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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Home > Category Index for Science Quotations > Category Index A > Category: Ability

Ability Quotes (152 quotes)

Die Wissenschaft ist ein Land, welches die Eigenschaft hat, um so mehr Menschen beherbergen zu können, je mehr Bewohner sich darin sammeln; sie ist ein Schatz, der um so grösser wird, je mehr man ihn teilt. Darum kann jeder von uns in seiner Art seine Arbeit tun, und die Gemeinsamkeit bedeutet nicht Gleichförmigkeit.
Science is one land, having the ability to accommodate even more people, as more residents gather in it; it is a treasure that is the greater the more it is shared. Because of that, each of us can do his work in his own way, and the common ground does not mean conformity.
Speaking (in German) at the Banquet to Past Presidents, the Chemical Society, as published in William Crookes (ed.) The Chemical News (16 Dec 1898), 78, 298. Also used as epigraph, in Paul Walden, Wilhelm Ostwald (1904), 1. Translation by Webmaster.
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Neque enim ingenium sine disciplina aut disciplina sine ingenio perfectum artificem potest efficere
For neither talent without instruction nor instruction without talent can produce the perfect craftsman.
Vitruvius
In De Architectura, Book 1, Chap 1, Sec. 3. As in Frank Granger (trans.), Vitruvius: De Architectura (1931), 8-9. Also translated as “Neither natural ability without instruction nor instruction without natural ability can make the perfect artist.” In Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 3.
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[Student describing Niels Bohr's main gift, the ability to synthesize:] Like Socrates, he wages a fight to bring harmony out of chaos and diversity.
Anonymous
Quoted in Bill Becker, 'Pioneer of the Atom', New York Times Sunday Magazine (20 Oct 1957), 52.
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A man of very moderate ability may be a good physician, if he devotes himself faithfully to the work.
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A person who is religiously enlightened appears to me to be one who has, to the best of his ability, liberated himself from the fetters of his selfish desires and is preoccupied with thoughts, feelings, and aspirations to which he clings because of their superpersonal value. It seems to me that what is important is the force of this superpersonal content and the depth of the conviction concerning its overpowering meaningfulness, regardless of whether any attempt is made to unite this content with a divine Being, for otherwise it would not be possible to count Buddha and Spinoza as religious personalities. Accordingly, a religious person is devout in the sense that he has no doubt of the significance and loftiness of those superpersonal objects and goals which neither require nor are capable of rational foundation. They exist with the same necessity and matter-of-factness as he himself. In this sense religion is the age-old endeavor of mankind to become clearly and completely conscious of these values and goals and constantly to strengthen and extend their effect. If one conceives of religion and science according to these definitions then a conflict between them appears impossible. For science can only ascertain what is, but not what should be, and outside of its domain value judgments of all kinds remain necessary.
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A physician is judged by the three A’s, Ability, Availability and Affability.
Quoted in: Familiar Medical Quotations, by M. B. Strauss.
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A scientist can be productive in various ways. One is having the ability to plan and carry out experiments, but the other is having the ability to formulate new ideas, which can be about what experiments can be carried out … by making [the] proper calculations. Individual scientists who are successful in their work are successful for different reasons.
Interview with George B. Kauffman and Laurie M. Kauffman, in 'Linus Pauling: Reflections', American Scientist (Nov-Dec 1994), 82, No. 6, 522.
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A scientist's accomplishments are equal to the integral of his ability integrated over the hours of his effort.
J. O. Hirschfelder, in essay on Eyring, 'A Forecast for Theoretical Chemistry', Journal of Chemical Education, 1966, 45, 457.
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A taxonomy of abilities, like a taxonomy anywhere else in science, is apt to strike a certain type of impatient student as a gratuitous orgy of pedantry. Doubtless, compulsions to intellectual tidiness express themselves prematurely at times, and excessively at others, but a good descriptive taxonomy, as Darwin found in developing his theory, and as Newton found in the work of Kepler, is the mother of laws and theories.
From Intelligence: Its Structure, Growth and Action: Its Structure, Growth and Action (1987), 61.
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Ability is what you’re capable of doing. Motivation determines what you do. Attitude determines how well you do it.
Lou Holtz
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Add to this the pride of achievement; the desire to rank among the successful souls on earth, and we have the factors which have brought some of the ablest of human beings into the limelight that revealed them to an admiring world, as leaders and examples.
Quoted, without citation, in front matter to T. A. Edison Foundation, Lewis Howard Latimer: A Black Inventor: a Biography and Related Experiments You Can Do (1973). If you know the primary source, please contact Webmaster.
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All interpretations made by a scientist are hypotheses, and all hypotheses are tentative. They must forever be tested and they must be revised if found to be unsatisfactory. Hence, a change of mind in a scientist, and particularly in a great scientist, is not only not a sign of weakness but rather evidence for continuing attention to the respective problem and an ability to test the hypothesis again and again.
The Growth of Biological Thought: Diversity, Evolution and Inheritance (1982), 831.
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All science is concerned with the relationship of cause and effect. Each scientific discovery increases man’s ability to predict the consequences of his actions and thus his ability to control future events.
