… the definition of irrational numbers, on which geometric representations have often had a confusing influence. … I take in my definition a purely formal point of view, calling some given symbols numbers, so that the existence of these numbers is beyond doubt.

A closer look at the course followed by developing theory reveals for a start that it is by no means as continuous as one might expect, but full of breaks and at least apparently not along the shortest logical path. Certain methods often afforded the most handsome results only the other day, and many might well have thought that the development of science to infinity would consist in no more than their constant application. Instead, on the contrary, they suddenly reveal themselves as exhausted and the attempt is made to find other quite disparate methods. In that event there may develop a struggle between the followers of the old methods and those of the newer ones. The former's point of view will be termed by their opponents as out-dated and outworn, while its holders in turn belittle the innovators as corrupters of true classical science.

A mathematician of the first rank, Laplace quickly revealed himself as only a mediocre administrator; from his first work we saw that we had been deceived. Laplace saw no question from its true point of view; he sought subtleties everywhere; had only doubtful ideas, and finally carried the spirit of the infinitely small into administration.

Antiqua consuetudo difficulter relinquitur: & ultra proprium videre nemo libenter ducitur.
Old habits are hard to break: and no one is easily led beyond his own point of view.

By a recent estimate, nearly half the bills before the U.S. Congress have a substantial science-technology component and some two-thirds of the District of Columbia Circuit Court’s case load now involves review of action by federal administrative agencies; and more and more of such cases relate to matters on the frontiers of technology.
If the layman cannot participate in decision making, he will have to turn himself over, essentially blind, to a hermetic elite. … [The fundamental question becomes] are we still capable of self-government and therefore freedom?
Margaret Mead wrote in a 1959 issue of Daedalus about scientists elevated to the status of priests. Now there is a name for this elevation, when you are in the hands of—one hopes—a benevolent elite, when you have no control over your political decisions. From the point of view of John Locke, the name for this is slavery.

By destroying the biological character of phenomena, the use of averages in physiology and medicine usually gives only apparent accuracy to the results. From our point of view, we may distinguish between several kinds of averages: physical averages, chemical averages and physiological and pathological averages. If, for instance, we observe the number of pulsations and the degree of blood pressure by means of the oscillations of a manometer throughout one day, and if we take the average of all our figures to get the true or average blood pressure and to learn the true or average number of pulsations, we shall simply have wrong numbers. In fact, the pulse decreases in number and intensity when we are fasting and increases during digestion or under different influences of movement and rest; all the biological characteristics of the phenomenon disappear in the average. Chemical averages are also often used. If we collect a man's urine during twenty-four hours and mix all this urine to analyze the average, we get an analysis of a urine which simply does not exist; for urine, when fasting, is different from urine during digestion. A startling instance of this kind was invented by a physiologist who took urine from a railroad station urinal where people of all nations passed, and who believed he could thus present an analysis of average European urine! Aside from physical and chemical, there are physiological averages, or what we might call average descriptions of phenomena, which are even more false. Let me assume that a physician collects a great many individual observations of a disease and that he makes an average description of symptoms observed in the individual cases; he will thus have a description that will never be matched in nature. So in physiology, we must never make average descriptions of experiments, because the true relations of phenomena disappear in the average; when dealing with complex and variable experiments, we must study their various circumstances, and then present our most perfect experiment as a type, which, however, still stands for true facts. In the cases just considered, averages must therefore be rejected, because they confuse, while aiming to unify, and distort while aiming to simplify. Averages are applicable only to reducing very slightly varying numerical data about clearly defined and absolutely simple cases.

Certain elements have the property of producing the same crystal form when in combination with an equal number of atoms of one or more common elements, and the elements, from his point of view, can be arranged in certain groups. For convenience I have called the elements belonging to the same group … isomorphous.

