodes, which strikes such far-spreading and tenacious roots into the profoundest strata of denumeration, and, by this and the multitudinous and multifarious dependent theories which cluster around it, reminds one of the Scriptural comparison of the Kingdom of Heaven “to a grain of mustard-seed which a man took and cast into his garden, and it grew and waxed a great tree, and the fowls of the air lodged in the branches of it.”

As I strayed into the study of an eminent physicist, I observed hanging against the wall, framed like a choice engraving, several dingy, ribbon-like strips of, I knew not what... My curiosity was at once aroused. What were they? ... They might be shreds of mummy-wraps or bits of friable bark-cloth from the Pacific, ... [or] remnants from a grandmother’s wedding dress... They were none of these... He explained that they were carefully-prepared photographs of portions of the Solar Spectrum. I stood and mused, absorbed in the varying yet significant intensities of light and shade, bordered by mystic letters and symbolic numbers. As I mused, the pale legend began to glow with life. Every line became luminous with meaning. Every shadow was suffused with light shining from behind, suggesting some mighty achievement of knowledge; of knowledge growing more daring in proportion to the remoteness of the object known; of knowledge becoming more positive in its answers, as the questions which were asked seemed unanswerable. No Runic legend, no Babylonish arrowhead, no Egyptian hieroglyph, no Moabite stone, could present a history like this, or suggest thoughts of such weighty import or so stimulate and exalt the imagination.

As soon as we touch the complex processes that go on in a living thing, be it plant or animal, we are at once forced to use the methods of this science [chemistry]. No longer will the microscope, the kymograph, the scalpel avail for the complete solution of the problem. For the further analysis of these phenomena which are in flux and flow, the investigator must associate himself with those who have labored in fields where molecules and atoms, rather than multicellular tissues or even unicellular organisms, are the units of study.

As there is no study which may be so advantageously entered upon with a less stock of preparatory knowledge than mathematics, so there is none in which a greater number of uneducated men have raised themselves, by their own exertions, to distinction and eminence. … Many of the intellectual defects which, in such cases, are commonly placed to the account of mathematical studies, ought to be ascribed to the want of a liberal education in early youth.

As turning the logs, will make a dull fire burn, so change of studies a dull brain.

Astronomy is a science in which you are not able to touch anything you study.

Astronomy may be revolutionized more than any other field of science by observations from above the atmosphere. Study of the planets, the Sun, the stars, and the rarified matter in space should all be profoundly influenced by measurements from balloons, rockets, probes and satellites. ... In a new adventure of discovery no one can foretell what will be found, and it is probably safe to predict that the most important new discovery that will be made with flying telescopes will be quite unexpected and unforeseen. (1961)

Astronomy was not studied by Kepler, Galileo, or Newton for the practical applications which might result from it, but to enlarge the bounds of knowledge, to furnish new objects of thought and contemplation in regard to the universe of which we form a part; yet how remarkable the influence which this science, apparently so far removed from the sphere of our material interests, has exerted on the destinies of the world!

Astronomy, as the science of cyclical motions, has nothing in common with Geology. But look at Astronomy where she has an analogy with Geology; consider our knowledge of the heavens as a palaetiological science;—as the study of a past condition, from which the present is derived by causes acting in time. Is there no evidence of a beginning, or of a progress?

Astrophysicists have the formidable privilege of having the largest view of the Universe; particle detectors and large telescopes are today used to study distant stars, and throughout space and time, from the infinitely large to the infinitely small, the Universe never ceases to surprise us by revealing its structures little by little.

At night I would return home, set out a lamp before me, and devote myself to reading and writing. Whenever sleep overcame me or I became conscious of weakening, I would turn aside to drink a cup of wine, so that my strength would return to me. Then I would return to reading. And whenever sleep seized me I would see those very problems in my dream; and many questions became clear to me in my sleep. I continued in this until all of the sciences were deeply rooted within me and I understood them as is humanly possible. Everything which I knew at the time is just as I know it now; I have not added anything to it to this day. Thus I mastered the logical, natural, and mathematical sciences, and I had now reached the science.

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.

Attempts have been made from a study of the changes produced by mutation to obtain the relative order of the bases within various triplets, but my own view is that these are premature until there is more extensive and more reliable data on the composition of the triplets.

Bacon first taught the world the true method of the study of nature, and rescued science from that barbarism in which the followers of Aristotle, by a too servile imitation of their master.