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All scientists must focus closely on limited targets. Whether or not one’s findings on a limited subject will have wide applicability depends to some extent on chance, but biologists of superior ability repeatedly focus on questions the answers to which either have wide ramifications or lead to new areas of investigation. One procedure that can be effective is to attempt both reduction and synthesis; that is, direct a question at a phenomenon on one integrative level, identify its mechanism at a simpler level, then extrapolate its consequences to a more complex level of integration.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 230-231,
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Analogy is a wonderful, useful and most important form of thinking, and biology is saturated with it. Nothing is worse than a horrible mass of undigested facts, and facts are indigestible unless there is some rhyme or reason to them. The physicist, with his facts, seeks reason; the biologist seeks something very much like rhyme, and rhyme is a kind of analogy.... This analogizing, this fine sweeping ability to see likenesses in the midst of differences is the great glory of biology, but biologists don't know it.... They have always been so fascinated and overawed by the superior prestige of exact physical science that they feel they have to imitate it.... In its central content, biology is not accurate thinking, but accurate observation and imaginative thinking, with great sweeping generalizations.
In Science is a Sacred Cow (1950), 98-100.
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As never before, the work of the engineer is basic to the kind of society to which our best efforts are committed. Whether it be city planning, improved health care in modern facilities, safer and more efficient transportation, new techniques of communication, or better ways to control pollution and dispose of wastes, the role of the engineer—his initiative, creative ability, and hard work—is at the root of social progress.
Remarks for National Engineers Week (1971). As quoted in Consulting Engineer (1971), 36, 18.
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As regards authority I so proceed. Boetius says in the second prologue to his Arithmetic, “If an inquirer lacks the four parts of mathematics, he has very little ability to discover truth.” And again, “Without this theory no one can have a correct insight into truth.” And he says also, “I warn the man who spurns these paths of knowledge that he cannot philosophize correctly.” And Again, “It is clear that whosoever passes these by, has lost the knowledge of all learning.”
Opus Majus [1266-1268], Part IV, distinction I, chapter I, trans. R. B. Burke, The Opus Majus of Roger Bacon (1928), Vol. I, 117.
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As soon as we got rid of the backroom attitude and brought our apparatus fully into the Department with an inexhaustible supply of living patients with fascinating clinical problems, we were able to get ahead really fast. Any new technique becomes more attractive if its clinical usefulness can be demonstrated without harm, indignity or discomfort to the patient... Anyone who is satisfied with his diagnostic ability and with his surgical results is unlikely to contribute much to the launching of a new medical science. He should first be consumed with a divine discontent with things as they are. It greatly helps, of course, to have the right idea at the right time, and quite good ideas may come, Archimedes fashion, in one's bath..
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As we advance in life we learn the limits of our abilities.
Inaugural Address Delivered to the University of St. Andrews, March 19, 1869 (1869), 3.
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At the present time there exist problems beyond our ability to solve, not because of theoretical difficulties, but because of insufficient means of mechanical computation.
In 'Proposed Automatic Calculating Machine' (1937). As quoted in I. Bernard Cohen, Gregory W. Welch (eds.), Makin' Numbers: Howard Aiken and the Computer (1999), 13.
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Because intelligence is our own most distinctive feature, we may incline to ascribe superior intelligence to the basic primate plan, or to the basic plan of the mammals in general, but this point requires some careful consideration. There is no question at all that most mammals of today are more intelligent than most reptiles of today. I am not going to try to define intelligence or to argue with those who deny thought or consciousness to any animal except man. It seems both common and scientific sense to admit that ability to learn, modification of action according to the situation, and other observable elements of behavior in animals reflect their degrees of intelligence and permit us, if only roughly, to compare these degrees. In spite of all difficulties and all the qualifications with which the expert (quite properly) hedges his conclusions, it also seems sensible to conclude that by and large an animal is likely to be more intelligent if it has a larger brain at a given body size and especially if its brain shows greater development of those areas and structures best developed in our own brains. After all, we know we are intelligent, even though we wish we were more so.
In The Meaning of Evolution: A Study of the History of Life and of its Significance for Man (1949), 78.
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Being also in accord with Goethe that discoveries are made by the age and not by the individual, I should consider the instances to be exceedingly rare of men who can be said to be living before their age, and to be the repository of knowledge quite foreign to the thought of the time. The rule is that a number of persons are employed at a particular piece of work, but one being a few steps in advance of the others is able to crown the edifice with his name, or, having the ability to generalise already known facts, may become in time to be regarded as their originator. Therefore it is that one name is remembered whilst those of coequals have long been buried in obscurity.
In Historical Notes on Bright's Disease, Addison's Disease, and Hodgkin's Disease', Guy's Hospital Reports (1877), 22, 259-260.
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But does Man have any “right” to spread through the universe? Man is what he is, a wild animal with the will to survive, and (so far) the ability, against all competition. Unless one accepts that, anything one says about morals, war, politics, you name it, is nonsense. Correct morals arise from knowing what man is, not what do-gooders and well-meaning old Aunt Nellies would like him to be. The Universe will let us know—later—whether or not Man has any “right” to expand through it.
In Starship Troopers (1959), 186.
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Consider a cow. A cow doesn’t have the problem-solving skill of a chimpanzee, which has discovered how to get termites out of the ground by putting a stick into a hole. Evolution has developed the brain’s ability to solve puzzles, and at the same time has produced in our brain a pleasure of solving problems.
In John Tierney, 'For Decades, Puzzling People With Mathematics', New York Times (20 Oct 2009), D2.
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Consider the very roots of our ability to discern truth. Above all (or perhaps I should say “underneath all”), common sense is what we depend on—that crazily elusive, ubiquitous faculty we all have to some degree or other. … If we apply common sense to itself over and over again, we wind up building a skyscraper. The ground floor of the structure is the ordinary common sense we all have, and the rules for building news floors are implicit in the ground floor itself. However, working it all out is a gigantic task, and the result is a structure that transcends mere common sense.
In Metamagical Themas: Questing for the Essence of Mind and Pattern (1985), 93–94.