Darwin's characteristic perspicacity is nowhere better illustrated than in his prophecy of the reaction of the world of science. He admitted at once that it would be impossible to convince those older men '...whose minds are stocked with a multitude of facts, all viewed ... from a point of view directly opposite to mine ... A few naturalists endowed with much flexibility of mind and who have already begun to doubt the immutability of species, may be influenced by this volume; but I look with confidence to the young and rising naturalists, who will be able to view both sides with equal impartiality.

Dissection … teaches us that the body of man is made up of certain kinds of material, so differing from each other in optical and other physical characters and so built up together as to give the body certain structural features. Chemical examination further teaches us that these kinds of material are composed of various chemical substances, a large number of which have this characteristic that they possess a considerable amount of potential energy capable of being set free, rendered actual, by oxidation or some other chemical change. Thus the body as a whole may, from a chemical point of view, be considered as a mass of various chemical substances, representing altogether a considerable capital of potential energy.

During the half-century that has elapsed since the enunciation of the cell-theory by Schleiden and Schwann, in 1838-39, it has became ever more clearly apparent that the key to all ultimate biological problems must, in the last analysis, be sought in the cell. It was the cell-theory that first brought the structure of plants and animals under one point of view by revealing their common plan of organization. It was through the cell-theory that Kolliker and Remak opened the way to an understanding of the nature of embryological development, and the law of genetic continuity lying at the basis of inheritance. It was the cell-­theory again which, in the hands of Virchaw and Max Schultze, inaugurated a new era in the history of physiology and pathology, by showing that all the various functions of the body, in health and in disease, are but the outward expression of cell­-activities. And at a still later day it was through the cell-theory that Hertwig, Fol, Van Beneden, and Strasburger solved the long-standing riddle of the fertilization of the egg, and the mechanism of hereditary transmission. No other biological generalization, save only the theory of organic evolution, has brought so many apparently diverse phenomena under a common point of view or has accomplished more far the unification of knowledge. The cell-theory must therefore be placed beside the evolution-theory as one of the foundation stones of modern biology.

Electricity is often called wonderful, beautiful; but it is so only in common with the other forces of nature. The beauty of electricity or of any other force is not that the power is mysterious, and unexpected, touching every sense at unawares in turn, but that it is under law, and that the taught intellect can even govern it largely. The human mind is placed above, and not beneath it, and it is in such a point of view that the mental education afforded by science is rendered super-eminent in dignity, in practical application and utility; for by enabling the mind to apply the natural power through law, it conveys the gifts of God to man.

Ethnologists regard man as the primitive element of tribes, races, and peoples. The anthropologist looks at him as a member of the fauna of the globe, belonging to a zoölogical classification, and subject to the same laws as the rest of the animal kingdom. To study him from the last point of view only would be to lose sight of some of his most interesting and practical relations; but to be confined to the ethnologist’s views is to set aside the scientific rule which requires us to proceed from the simple to the compound, from the known to the unknown, from the material and organic fact to the functional phenomenon.

Every definition implies an axiom, since it asserts the existence of the object defined. The definition then will not be justified, from the purely logical point of view, until we have ‘proved’ that it involves no contradiction either in its terms or with the truths previously admitted.

Everything is made of atoms ... Everything that animals do, atoms do. ... There is nothing that living things do that cannot be understood from the point of view that they are made of atoms acting according to the laws of physics.

Following the original proposal of Belinfante, “the writer has in a recent note on the meson theory of nuclear forces” used the word “nuclon” as a common notation for the heavy nuclear constituents, neutrons and protons. In the meantime, however, it has been pointed out to me that, since the root of the word nucleus is “nucle”, the notation “nucleon” would from a philological point of view be more appropriate for this purpose….

For we may remark generally of our mathematical researches, that these auxiliary quantities, these long and difficult calculations into which we are often drawn, are almost always proofs that we have not in the beginning considered the objects themselves so thoroughly and directly as their nature requires, since all is abridged and simplified, as soon as we place ourselves in a right point of view.

From a pragmatic point of view, the difference between living against a background of foreigness (an indifferent Universe) and one of intimacy (a benevolent Universe) means the difference between a general habit of wariness and one of trust.

