[At DuPont,] I was very fortunate that I worked under men who were very much interested in making discoveries and inventions. They were very much interested in what they were doing, and they left me alone. And I was able to experiment on my own, and I found this very stimulating. It appealed to the creative person in me.

[To give insight to statistical information] it occurred to me, that making an appeal to the eye when proportion and magnitude are concerned, is the best and readiest method of conveying a distinct idea.

A man with a conviction is a hard man to change. Tell him you disagree and he turns away. Show him facts or figures and he questions your sources. Appeal to logic and he fails to see your point.

After 16 months of teaching, consulting, fellowship, and special project activities on matters ranging from conservation to healthcare to international trade, Gov. Ventura appointed me to the Minnesota Court of Appeals.

Although I must say that research problems I worked on were frequently the result of serendipity and often grew out of my interest in some species or some environment which I found to be particularly appealing—marine birds and tropical islands for example.

I am absolutely convinced that no wealth in the world can help humanity forward, even in the hands of the most devoted worker. The example of great and pure individuals is the only thing that can lead us to noble thoughts and deeds. Money only appeals to selfishness and irresistibly invites abuse. Can anyone imagine Moses, Jesus or Gandhi armed with the moneybags of Carnegie?

I do not think words alone will solve humanity’s present problems. The sound of bombs drowns out men’s voices. In times of peace I have great faith in the communication of ideas among thinking men, but today, with brute force dominating so many millions of lives, I fear that the appeal to man’s intellect is fast becoming virtually meaningless.

I suspect one of the reasons that fantasy and science fiction appeal so much to younger readers is that, when the space and time have been altered to allow characters to travel easily anywhere through the continuum and thus escape physical dangers and timepiece inevitabilities, mortality is so seldom an issue.

If order appeals to the intellect, then disorder titillates the imagination.

In Science the paramount appeal is to the Intellect—its purpose being instruction; in Art, the paramount appeal is to the Emotions—its purpose being pleasure.

It gave me great pleasure to tell you about the mysteries with which physics confronts us. As a human being, one has been endowed with just enough intelligence to be able to see clearly how utterly inadequate that intelligence is when confronted with what exists. If such humility could be conveyed to everybody, the world of human activities would be more appealing.

It is the mark of great art that its appeal is universal and eternal.

Logic is like the sword—those who appeal to it shall perish by it.

Metaphysics: An attempt to prove the incredible by an appeal to the unintelligible.

Most of the arts, as painting, sculpture, and music, have emotional appeal to the general public. This is because these arts can be experienced by some one or more of our senses. Such is not true of the art of mathematics; this art can be appreciated only by mathematicians, and to become a mathematician requires a long period of intensive training. The community of mathematicians is similar to an imaginary community of musical composers whose only satisfaction is obtained by the interchange among themselves of the musical scores they compose.

Neither in the subjective nor in the objective world can we find a criterion for the reality of the number concept, because the first contains no such concept, and the second contains nothing that is free from the concept. How then can we arrive at a criterion? Not by evidence, for the dice of evidence are loaded. Not by logic, for logic has no existence independent of mathematics: it is only one phase of this multiplied necessity that we call mathematics.
How then shall mathematical concepts be judged? They shall not be judged. Mathematics is the supreme arbiter. From its decisions there is no appeal. We cannot change the rules of the game, we cannot ascertain whether the game is fair. We can only study the player at his game; not, however, with the detached attitude of a bystander, for we are watching our own minds at play.

No school subject so readily furnishes tasks whose purpose can be made so clear, so immediate and so appealing to the sober second-thought of the immature learner as the right sort of elementary school mathematics.

Now I should like to ask you for an observation; since I possess no instruments, I must appeal to others.

Of possible quadruple algebras the one that had seemed to him by far the most beautiful and remarkable was practically identical with quaternions, and that he thought it most interesting that a calculus which so strongly appealed to the human mind by its intrinsic beauty and symmetry should prove to be especially adapted to the study of natural phenomena. The mind of man and that of Nature’s God must work in the same channels.

Our world faces a crisis as yet unperceived by those possessing power to make great decisions for good or evil. The unleashed power of the atom has changed everything save our modes of thinking and we thus drift toward unparalleled catastrophe. We scientists who released this immense power have an overwhelming responsibility in this world life-and-death struggle to harness the atom for the benefit of mankind and not for humanity’s destruction. … We need two hundred thousand dollars at once for a nation-wide campaign to let people know that a new type of thinking is essential if mankind is to survive and move toward higher levels. This appeal is sent to you only after long consideration of the immense crisis we face. … We ask your help at this fateful moment as a sign that we scientists do not stand alone.