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During my eighty-seven years I have witnessed a whole succession of technological revolutions. But none of them has done away with the need for character in the individual or the ability to think.
From My Own Story (1957), 320.
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Ecologically speaking, a spilt tanker load is like sticking a safety pin into an elephant’s foot. The planet barely notices. After the Exxon Valdez accident in Alaska the oil company spent billions tidying up the coastline, but it was a waste of money because the waves were cleaning up faster than Exxon could. Environmentalists can never accept the planet’s ability to self-heal.
'Seat Leon Cupra SR1, in The Times (22 Dec 2002)
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Education is not the piling on of learning, information, data, facts, skills, or abilities—that's training or instruction—but is rather making visible what is hidden as a seed.
The Education of the Heart (1996), Introduction, 3.
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Exercise in the most rigorous thinking that is possible will of its own accord strengthen the sense of truth and right, for each advance in the ability to distinguish between correct and false thoughts, each habit making for rigour in thought development will increase in the sound pupil the ability and the wish to ascertain what is right in life and to defend it.
In Anleitung zum mathematischen Unterricht in den höheren Schulen (1906), 28.
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Thomas Robert Malthus quote Famine … the most dreadful resource of nature.
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Famine seems to be the last, the most dreadful resource of nature. The power of population is so superior to the power in the earth to produce subsistence for man, that premature death must in some shape or other visit the human race. The vices of mankind are active and able ministers of depopulation. They are the precursors in the great army of destruction; and often finish the dreadful work themselves. But should they fail in this war of extermination, sickly seasons, epidemics, pestilence, and plague, advance in terrific array, and sweep off their thousands and ten thousands. Should success be still incomplete, gigantic inevitable famine stalks in the rear, and with one mighty blow, levels the population with the food of the world.
In An Essay on the Principle of Population (1798), 140, and in new enlarged edition (1803), 350.
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Feeling weightless… it’s so many things together. A feeling of pride, of healthy solitude, of dignified freedom from everything that’s dirty, sticky. You feel exquisitely comfortable . . . and you feel you have so much energy, such an urge to do things, such an ability to do things. And you work well, yes, you think well, without sweat, without difficulty as if the biblical curse in the sweat of thy face and in sorrow no longer exists, As if you’ve been born again.
…...
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Foreshadowings of the principles and even of the language of [the infinitesimal] calculus can be found in the writings of Napier, Kepler, Cavalieri, Pascal, Fermat, Wallis, and Barrow. It was Newton's good luck to come at a time when everything was ripe for the discovery, and his ability enabled him to construct almost at once a complete calculus.
In History of Mathematics (3rd Ed., 1901), 366.
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From our best qualities come our worst. From our urge to pull together comes our tendency to pull apart. From our devotion to higher good comes our propensity to the foulest atrocities. From out commitment to ideals come our excuse to hate. Since the beginning of history, we have been blinded by evil’s ability to don a selfless disguise. We have failed to see that our finest qualities often lead us to the actions we most abhor—murder, torture, genocide, and war.
In 'Who is Lucifer?', The Lucifer Principle: A Scientific Expedition Into the Forces of History (1997), 3.
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Furthermore, it’s equally evident that what goes on is actually one degree better than self-reproduction, for organisms appear to have gotten more elaborate in the course of time. Today's organisms are phylogenetically descended from others which were vastly simpler than they are, so much simpler, in fact, that it’s inconceivable, how any kind of description of the latter, complex organism could have existed in the earlier one. It’s not easy to imagine in what sense a gene, which is probably a low order affair, can contain a description of the human being which will come from it. But in this case you can say that since the gene has its effect only within another human organism, it probably need not contain a complete description of what is to happen, but only a few cues for a few alternatives. However, this is not so in phylogenetic evolution. That starts from simple entities, surrounded by an unliving amorphous milieu, and produce, something more complicated. Evidently, these organisms have the ability to produce something more complicated than themselves.
From lecture series on self-replicating machines at the University of Illinois, Lecture 5 (Dec 1949), 'Re-evaluation of the Problems of Complicated Automata—Problems of Hierarchy and Evolution', Theory of Self-Reproducing Automata (1966).
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He had seen too much of the cosmos to have any great faith in man's ability to understand it.
Ghetto (1954)
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Hubble's observations suggested that there was a time, called the big bang, when the universe was infinitesimally small and infinitely dense. Under such conditions all the laws of science, and therefore all ability to predict the future, would break down. If there were events earlier than this time, then they could not affect what happens at the present time. Their existence can be ignored because it would have no observational consequences. One may say that time had a beginning at the big bang, in the sense that earlier times simply would not be defined. It should be emphasized that this beginning in time is very different from those that had been considered previously. In an unchanging universe a beginning in time is something that has to be imposed by some being outside the universe; there is no physical necessity for a beginning. One can imagine that God created the universe at literally any time in the past. On the other hand, if the universe is expanding, there may be physical reasons why there had to be a beginning. One could still imagine that God created the universe at the instant of the big bang, or even afterwards in just such a way as to make it look as though there had been a big bang, but it would be meaningless to suppose that it was created before the big bang. An expanding universe does not preclude a creator, but it does place limits on when he might have carried out his job!
A Brief History of Time: From the Big Bang to Black Holes (1988), 8-9.
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I am convinced that it is impossible to expound the methods of induction in a sound manner, without resting them upon the theory of probability. Perfect knowledge alone can give certainty, and in nature perfect knowledge would be infinite knowledge, which is clearly beyond our capacities. We have, therefore, to content ourselves with partial knowledge—knowledge mingled with ignorance, producing doubt.
The Principles of Science: A Treatise on Logic and Scientific Method, 2nd edition (1877), 197.