From an entertainment point of view, the Solar System has been a bust. None of the planets turns out to have any real-estate potential, and most of them are probably even useless for filming Dune sequels.

From the point of view of a tapeworm, man was created by God to serve the appetite of the tapeworm.

From the point of view of the physicist, a theory of matter is a policy rather than a creed; its object is to connect or co-ordinate apparently diverse phenomena, and above all to suggest, stimulate and direct experiment. It ought to furnish a compass which, if followed, will lead the observer further and further into previously unexplored regions.

From the point of view of the pure morphologist the recapitulation theory is an instrument of research enabling him to reconstruct probable lines of descent; from the standpoint of the student of development and heredity the fact of recapitulation is a difficult problem whose solution would perhaps give the key to a true understanding of the real nature of heredity.

Generality of points of view and of methods, precision and elegance in presentation, have become, since Lagrange, the common property of all who would lay claim to the rank of scientific mathematicians. And, even if this generality leads at times to abstruseness at the expense of intuition and applicability, so that general theorems are formulated which fail to apply to a single special case, if furthermore precision at times degenerates into a studied brevity which makes it more difficult to read an article than it was to write it; if, finally, elegance of form has well-nigh become in our day the criterion of the worth or worthlessness of a proposition,—yet are these conditions of the highest importance to a wholesome development, in that they keep the scientific material within the limits which are necessary both intrinsically and extrinsically if mathematics is not to spend itself in trivialities or smother in profusion.

He [Heinrich Rose] looked upon the various substances that he was manipulating, as well as their reactions, under a thoroughly familial point of view: they were like so many children entrusted to his tutelage. Every time he explained simple, clear, well-defined phenomena, he assumed a jovial and smiling countenance; on the other hand, he almost got angry at certain mischievous bodies, the properties of which did not obey ordinary laws and troubled general theoretical views; in his eyes, this was unruly behavior.

I feel that the recent ruling of the United States Army and Navy regarding the refusal of colored blood donors is an indefensible one from any point of view. As you know, there is no scientific basis for the separation of the bloods of different races except on the basis of the individual blood types or groups. (1942)

I read them. Not to grade them. No, I read them to see how I am doing. Where am I failing? What don’t they understand? Why do they give wrong answers? Why do they have some point of view that I don’t think is right? Where am I failing? Where do I need to build up.

I was interested in truth from the point of view of salvation just as much as in truth from the point of view of scientific certainty. It appeared to me that there were two paths to truth, and I decided to follow both of them.

I well know what a spendidly great difference there is [between] a man and a bestia when I look at them from a point of view of morality. Man is the animal which the Creator has seen fit to honor with such a magnificent mind and has condescended to adopt as his favorite and for which he has prepared a nobler life; indeed, sent out for its salvation his only son; but all this belongs to another forum; it behooves me like a cobbler to stick to my last, in my own workshop, and as a naturalist to consider man and his body, for I know scarcely one feature by which man can be distinguished from apes, if it be not that all the apes have a gap between their fangs and their other teeth, which will be shown by the results of further investigation.

I’ve always been inspired by Dr. Martin Luther King, who articulated his Dream of an America where people are judged not by skin color but “by the content of their character.” In the scientific world, people are judged by the content of their ideas. Advances are made with new insights, but the final arbitrator of any point of view are experiments that seek the unbiased truth, not information cherry picked to support a particular point of view.

If a specific question has meaning, it must be possible to find operations by which an answer may be given to it ... I believe that many of the questions asked about social and philosophical subjects will be found to be meaningless when examined from the point of view of operations.

If you do not agree with the prevalent point of view, be ready to explain why.

In the field of thinking, the whole history of science from geocentrism to the Copernican revolution, from the false absolutes of Aristotle’s physics to the relativity of Galileo’s principle of inertia and to Einstein’s theory of relativity, shows that it has taken centuries to liberate us from the systematic errors, from the illusions caused by the immediate point of view as opposed to “decentered” systematic thinking.