Basic research at universities comes in two varieties: research that requires big bucks and research that requires small bucks. Big bucks research is much like government research and in fact usually is government research but done for the government under contract. Like other government research, big bucks academic research is done to understand the nature and structure of the universe or to understand life, which really means that it is either for blowing up the world or extending life, whichever comes first. Again, that's the government's motivation. The universities' motivation for conducting big bucks research is to bring money in to support professors and graduate students and to wax the floors of ivy-covered buildings. While we think they are busy teaching and learning, these folks are mainly doing big bucks basic research for a living, all the while priding themselves on their terrific summer vacations and lack of a dress code.
Smalls bucks research is the sort of thing that requires paper and pencil, and maybe a blackboard, and is aimed primarily at increasing knowledge in areas of study that don't usually attract big bucks - that is, areas that don't extend life or end it, or both. History, political science, and romance languages are typically small bucks areas of basic research. The real purpose of small bucks research to the universities is to provide a means of deciding, by the quality of their small bucks research, which professors in these areas should get tenure.

Before beginning I should put in three years of intensive study, and I haven’t that much time to squander on a probable failure.

Besides accustoming the student to demand, complete proof, and to know when he has not obtained it, mathematical studies are of immense benefit to his education by habituating him to precision. It is one of the peculiar excellencies of mathematical discipline, that the mathematician is never satisfied with à peu près. He requires the exact truth. Hardly any of the non-mathematical sciences, except chemistry, has this advantage. One of the commonest modes of loose thought, and sources of error both in opinion and in practice, is to overlook the importance of quantities. Mathematicians and chemists are taught by the whole course of their studies, that the most fundamental difference of quality depends on some very slight difference in proportional quantity; and that from the qualities of the influencing elements, without careful attention to their quantities, false expectation would constantly be formed as to the very nature and essential character of the result produced.

Besides electrical engineering theory of the transmission of messages, there is a larger field [cybernetics] which includes not only the study of language but the study of messages as a means of controlling machinery and society, the development of computing machines and other such automata, certain reflections upon psychology and the nervous system, and a tentative new theory of scientific method.

Between men of different studies and professions, may be observed a constant reciprocation of reproaches. The collector of shells and stones derides the folly of him who pastes leaves and flowers upon paper, pleases himself with colours that are perceptibly fading, and amasses with care what cannot be preserved. The hunter of insects stands amazed that any man can waste his short time upon lifeless matter, while many tribes of animals yet want their history. Every one is inclined not only to promote his own study, but to exclude all others from regard, and having heated his imagination with some favourite pursuit, wonders that the rest of mankind are not seized with the same passion.

Biology can be divided into the study of proximate causes, the study of the physiological sciences (broadly conceived), and into the study of ultimate (evolutionary) causes, the subject of natural history.

Biology is a science of three dimensions. The first is the study of each species across all levels of biological organization, molecule to cell to organism to population to ecosystem. The second dimension is the diversity of all species in the biosphere. The third dimension is the history of each species in turn, comprising both its genetic evolution and the environmental change that drove the evolution. Biology, by growing in all three dimensions, is progressing toward unification and will continue to do so.

Biology occupies a position among the sciences both marginal and central. Marginal because, the living world, constituting only a tiny and very “special” part of the universe, it does not seem likely that the study of living beings will ever uncover general laws applicable outside the biosphere. But if the ultimate aim of the whole of science is indeed, as I believe, to clarify man's relationship to the universe, then biology must be accorded a central position, since of all the disciplines it is the one that endeavours to go most directly to the heart of the problems that must be resolved before that of “human nature” can even be framed in other than metaphysical terms.

Both social and biosocial factors are necessary to interpret crosscultural studies, with the general proviso that one’s research interest determines which elements, in what combinations, are significant for the provision of understanding.

But for the persistence of a student of this university in urging upon me his desire to study with me the modern algebra I should never have been led into this investigation; and the new facts and principles which I have discovered in regard to it (important facts, I believe), would, so far as I am concerned, have remained still hidden in the womb of time. In vain I represented to this inquisitive student that he would do better to take up some other subject lying less off the beaten track of study, such as the higher parts of the calculus or elliptic functions, or the theory of substitutions, or I wot not what besides. He stuck with perfect respectfulness, but with invincible pertinacity, to his point. He would have the new algebra (Heaven knows where he had heard about it, for it is almost unknown in this continent), that or nothing. I was obliged to yield, and what was the consequence? In trying to throw light upon an obscure explanation in our text-book, my brain took fire, I plunged with re-quickened zeal into a subject which I had for years abandoned, and found food for thoughts which have engaged my attention for a considerable time past, and will probably occupy all my powers of contemplation advantageously for several months to come.

But if anyone, well seen in the knowledge, not onely of Sacred and exotick History, but of Astronomical Calculation, and the old Hebrew Kalendar, shall apply himself to these studies, I judge it indeed difficult, but not impossible for such a one to attain, not onely the number of years, but even, of dayes from the Creation of the World.

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 nothing is more estimable than a physician who, having studied nature from his youth, knows the properties of the human body, the diseases which assail it, the remedies which will benefit it, exercises his art with caution, and pays equal attention to the rich and the poor.