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I am giving this winter two courses of lectures to three students, of which one is only moderately prepared, the other less than moderately, and the third lacks both preparation and ability. Such are the onera of a mathematical profession.
Letter to Friedrich Bessel (4 Dec 1808). In Gauss-Bessel Briefwechsel (1880), 107. In Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914), 158.
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I believe in “intelligence,” and I believe also that there are inherited differences in intellectual ability, but I do not believe that intelligence is a simple scalar endowment that can be quantified by attaching a single figure to it—an I.Q. or the like.
In Advice to a Young Scientist (1979), 25. Footnoted with reference to his own earlier review article of books about IQ, in which he stated “misgivings about whether it is indeed possible to attach a single-number valuation to an endowment as complex and as various as intelligence.” That review was titled 'Unnatural Science', in New York Review of Books (3 Feb 1977), 24, No. 1, 13,
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I can think of a few microorganisms, possibly the tubercle bacillus, the syphilis spirochete, the malarial parasite, and a few others, that have a selective advantage in their ability to infect human beings, but there is nothing to be gained, in an evolutionary sense, by the capacity to cause illness or death. Pathogenicity may be something of a disadvantage for most microbes…
In 'Germs', The Lives of a Cell: Notes of a Biology Watcher (1974), 90.
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I found out that the main ability to have was a visual, and also an almost tactile, way to imagine the physical situations, rather than a merely logical picture of the problems. … Very soon I discovered that if one gets a feeling for no more than a dozen … radiation and nuclear constants, one can imagine the subatomic world almost tangibly, and manipulate the picture dimensionally and qualitatively, before calculating more precise relationships.
In Adventures of a Mathematician (1976), 147.
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I had never doubted my own abilities, but I was quite prepared to believe that “the world” would decline to recognize them.
In Postscript to the Outsider (1967), 3.
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I shall explain a System of the World differing in many particulars from any yet known, answering in all things to the common Rules of Mechanical Motions: This depends upon three Suppositions. First, That all Cœlestial Bodies whatsoever, have an attraction or gravitating power towards their own Centers, whereby they attract not only their own parts, and keep them from flying from them, as we may observe the Earth to do, but that they do also attract all the other Cœlestial bodies that are within the sphere of their activity; and consequently that not only the Sun and Moon have an influence upon the body and motion the Earth, and the Earth upon them, but that Mercury also Venus, Mars, Saturn and Jupiter by their attractive powers, have a considerable influence upon its motion in the same manner the corresponding attractive power of the Earth hath a considerable influence upon every one of their motions also. The second supposition is this, That all bodies whatsoever that are put into a direct and simple motion, will continue to move forward in a streight line, till they are by some other effectual powers deflected and bent into a Motion, describing a Circle, Ellipse, or some other more compounded Curve Line. The third supposition is, That these attractive powers are so much the more powerful in operating, by how much the nearer the body wrought upon is to their own Centers. Now what these several degrees are I have not yet experimentally verified; but it is a notion, which if fully prosecuted as it ought to be, will mightily assist the Astronomer to reduce all the Cœlestial Motions to a certain rule, which I doubt will never be done true without it. He that understands the nature of the Circular Pendulum and Circular Motion, will easily understand the whole ground of this Principle, and will know where to find direction in Nature for the true stating thereof. This I only hint at present to such as have ability and opportunity of prosecuting this Inquiry, and are not wanting of Industry for observing and calculating, wishing heartily such may be found, having myself many other things in hand which I would first compleat and therefore cannot so well attend it. But this I durst promise the Undertaker, that he will find all the Great Motions of the World to be influenced by this Principle, and that the true understanding thereof will be the true perfection of Astronomy.
An Attempt to Prove the Motion of the Earth from Observations (1674), 27-8. Based on a Cutlerian Lecture delivered by Hooke at the Royal Society four years earlier.
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I think that space flight is a condition of Nature that comes into effect when an intelligent species reaches the saturation point of its planetary habitat combined with a certain level of technological ability... I think it is a built-in gene-directed drive for the spreading of the species and its continuation.
…...
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I will now direct the attention of scientists to a previously unnoticed cause which brings about the metamorphosis and decomposition phenomena which are usually called decay, putrefaction, rotting, fermentation and moldering. This cause is the ability possessed by a body engaged in decomposition or combination, i.e. in chemical action, to give rise in a body in contact with it the same ability to undergo the same change which it experiences itself.
Annalen der Pharmacie 1839, 30, 262. Trans. W. H. Brock.
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I would proclaim that the vast majority of what [say, Scientific American] is true—yet my ability to defend such a claim is weaker than I would like. And most likely the readers, authors, and editors of that magazine would be equally hard pressed to come up with cogent, non-technical arguments convincing a skeptic of this point, especially if pitted against a clever lawyer arguing the contrary. How come Truth is such a slippery beast?
Metamagical Themas (1985), 93.
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Ideologues of all persuasions think they know how the economy will respond to the Administration’s strange mixture of Lafferism and monetarism. Indeed, their self-confidence is so vast, and their ability to rationalize so crafty, that one cannot imagine a scenario for the next few years, that they would regard as falsifying their dogma. The failure of any prediction can always be blamed on quirky political decisions or unforeseen historical events.
In 'Mathematical Games: The Laffer Curve', Scientific American (Dec 1981), 245, No. 6, 30. Collected in The Night Is Large: Collected Essays, 1938-1995 (1997), 135.