In the mathematical investigations I have usually employed such methods as present themselves naturally to a physicist. The pure mathematician will complain, and (it must be confessed) sometimes with justice, of deficient rigour. But to this question there are two sides. For, however important it may be to maintain a uniformly high standard in pure mathematics, the physicist may occasionally do well to rest content with arguments which are fairly satisfactory and conclusive from his point of view. To his mind, exercised in a different order of ideas, the more severe procedure of the pure mathematician may appear not more but less demonstrative. And further, in many cases of difficulty to insist upon the highest standard would mean the exclusion of the subject altogether in view of the space that would be required.

Isolated facts and experiments have in themselves no value, however great their number may be. They only become valuable in a theoretical or practical point of view when they make us acquainted with the law of a series of uniformly recurring phenomena, or, it may be, only give a negative result showing an incompleteness in our knowledge of such a law, till then held to be perfect.

It is more important to have beauty in one's equations than to have them fit experiment... It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further developments of the theory.

It is odd to think that there is a word for something which, strictly speaking, does not exist, namely, “rest.” We distinguish between living and dead matter; between moving bodies and bodies at rest. This is a primitive point of view. What seems dead, a stone or the proverbial “door-nail,” say, is actually forever in motion. We have merely become accustomed to judge by outward appearances; by the deceptive impressions we get through our senses.

It is the task of science, as a collective human undertaking, to describe from the external side, (on which alone agreement is possible), such statistical regularity as there is in a world “in which every event has a unique aspect, and to indicate where possible the limits of such description. It is not part of its task to make imaginative interpretation of the internal aspect of reality—what it is like, for example, to be a lion, an ant or an ant hill, a liver cell, or a hydrogen ion. The only qualification is in the field of introspective psychology in which each human being is both observer and observed, and regularities may be established by comparing notes. Science is thus a limited venture. It must act as if all phenomena were deterministic at least in the sense of determinable probabilities. It cannot properly explain the behaviour of an amoeba as due partly to surface and other physical forces and partly to what the amoeba wants to do, with out danger of something like 100 per cent duplication. It must stick to the former. It cannot introduce such principles as creative activity into its interpretation of evolution for similar reasons. The point of view indicated by a consideration of the hierarchy of physical and biological organisms, now being bridged by the concept of the gene, is one in which science deliberately accepts a rigorous limitation of its activities to the description of the external aspects of events. In carrying out this program, the scientist should not, however, deceive himself or others into thinking that he is giving an account of all of reality. The unique inner creative aspect of every event necessarily escapes him.

It is true that Fourier had the opinion that the principal end of mathematics was public utility and the explanation of natural phenomena; but a philosopher as he is should have known that the unique end of science is the honor of the human mind and that from this point of view a question of [the theory of] number is as important as a question of the system of the world.

It would appear... that moral phenomena, when observed on a great scale, are found to resemble physical phenomena; and we thus arrive, in inquiries of this kind, at the fundamental principle, that the greater the number of individuals observed, the more do individual peculiarities, whether physical or moral, become effaced, and leave in a prominent point of view the general facts, by virtue of which society exists and is preserved.

Let him who so wishes take pleasure in boring us with all the wonders of nature: let one spend his life observing insects, another counting the tiny bones in the hearing membrane of certain fish, even in measuring, if you will, how far a flea can jump, not to mention so many other wretched objects of study; for myself, who am curious only about philosophy, who am sorry only not to be able to extend its horizons, active nature will always be my sole point of view; I love to see it from afar, in its breadth and its entirety, and not in specifics or in little details, which, although to some extent necessary in all the sciences, are generally the mark of little genius among those who devote themselves to them.

Like all sciences and all valuations, the psychology of women has hitherto been considered only from the point of view of men. (1926)

Man does not live by bread alone, there are other wants to be supplied, and even in a practical point of view, a single thought may be fraught with a thousand useful inventions.