Part of the appeal was that Medawar was not only a Nobel Laureate, but he seemed like a Nobel Laureate; he was everything one thought a Nobel Laureate ought to be. If you have ever wondered why scientists like Popper, try Medawar's exposition. Actually most Popperian scientists have probably never tried reading anything but Medawar's exposition.

Pure mathematics is a collection of hypothetical, deductive theories, each consisting of a definite system of primitive, undefined, concepts or symbols and primitive, unproved, but self-consistent assumptions (commonly called axioms) together with their logically deducible consequences following by rigidly deductive processes without appeal to intuition.

Reason is always a kind of brute force; those who appeal to the head rather than the heart, however pallid and polite, are necessarily men of violence. We speak of “touching” a man’s heart, but we can do nothing to his head but hit it.

Science deals with judgments on which it is possible to obtain universal agreement. These judgments do not concern individual facts and events, but the invariable association of facts and events known as the laws of science. Agreement is secured by observation and experiment—impartial courts of appeal to which all men must submit if they wish to survive. The laws are grouped and explained by theories of ever increasing generality. The theories at first are ex post facto—merely plausible interpretations of existing bodies of data. However, they frequently lead to predictions that can be tested by experiments and observations in new fields, and, if the interpretations are verified, the theories are accepted as working hypotheses until they prove untenable. The essential requirements are agreement on the subject matter and the verification of predictions. These features insure a body of positive knowledge that can be transmitted from person to person, and that accumulates from generation to generation.

Scientific research is one of the most exciting and rewarding of occupations. It is like a voyage of discovery into unknown lands, seeking not for new territory but for new knowledge. It should appeal to those with a good sense of adventure.

Since the world is what it is, it is clear that valid reasoning from sound principles cannot lead to error; but a principle may be so nearly true as to deserve theoretical respect, and yet may lead to practical consequences which we feel to be absurd. There is therefore a justification for common sense in philosophy, but only as showing that our theoretical principles cannot be quite correct so long as their consequences are condemned by an appeal to common sense which we feel to be irresistible.

Some writers, rejecting the idea which science had reached, that reefs of rocks could be due in any way to “animalcules,” have talked of electrical forces, the first and last appeal of ignorance.

That form of popular science which merely recites the results of investigations, which merely communicates useful knowledge, is from this standpoint bad science, or no science at all. … Apply this test to every work professing to give a popular account of any branch of science. If any such work gives a description of phenomena that appeals to his imagination rather than to his reason, then it is bad science.

The canons of art depend on what they appeal to. Painting appeals to the eye, and is founded on the science of optics. Music appeals to the ear and is founded on the science of acoustics. The drama appeals to human nature, and must have as its ultimate basis the science of psychology and physiology.

The follow-on space shuttle program has fallen far short of the Apollo program in its appeal to human aspirations. The launching of the Hubble Space Telescope and the subsequent repair and servicing missions by skilled crews are highlights of the shuttle’s service to science. … Otherwise, the shuttle’s contribution to science has been modest, and its contribution to utilitarian applications of space technology has been insignificant.

The great mathematician, like the great poet or naturalist or great administrator, is born. My contention shall be that where the mathematic endowment is found, there will usually be found associated with it, as essential implications in it, other endowments in generous measure, and that the appeal of the science is to the whole mind, direct no doubt to the central powers of thought, but indirectly through sympathy of all, rousing, enlarging, developing, emancipating all, so that the faculties of will, of intellect and feeling learn to respond, each in its appropriate order and degree, like the parts of an orchestra to the “urge and ardor” of its leader and lord.

The history of psychiatry to the present day is replete with examples of loose thinking and a failure to apply even the simplest rules of logic. “A Court of Statistical Appeal” has now been equated with scientific method.

The ideals which have always shone before me and filled me with the joy of living are goodness, beauty, and truth. To make a goal of comfort or happiness has never appealed to me.