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If arithmetical skill is the measure of intelligence, then computers have been more intelligent than all human beings all along. If the ability to play chess is the measure, then there are computers now in existence that are more intelligent than any but a very few human beings. However, if insight, intuition, creativity, the ability to view a problem as a whole and guess the answer by the “feel” of the situation, is a measure of intelligence, computers are very unintelligent indeed. Nor can we see right now how this deficiency in computers can be easily remedied, since human beings cannot program a computer to be intuitive or creative for the very good reason that we do not know what we ourselves do when we exercise these qualities.
In Machines That Think (1983).
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If I were summing up the qualities of a good teacher of medicine, I would enumerate human sympathy, moral and intellectual integrity, enthusiasm, and ability to talk, in addition, of course, to knowledge of his subject.
Anonymous
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If science is to progress, what we need is the ability to experiment, honesty in reporting results—the results must be reported without somebody saying what they would like the results to have been—and finally—an important thing—the intelligence to interpret the results.
In The Character of Physical Law (1965, 2001), 148.
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If we lived on a planet where nothing ever changed, there would be little to do. There would be nothing to figure out. There would be no impetus for science. And if we lived in an unpredictable world, where things changed in random or very complex ways, we would not be able to figure things out. But we live in an in-between universe, where things change, but according to patterns, rules, or as we call them, laws of nature. If I throw a stick up in the air, it always falls down. If the sun sets in the west, it always rises again the next morning in the east. And so it becomes possible to figure things out. We can do science, and with it we can improve our lives.
Cosmos (1980, 1985), 32.
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If we sink to the biochemical level, then the human being has lost a great many synthetic abilities possessed by other species and, in particular, by plants and microorganisms. Our loss of ability to manufacture a variety of vitamins makes us dependent on our diet and, therefore, on the greater synthetic versatility of other creatures. This is as much a “degenerative” change as the tapeworm’s abandonment of a stomach it no longer needs, but since we are prejudiced in our own favor, we don’t mention it.
In 'The Modern Demonology' (Jan 1962). Collected in Asimov on Physics (1976), 150.
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If you have great talents, industry will improve them; if moderate abilities, industry will supply their deficiencies. Nothing is denied to well-directed labour; nothing is ever to be attained without it.
From 'A Discourse Delivered to the Students of the Royal Academy, on the Distribution of Prizes' (11 Dec 1769), in Seven Discourses Delivered in the Royal Academy (1778), 57.
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If you hope to make a success of life you must be willing to do whatever comes your way to the best of your ability.
From address to the Brown University YMCA, as quoted in 'Young Rockefeller: Defending Trusts, Uses American Beauty Similitude,' Cincinnati Enquirer (9 Feb 1902), 4, citing the New York Journal.
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In the discovery of lemmas the best aid is a mental aptitude for it. For we may see many who are quick at solutions and yet do not work by method ; thus Cratistus in our time was able to obtain the required result from first principles, and those the fewest possible, but it was his natural gift which helped him to the discovery.
Proclus
As given in Euclid, The Thirteen Books of Euclid's Elements, translated from the text of Johan Ludvig Heiberg by Sir Thomas Little Heath, Vol. 1, Introduction and Books 1,2 (1908), 133. The passage also states that Proclus gives the definition of the term lemma as a proposition not proved beforehand. Glenn Raymond Morrow in A Commentary on the First Book of Euclid's Elements (1992), 165, states nothing more seems to be known of Cratistus.
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In the school of political projectors, I was but ill entertained, the professors appearing, in my judgment, wholly out of their senses; which is a scene that never fails to make me melancholy. These unhappy people were proposing schemes for persuading monarchs to choose favourites upon the score of their wisdom, capacity, and virtue; of teaching ministers to consult the public good; of rewarding merit, great abilities, and eminent services; of instructing princes to know their true interest, by placing it on the same foundation with that of their people; of choosing for employment persons qualified to exercise them; with many other wild impossible chimeras, that never entered before into the heart of man to conceive, and confirmed in me the old observation, that there is nothing so extravagant and irrational which some philosophers have not maintained for truth.
Gulliver's Travels (1726, Penguin ed. 1967), Part III, Chap. 6, 232.
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In the secondary schools mathematics should be a part of general culture and not contributory to technical training of any kind; it should cultivate space intuition, logical thinking, the power to rephrase in clear language thoughts recognized as correct, and ethical and esthetic effects; so treated, mathematics is a quite indispensable factor of general education in so far as the latter shows its traces in the comprehension of the development of civilization and the ability to participate in the further tasks of civilization.
The purposes of instruction in mathematics in secondary schools formulated by the German Society for the Advancement of Instruction. From Unterrichtsblätter fur Mathematik und Naturwissenschaft (1904), 128. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 72-73.
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In this lecture I would like to conclude with … some characteristics [of] gravity … The most impressive fact is that gravity is simple. It is simple to state the principles completely and not have left any vagueness for anybody to change the ideas of the law. It is simple, and therefore it is beautiful. It is simple in its pattern. I do not mean it is simple in its action—the motions of the various planets and the perturbations of one on the other can be quite complicated to work out, and to follow how all those stars in a globular cluster move is quite beyond our ability. It is complicated in its actions, but the basic pattern or the system beneath the whole thing is simple. This is common to all our laws; they all turn out to be simple things, although complex in their actual actions.
In 'The Law of Gravitation, as Example of Physical Law', the first of his Messenger Lectures (1964), Cornell University. Collected in The Character of Physical Law (1967), 33-34.
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Included in this ‘almost nothing,’ as a kind of geological afterthought of the last few million years, is the first development of self-conscious intelligence on this planet–an odd and unpredictable invention of a little twig on the mammalian evolutionary bush. Any definition of this uniqueness, embedded as it is in our possession of language, must involve our ability to frame the world as stories and to transmit these tales to others. If our propensity to grasps nature as story has distorted our perceptions, I shall accept this limit of mentality upon knowledge, for we receive in trade both the joys of literature and the core of our being.