Mathematics gives the young man a clear idea of demonstration and habituates him to form long trains of thought and reasoning methodically connected and sustained by the final certainty of the result; and it has the further advantage, from a purely moral point of view, of inspiring an absolute and fanatical respect for truth. In addition to all this, mathematics, and chiefly algebra and infinitesimal calculus, excite to a high degree the conception of the signs and symbols—necessary instruments to extend the power and reach of the human mind by summarizing an aggregate of relations in a condensed form and in a kind of mechanical way. These auxiliaries are of special value in mathematics because they are there adequate to their definitions, a characteristic which they do not possess to the same degree in the physical and mathematical [natural?] sciences.
There are, in fact, a mass of mental and moral faculties that can be put in full play only by instruction in mathematics; and they would be made still more available if the teaching was directed so as to leave free play to the personal work of the student.

Mathematics is often erroneously referred to as the science of common sense. Actually, it may transcend common sense and go beyond either imagination or intuition. It has become a very strange and perhaps frightening subject from the ordinary point of view, but anyone who penetrates into it will find a veritable fairyland, a fairyland which is strange, but makes sense, if not common sense.

Mathematics, the science of the ideal, becomes the means of investigating, understanding and making known the world of the real. The complex is expressed in terms of the simple. From one point of view mathematics may be defined as the science of successive substitutions of simpler concepts for more complex.

My point of view is that science is essentially private, whereas the almost universal counter point of view, explicitly stated in many of the articles in the Encyclopaedia, is that it must be public.

Now that we locate them [genes] in the chromosomes are we justified in regarding them as material units; as chemical bodies of a higher order than molecules? Frankly, these are questions with which the working geneticist has not much concern himself, except now and then to speculate as to the nature of the postulated elements. There is no consensus of opinion amongst geneticists as to what the genes are—whether they are real or purely fictitious—because at the level at which the genetic experiments lie, it does not make the slightest difference whether the gene is a hypothetical unit, or whether the gene is a material particle. In either case the unit is associated with a specific chromosome, and can be localized there by purely genetic analysis. Hence, if the gene is a material unit, it is a piece of chromosome; if it is a fictitious unit, it must be referred to a definite location in a chromosome—the same place as on the other hypothesis. Therefore, it makes no difference in the actual work in genetics which point of view is taken. Between the characters that are used by the geneticist and the genes that his theory postulates lies the whole field of embryonic development.

One and all
We lend an ear—nay, Science takes thereto—
Encourages the meanest who has racked
Nature until he gains from her some fact,
To state what truth is from his point of view,
Mere pin-point though it be: since many such
Conduce to make a whole, she bids our friend
Come forward unabashed and haply lend
His little life-experience to our much
Of modern knowledge.

One Form of Failure. From a worldly point of view there is no mistake so great as that of being always right.

One of Euler’s main recreations was music, and by cultivating it he brought with it all his geometrical spirit; … he rested his serious researches and composed his Essay of a New Theory of Music, published in 1739; a book full of new ideas presented in a new point of view, but that did not have a great success, apparently for the sole reason that it contains too much of geometry for the musician and too much music for the geometer.

One of the great problems of philosophy, is the relationship between the realm of knowledge and the realm of values. Knowledge is what is; values are what ought to be. I would say that all traditional philosophies up to and including Marxism have tried to derive the “ought” from the “is.” My point of view is that this is impossible, this is a farce.

One of the principal objects of theoretical research in my department of knowledge is to find the point of view from which the subject appears in its greatest simplicity.

Science is, according to Mach, nothing but the comparison and orderly arrangement of factually given contents of our consciousness, in accord with certain gradually acquired points of view and methods. Therefore, physics and psychology differ from each other not so much in the subject matter, but rather only in the points of view of the arrangement and connection of the various topics.