The motive for the study of mathematics is insight into the nature of the universe. Stars and strata, heat and electricity, the laws and processes of becoming and being, incorporate mathematical truths. If language imitates the voice of the Creator, revealing His heart, mathematics discloses His intellect, repeating the story of how things came into being. And Value of Mathematics, appealing as it does to our energy and to our honor, to our desire to know the truth and thereby to live as of right in the household of God, is that it establishes us in larger and larger certainties. As literature develops emotion, understanding, and sympathy, so mathematics develops observation, imagination, and reason.

The whole inherent pride of human nature revolts at the idea that the lord of the creation is to be treated like any other natural object. No sooner does the naturalist discover the resemblance of some higher mammals, such as the ape, to man, than there is a general outcry against the presumptuous audacity that ventures to touch man in his inmost sanctuary. The whole fraternity of philosophers, who have never seen monkeys except in zoological gardens, at once mount the high horse, and appeal to the mind, the soul, to reason, to consciousness, and to all the rest of the innate faculties of man, as they are refracted in their own philosophical prisms.

There can be no doubt that science is in many ways the natural enemy of language. Language, either literary or colloquial, demands a rich store of living and vivid words—words that are “thoughtpictures,” and appeal to the senses, and also embody our feelings about the objects they describe. But science cares nothing about emotion or vivid presentation; her ideal is a kind of algebraic notation, to be used simply as an instrument of analysis; and for this she rightly prefers dry and abstract terms, taken from some dead language, and deprived of all life and personality.

This skipping is another important point. It should be done whenever a proof seems too hard or whenever a theorem or a whole paragraph does not appeal to the reader. In most cases he will be able to go on and later he may return to the parts which he skipped.

Those of us who were familiar with the state of inorganic chemistry in universities twenty to thirty years ago will recall that at that time it was widely regarded as a dull and uninteresting part of the undergraduate course. Usually, it was taught almost entirely in the early years of the course and then chiefly as a collection of largely unconnected facts. On the whole, students concluded that, apart from some relationships dependent upon the Periodic table, there was no system in inorganic chemistry comparable with that to be found in organic chemistry, and none of the rigour and logic which characterised physical chemistry. It was widely believed that the opportunities for research in inorganic chemistry were few, and that in any case the problems were dull and uninspiring; as a result, relatively few people specialized in the subject... So long as inorganic chemistry is regarded as, in years gone by, as consisting simply of the preparations and analysis of elements and compounds, its lack of appeal is only to be expected. The stage is now past and for the purpose of our discussion we shall define inorganic chemistry today as the integrated study of the formation, composition, structure and reactions of the chemical elements and compounds, excepting most of those of carbon.

To appeal to contemporary man to revert, in this twentieth century, to a pagan-like nature worship in order to restrain technology from further encroachment and devastation of the resources of nature, is a piece of atavistic nonsense.

To find the cause of our ills in something outside ourselves, something specific that can be spotted and eliminated, is a diagnosis that cannot fail to appeal. To say that the cause of our troubles is not in us but in the Jews, and pass immediately to the extermination of the Jews, is a prescription likely to find a wide acceptance.

To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency ... . The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds.

Two of his [Euler’s] pupils having computed to the 17th term, a complicated converging series, their results differed one unit in the fiftieth cipher; and an appeal being made to Euler, he went over the calculation in his mind, and his decision was found correct.

Two years ago 1 tried to appeal to Rockefeller’s conscience about the absurd method of allocating grants, unfortunately without success. Bohr has now gone to see him, in an attempt to persuade him to take some action on behalf of the exiled German scientists.

We now live in an age in which science is a court from which there is no appeal. And this issue this time around, at the beginning of the twenty-first century, is not the evolution of the species, which can seem a remote business, but the nature of our own precious inner selves.

Where we reach the sphere of mathematics we are among processes which seem to some the most inhuman of all human activities and the most remote from poetry. Yet it is just here that the artist has the fullest scope for his imagination. … We are in the imaginative sphere of art, and the mathematician is engaged in a work of creation which resembles music in its orderliness, … It is not surprising that the greatest mathematicians have again and again appealed to the arts in order to find some analogy to their own work. They have indeed found it in the most varied arts, in poetry, in painting, and in sculpture, although it would certainly seem that it is in music, the most abstract of all the arts, the art of number and time, that we find the closest analogy.

Young writers find out what kinds of writers they are by experiment. If they choose from the outset to practice exclusively a form of writing because it is praised in the classroom or otherwise carries appealing prestige, they are vastly increasing the risk inherent in taking up writing in the first place.