…...
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Instinct is defined as the untaught ability to perform actions of all kinds, and more especially such as are necessary or useful to the animal.
The Senses and the Intellect (1855, 1974), p. 246.
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Intelligence increases mere physical ability one half. The use of the head abridges the labor of the hands.
In Proverbs from Plymouth Pulpit (1887), 44.
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Intelligence is an extremely subtle concept. It’s a kind of understanding that flourishes if it’s combined with a good memory, but exists anyway even in the absence of good memory. It’s the ability to draw consequences from causes, to make correct inferences, to foresee what might be the result, to work out logical problems, to be reasonable, rational, to have the ability to understand the solution from perhaps insufficient information. You know when a person is intelligent, but you can be easily fooled if you are not yourself intelligent.
In Irv Broughton (ed.), The Writer's Mind: Interviews with American Authors (1990), Vol. 2, 57.
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It has always seemed to me extreme presumptuousness on the part of those who want to make human ability the measure of what nature can and knows how to do, since, when one comes down to it, there is not one effect in nature, no matter how small, that even the most speculative minds can fully understand.
…...
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It is above all the duty of the methodical text-book to adapt itself to the pupil’s power of comprehension, only challenging his higher efforts with the increasing development of his imagination, his logical power and the ability of abstraction. This indeed constitutes a test of the art of teaching, it is here where pedagogic tact becomes manifest. In reference to the axioms, caution is necessary. It should be pointed out comparatively early, in how far the mathematical body differs from the material body. Furthermore, since mathematical bodies are really portions of space, this space is to be conceived as mathematical space and to be clearly distinguished from real or physical space. Gradually the student will become conscious that the portion of the real space which lies beyond the visible stellar universe is not cognizable through the senses, that we know nothing of its properties and consequently have no basis for judgments concerning it. Mathematical space, on the other hand, may be subjected to conditions, for instance, we may condition its properties at infinity, and these conditions constitute the axioms, say the Euclidean axioms. But every student will require years before the conviction of the truth of this last statement will force itself upon him.
In Methodisches Lehrbuch der Elementar-Mathemalik (1904), Teil I, Vorwort, 4-5.
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It is not surprising that our language should be incapable of describing the processes occurring within the atoms, for, as has been remarked, it was invented to describe the experiences of daily life, and these consists only of processes involving exceedingly large numbers of atoms. Furthermore, it is very difficult to modify our language so that it will be able to describe these atomic processes, for words can only describe things of which we can form mental pictures, and this ability, too, is a result of daily experience. Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme—the quantum theory—which seems entirely adequate for the treatment of atomic processes; for visualization, however, we must content ourselves with two incomplete analogies—the wave picture and the corpuscular picture.
The Physical Principles of the Quantum Theory, trans. Carl Eckart and Frank C. Hoyt (1949), 11.
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It is true that M. Fourier believed that the main aim of mathematics was public utility and the explanation of natural phenomena; but a philosopher of his ability ought to have known that the sole aim of science is the honour of the human intellect, and that on this ground a problem in numbers is as important as a problem on the system of the world.
In Letter to Legendre, as quoted in an Address by Emile Picard to the Congress of Science and Art, St. Louis (22 Sep 1904), translated in 'Development of Mathematical Analysis', The Mathematical Gazette (Jul 1905), 3, No. 52, 200. A different translation begins, “It is true that Fourier had the opinion…” on the Karl Jacobi Quotes web page on this site.
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It just so happens that during the 1950s, the first great age of molecular biology, the English schools of Oxford and particularly of Cambridge produced more than a score of graduates of quite outstanding ability—much more brilliant, inventive, articulate and dialectically skillful than most young scientists; right up in the Jim Watson class. But Watson had one towering advantage over all of them: in addition to being extremely clever he had something important to be clever about.
From the postscript to 'Lucky Jim', New York Review of Books (28 Mar 1968). Also collected in 'Lucky Jim', Pluto’s Republic (1982), 275. Also excerpted in Richard Dawkins (ed.), The Oxford Book of Modern Science Writing (2008), 186.
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It may sound like a lot of work to keep up with organic chemistry, and it is; however, those who haven't the time to do it become subject to decay in the ability to teach and to contribute to the Science—a sort of first-order process the half-life of which can't be much more than a year or two.
Highlights of Organic Chemistry: An Advanced Textbook (1974), 112.
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Joad, the philosopher, said … “science changes our environment faster than we have the ability to adjust ourselves to it.”
In 'The Talk of the Town', in The New Yorker (18 Aug 1945), 13.
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John Young and Bob Crippen have made us very proud. Their deeds reminded us that we as a free people can accomplish whatever we set out to do. Nothing binds our abilities except our expectations, and, given that, the farthest star is within our reach.
At Oval Office ceremony (20 May 1981) awarding NASA Distinguished Service medals to Young and Crippen, and a Congressional Space Medal of Honor to Young.
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Knowledge and ability must be combined with ambition as well as with a sense of honesty and a severe conscience. Every analyst occasionally has doubts about the accuracy of his results, and also there are times when he knows his results to be incorrect. Sometimes a few drops of the solution were spilt, or some other slight mistake made. In these cases it requires a strong conscience to repeat the analysis and to make a rough estimate of the loss or apply a correction. Anyone not having sufficient will-power to do this is unsuited to analysis no matter how great his technical ability or knowledge. A chemist who would not take an oath guaranteeing the authenticity, as well as the accuracy of his work, should never publish his results, for if he were to do so, then the result would be detrimental not only to himself, but to the whole of science.