Scientific truth, like puristic truth, must come about by controversy. Personally this view is abhorrent to me. It seems to mean that scientific truth must transcend the individual, that the best hope of science lies in its greatest minds being often brilliantly and determinedly wrong, but in opposition, with some third, eclectically minded, middle-of-the-road nonentity seizing the prize while the great fight for it, running off with it, and sticking it into a textbook for sophomores written from no point of view and in defense of nothing whatsoever. I hate this view, for it is not dramatic and it is not fair; and yet I believe that it is the verdict of the history of science.

Society can, and does, and must control research enormously, negatively and positively, by selectively cutting off or supplying funds. At present it cuts—not so selectively. That is all right with me, as far as my own research is concerned. I certainly do not think society owes me a living or support for my research. If it does not support my research, I can always do something else and not be worse off, perhaps better. However, the question, from society's point of view, is exceedingly complicated.

That this subject [of imaginary magnitudes] has hitherto been considered from the wrong point of view and surrounded by a mysterious obscurity, is to be attributed largely to an ill-adapted notation. If, for example, +1, -1, and the square root of -1 had been called direct, inverse and lateral units, instead of positive, negative and imaginary (or even impossible), such an obscurity would have been out of the question.

The ‘mad idea’ which will lie at the basis of a future fundamental physical theory will come from a realization that physical meaning has some mathematical form not previously associated with reality. From this point of view the problem of the ‘mad idea’ is the problem of choosing, not of generating, the right idea. One should not understand that too literally. In the 1960s it was said (in a certain connection) that the most important discovery of recent years in physics was the complex numbers. The author [Yuri Manin] has something like that in mind.

The automatic computing engine now being designed at N.P.L. [National Physics Laboratory] is atypical large scale electronic digital computing machine. In a single lecture it will not be possible to give much technical detail of this machine, and most of what I shall say will apply equally to any other machine of this type now being planned. From the point of view of the mathematician the property of being digital should be of greater interest than that of being electronic. That it is electronic is certainly important because these machines owe their high speed to this, and without the speed it is doubtful if financial support for their construction would be forthcoming. But this is virtually all that there is to be said on that subject. That the machine is digital however has more subtle significance. It means firstly that numbers are represented by sequences of digits which can be as long as one wishes. One can therefore work to any desired degree of accuracy. This accuracy is not obtained by more careful machining of parts, control of temperature variations, and such means, but by a slight increase in the amount of equipment in the machine.

The cases of action at a distance are becoming, in a physical point of view, daily more and more important. Sound, light, electricity, magnetism, gravitation, present them as a series.
The nature of sound and its dependence on a medium we think we understand, pretty well. The nature of light as dependent on a medium is now very largely accepted. The presence of a medium in the phenomena of electricity and magnetism becomes more and more probable daily. We employ ourselves, and I think rightly, in endeavouring to elucidate the physical exercise of these forces, or their sets of antecedents and consequents, and surely no one can find fault with the labours which eminent men have entered upon in respect of light, or into which they may enter as regards electricity and magnetism. Then what is there about gravitation that should exclude it from consideration also? Newton did not shut out the physical view, but had evidently thought deeply of it; and if he thought of it, why should not we, in these advanced days, do so too?

The determination of the average man is not merely a matter of speculative curiosity; it may be of the most important service to the science of man and the social system. It ought necessarily to precede every other inquiry into social physics, since it is, as it were, the basis. The average man, indeed, is in a nation what the centre of gravity is in a body; it is by having that central point in view that we arrive at the apprehension of all the phenomena of equilibrium and motion.

The examination system, and the fact that instruction is treated mainly as a training for a livelihood, leads the young to regard knowledge from a purely utilitarian point of view as the road to money, not as the gateway to wisdom.

The existence of life must be considered as an elementary fact that can not be explained, but must be taken as a starting point in biology, in a similar way as the quantum of action, which appears as an irrational element from the point of view of classical mechanical physics, taken together with the existence of elementary particles, forms the foundation of atomic physics. The asserted impossibility of a physical or chemical explanation of the function peculiar to life would in this sense be analogous to the insufficiency of the mechanical analysis for the understanding of the stability of atoms.