Anleitung zur Quantitativen Analyse (1847), preface. F. Szabadvary, History of Analytical Chemistry (1966), trans. Gyula Svehla, 176.
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Man may be excused for feeling some pride at having risen, though not through his own exertions, to the very summit of the organic scale; and the fact of his having thus risen, instead of having been aboriginally placed there, may give him hopes for a still higher destiny in the distant future. But we are not here concerned with hopes or fears, only with the truth as far as our reason allows us to discover it. I have given the evidence to the best of my ability; and we must acknowledge, as it seems to me, that man with all his noble qualities, with sympathy which feels for the most debased, with benevolence which extends not only to other men but to the humblest living creature, with his god-like intellect which has penetrated into the movements and constitution of the solar system—with all these exalted powers—Man still bears in his bodily frame the indelible stamp of his lowly origin.
Concluding remarks. The Descent of Man (1871), Vol. 2, 405.
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Mathematics is a structure providing observers with a framework upon which to base healthy, informed, and intelligent judgment. Data and information are slung about us from all directions, and we are to use them as a basis for informed decisions. … Ability to critically analyze an argument purported to be logical, free of the impact of the loaded meanings of the terms involved, is basic to an informed populace.
In 'Mathematics Is an Edifice, Not a Toolbox', Notices of the AMS (Oct 1996), 43, No. 10, 1108.
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Mathematics, a creation of the mind, so accurately fits the outside world. … [There is a] fantastic amount of uniformity in the universe. The formulas of physics are compressed descriptions of nature's weird repetitions. The accuracy of those formulas, coupled with nature’s tireless ability to keep doing everything the same way, gives them their incredible power.
In book review, 'Adventures Of a Mathematician: The Man Who Invented the H-Bomb', New York Times (9 May 1976), 201. The book is a biography of Stanislaw Ulam, and this is Gardner’s description of one of Ulam’s reflections on nature and mathematics.
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Models so constructed, though of no practical value, serve a useful academic function. The oldest problem in economic education is how to exclude the incompetent. The requirement that there be an ability to master difficult models, including ones for which mathematical competence is required, is a highly useful screening device.
In Economics, Peace, and Laughter (1981), 40-41.
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Natural abilities are like natural plants; they need pruning by study.
'L. Of Studies,' Essays (1597). In Francis Bacon and Basil Montagu, The Works of Francis Bacon, Lord Chancellor of England (1852), 55.
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Natural ability without education has more often attained to glory and virtue than education without natural ability.
In M. P. Singh, Quote Unquote (2005), 1.
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Nature, … in order to carry out the marvelous operations [that occur] in animals and plants has been pleased to construct their organized bodies with a very large number of machines, which are of necessity made up of extremely minute parts so shaped and situated as to form a marvelous organ, the structure and composition of which are usually invisible to the naked eye without the aid of a microscope. … Just as Nature deserves praise and admiration for making machines so small, so too the physician who observes them to the best of his ability is worthy of praise, not blame, for he must also correct and repair these machines as well as he can every time they get out of order.
'Reply to Doctor Sbaraglia' in Opera Posthuma (1697), in H. B. Adelmann (ed.), Marcello Malpighi and the Evolution of Embryology (1966), Vol. 1, 568.
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Neither the absolute nor the relative size of the brain can be used to measure the degree of mental ability in animal or in man. So far as man is concerned, the weights of the brains or the volumes of the cranial cavities of a hundred celebrities of all branches of knowledge all over the world have been listed. … At the bottom of those lists are Gall, the famous phrenologist, Anatole France, the French novelist, and Gambetta, the French statesman, each with about 1,100 cc brain mass. The lists are topped by Dean Jonathan Swift, the English writer, Lord Byron, the English poet, and Turgenev, the Russian novelist, all with about 2,000 cc … Now our mental test! Had Turgenev really twice the mental ability of Anatole France?
In 'The Human Brain in the Light of Its Phylogenetic Development', Scientific Monthly (Aug 1948), 67, No. 2, 104-105. Collected in Sherwood Larned Washburn and ‎Davida Wolffson (eds.), The Shorter Anthropological Papers of Franz Weidenreich Published in the Period 1939-1948: A Memorial Volume (1949), 18.
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No nation can be really great unless it is great in peace, in industry, integrity, honesty. Skilled intelligence in civic affairs and industrial enterprises alike; the special ability of the artist, the man of letters, the man of science, and the man of business; the rigid determination to wrong no man, and to stand for righteousness—all these are necessary in a great nation.
Address (2 Jun 1897) at U.S. Naval War College, Newport, Rhode Island. In 'Washington's Forgotten Maxim', United States Naval Institute Proceedings (1897), 23, 450.
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Nothing has such power to broaden the mind as the ability to investigate systematically and truly all that comes under thy observation in life.
Meditations. In Jehiel Keeler Hoyt, The Cyclopedia of Practical Quotations (1896), 326.
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One of the ways the telegraph changed us as humans was it gave us a new sense of what time it is. It gave us an understanding of simultaneity. It gave us the ability to synchronize clocks from one place to another. It made it possible for the world to have standard time and time zones and then Daylight Savings Time and then after that jetlag. All of that is due to the telegraph because, before that, the time was whatever it was wherever you were.
From transcript for video interview on bigthink website
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One wonders whether the rare ability to be completely attentive to, and to profit by, Nature’s slightest deviation from the conduct expected of her is not the secret of the best research minds and one that explains why some men turn to most remarkably good advantage seemingly trivial accidents. Behind such attention lies an unremitting sensitivity.