The extensive literature addressed to the definition or characterization of science is filled with inconsistent points of view and demonstrates that an adequate definition is not easy to attain. Part of the difficulty arises from the fact that the meaning of science is not fixed, but is dynamic. As science has evolved, so has its meaning. It takes on a new meaning and significance with successive ages.

The importance of a result is largely relative, is judged differently by different men, and changes with the times and circumstances. It has often happened that great importance has been attached to a problem merely on account of the difficulties which it presented; and indeed if for its solution it has been necessary to invent new methods, noteworthy artifices, etc., the science has gained more perhaps through these than through the final result. In general we may call important all investigations relating to things which in themselves are important; all those which have a large degree of generality, or which unite under a single point of view subjects apparently distinct, simplifying and elucidating them; all those which lead to results that promise to be the source of numerous consequences; etc.

The invention of the differential calculus marks a crisis in the history of mathematics. The progress of science is divided between periods characterized by a slow accumulation of ideas and periods, when, owing to the new material for thought thus patiently collected, some genius by the invention of a new method or a new point of view, suddenly transforms the whole subject on to a higher level.

The major credit I think Jim and I deserve … is for selecting the right problem and sticking to it. It’s true that by blundering about we stumbled on gold, but the fact remains that we were looking for gold. Both of us had decided, quite independently of each other, that the central problem in molecular biology was the chemical structure of the gene. … We could not see what the answer was, but we considered it so important that we were determined to think about it long and hard, from any relevant point of view.

The materialistic point of view in psychology can claim, at best, only the value of an heuristic hypothesis.

The metaphysical philosopher from his point of view recognizes mathematics as an instrument of education, which strengthens the power of attention, develops the sense of order and the faculty of construction, and enables the mind to grasp under the simple formulae the quantitative differences of physical phenomena.

The most fatal illusion is the settled point of view. Since life is growth and motion, a fixed point of view kills anybody who has one.

The most obvious and easy things in mathematics are not those that come logically at the beginning; they are things that, from the point of view of logical deduction, come somewhere in the middle. Just as the easiest bodies to see are those that are neither very near nor very far…

The most satisfactory definition of man from the scientific point of view is probably Man the Tool-maker.

The new appears as a minority point of view, and hence is unpopular. The function of a university is to give it a sanctuary.

The opinion appears to be gaining ground that this very general conception of functionality, born on mathematical ground, is destined to supersede the narrower notion of causation, traditional in connection with the natural sciences. As an abstract formulation of the idea of determination in its most general sense, the notion of functionality includes and transcends the more special notion of causation as a one-sided determination of future phenomena by means of present conditions; it can be used to express the fact of the subsumption under a general law of past, present, and future alike, in a sequence of phenomena. From this point of view the remark of Huxley that Mathematics “knows nothing of causation” could only be taken to express the whole truth, if by the term “causation” is understood “efficient causation.” The latter notion has, however, in recent times been to an increasing extent regarded as just as irrelevant in the natural sciences as it is in Mathematics; the idea of thorough-going determinancy, in accordance with formal law, being thought to be alone significant in either domain.

The purpose of the history of science is to establish the genesis and the development of scientific facts and ideas, taking into account all intellectual exchanges and all influences brought into play by the very progress of civilization. It is indeed a history of civilization considered from its highest point of view. The center of interest is the evolution of science, but general history remains always in the background.

The true excellence and importance of those arts and sciences which exert and display themselves in writing, may be seen, in a more general point of view, in the great influence which they have exerted on the character and fate of nations, throughout the history of the world.

The world probably being of much greater antiquity than physical science has thought to be possible, it is interesting and harmless to speculate whether man has shared with the world its more remote history. … Some of the beliefs and legends which have come down to us from antiquity are so universal and deep-rooted that we have are accustomed to consider them almost as old as the race itself. One is tempted to inquire how far the unsuspected aptness of some of these beliefs and sayings to the point of view so recently disclosed is the result of mere chance or coincidence, and how far it may be evidence of a wholly unknown and unsuspected ancient civilization of which all other relic has disappeared.

There could not be a language more universal and more simple, more exempt from errors and obscurities, that is to say, more worthy of expressing the invariable relations of natural objects. Considered from this point of view, it is coextensive with nature itself; it defines all the sensible relations, measures the times, the spaces, the forces, the temperatures; this difficult science is formed slowly, but it retains all the principles it has once acquired. It grows and becomes more certain without limit in the midst of so many errors of the human mind.

There is a curious illusion today that nature is both wise and good. The awful truth is that nature is a bitch from the human point of view I care about the whooping crane a little. I would even give $10 to save the whooping crane. The whooping crane doesn’t give a damn about me.

There is a point of view among astronomical researchers that is generally referred to as the Principle of Mediocrity. ... If the Sun and its retinue of worlds is only one system among many, then many other systems will be like ours: home to life. Indeed, to the extent that this is true, we should be prepared for the possibility that, even in the Milky Way galaxy, billions of planets may be carpeted by the dirty, nasty business known as life.

This is really the cornerstone of our situation. Now, I believe what we should try to bring about is the general conviction that the first thing you have to abolish is war at all costs, and every other point of view must be of secondary importance.

To fully understand the mathematical genius of Sophus Lie, one must not turn to books recently published by him in collaboration with Dr. Engel, but to his earlier memoirs, written during the first years of his scientific career. There Lie shows himself the true geometer that he is, while in his later publications, finding that he was but imperfectly understood by the mathematicians accustomed to the analytic point of view, he adopted a very general analytic form of treatment that is not always easy to follow.

To prove to an indignant questioner on the spur of the moment that the work I do was useful seemed a thankless task and I gave it up. I turned to him with a smile and finished, “To tell you the truth we don’t do it because it is useful but because it’s amusing.” The answer was thought of and given in a moment: it came from deep down in my soul, and the results were as admirable from my point of view as unexpected. My audience was clearly on my side. Prolonged and hearty applause greeted my confession. My questioner retired shaking his head over my wickedness and the newspapers next day, with obvious approval, came out with headlines “Scientist Does It Because It’s Amusing!” And if that is not the best reason why a scientist should do his work, I want to know what is. Would it be any good to ask a mother what practical use her baby is? That, as I say, was the first evening I ever spent in the United States and from that moment I felt at home. I realised that all talk about science purely for its practical and wealth-producing results is as idle in this country as in England. Practical results will follow right enough. No real knowledge is sterile. The most useless investigation may prove to have the most startling practical importance: Wireless telegraphy might not yet have come if Clerk Maxwell had been drawn away from his obviously “useless” equations to do something of more practical importance. Large branches of chemistry would have remained obscure had Willard Gibbs not spent his time at mathematical calculations which only about two men of his generation could understand. 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.

To us … the only acceptable point of view appears to be the one that recognizes both sides of reality—the quantitative and the qualitative, the physical and the psychical—as compatible with each other, and can embrace them simultaneously … It would be most satisfactory of all if physis and psyche (i.e., matter and mind) could be seen as complementary aspects of the same reality.

We cannot doubt the existence of an ultimate reality. It is the universe forever masked. We are a part of it, and the masks figured by us are the universe observing and understanding itself from a human point of view.

We have really, that I know of, no philosophical basis for high and low. Moreover, the vegetable kingdom does not culminate, as the animal kingdom does. It is not a kingdom, but a common-wealth; a democracy, and therefore puzzling and unaccountable from the former point of view.

We must not forget that when radium was discovered no one knew that it would prove useful in hospitals. The work was one of pure science. And this is a proof that scientific work must not be considered from the point of view of the direct usefulness of it. It must be done for itself, for the beauty of science, and then there is always the chance that a scientific discovery may become like the radium a benefit for humanity.