In The Furtherance of Medical Research (1941), 98.
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Organic chemistry has literally placed a new nature beside the old. And not only for the delectation and information of its devotees; the whole face and manner of society has been altered by its products. We are clothed, ornamented and protected by forms of matter foreign to Nature; we travel and are propelled, in, on and by them. Their conquest of our powerful insect enemies, their capacity to modify the soil and control its microscopic flora, their ability to purify and protect our water, have increased the habitable surface of the earth and multiplied our food supply; and the dramatic advances in synthetic medicinal chemistry comfort and maintain us, and create unparalleled social opportunities (and problems).
In 'Synthesis', in A. Todd (ed.), Perspectives in Organic Chemistry (1956), 180.
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Our ability to live and work on other places in the solar system will end up giving us the science and technology that we need to save the species. I’m talking about human beings. I’d hate to miss all that fun.
Told to Associated Press. As reported in Richard Goldstein, 'John Young, Who Led First Space Shuttle Mission, Dies at 87', New York Times (6 Jan 2018).
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Our ability to think is the one survival tool we have. Science is applied thought. Without science, we’re living in caves and eating cockroaches.
(2010)
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Our children will enjoy in their homes electrical energy too cheap to meter. ... Transmutation of the elements, unlimited power, ability to investigate the working of living cells by tracer atoms, the secret of photosynthesis about to be uncovered, these and a host of other results, all in about fifteen short years. It is not too much to expect that our children will know of great periodic famines in the world only as matters of history, will travel effortlessly over the seas and under the and through the air with a minimum of danger and at great speeds, and will experience a life span far longer than ours, as disease yields and man comes to understand what causes him to age.
Speech at the 20th anniversary of the National Association of Science Writers, New York City (16 Sep 1954), asquoted in 'Abundant Power From Atom Seen', New York Times (17 Sep 1954) 5.
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Our methods of communication with our fellow men take many forms. We share with other animals the ability to transmit information by such diverse means as the posture of our bodies, by the movements of our eyes, head, arms, and hands, and by our utterances of non-specific sounds. But we go far beyond any other species on earth in that we have evolved sophisticated forms of pictorial representation, elaborate spoken and written languages, ingenious methods of recording music and language on discs, on magnetic tape and in a variety of other kinds of code.
As quoted in epigraph before title page in John Wolfenden, Hermann Bondi, et al., The Languages of Science: A Survey of Techniques of Communication (1963), i.
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Plenty of mathematicians, Hardy knew, could follow a step-by-step discursus unflaggingly—yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan he gave 100.
In The Man who Knew Infinity: A Life of the Genius Ramanujan (1975), 226.
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Progress is man's ability to complicate simplicity.
Quoted in Richard R. Lineman, 'Two-Way Ticket to Paradise', book review of Thor Heyerdahl, Fatu-Hiva, in New York Times (29 Aug 1975), 58, col. 5.
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Publication has been extended far beyond our present ability to make real use of the record.
From article 'As We May Think', in Atlantic Magazine (Jul 1945). Bush was expressing concern that the vastly increasing body of research information and knowledge needed mechanical systems to store and effectively manage its retrieval.
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Reason is the only ability that makes it possible for humans to rule the Earth and to ruin it.
…...
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Relations between authors and referees are, of course, almost always strained. Authors are convinced that the malicious stupidity of the referee is alone preventing them from laying their discoveries before an admiring world. Referees are convinced that authors are too arrogant and obtuse to recognize blatant fallacies in their own reasoning, even when these have been called to their attention with crystalline lucidity. All physicists know this, because all physicists are both authors and referees, but it does no good. The ability of one person to hold both views is an example of what Bohr called complementarity.
In Boojums All the Way Through: Communicating Science in a Prosaic Age (1990), 19-20.
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So I want to admit the assumption which the astronomer—and indeed any scientist—makes about the Universe he investigates. It is this: that the same physical causes give rise to the same physical results anywhere in the Universe, and at any time, past, present, and future. The fuller examination of this basic assumption, and much else besides, belongs to philosophy. The scientist, for his part, makes the assumption I have mentioned as an act of faith; and he feels confirmed in that faith by his increasing ability to build up a consistent and satisfying picture of the universe and its behavior.
From Science and the Nation (1957), 49. Also quoted in Ronald Keast, Dancing in the Dark: The Waltz in Wonder of Quantum Metaphysics (2009), 106.
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Success is achievable without public recognition, and the world has many unsung heroes. The teacher who inspires you to pursue your education to your ultimate ability is a success. The parents who taught you the noblest human principles are a success. The coach who shows you the importance of teamwork is a success. The spiritual leader who instills in you spiritual values and faith is a success. The relatives, friends, and neighbors with whom you develop a reciprocal relationship of respect and support - they, too, are successes. The most menial workers can properly consider themselves successful if they perform their best and if the product of their work is of service to humanity.
From 'Getting to the Heart of Success', in Jim Stovall, Success Secrets of Super Achievers: Winning Insights from Those Who Are at the Top (1999), 42-43.
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Taking … the mathematical faculty, probably fewer than one in a hundred really possess it, the great bulk of the population having no natural ability for the study, or feeling the slightest interest in it*. And if we attempt to measure the amount of variation in the faculty itself between a first-class mathematician and the ordinary run of people who find any kind of calculation confusing and altogether devoid of interest, it is probable that the former could not be estimated at less than a hundred times the latter, and perhaps a thousand times would more nearly measure the difference between them.
[* This is the estimate furnished me by two mathematical masters in one of our great public schools of the proportion of boys who have any special taste or capacity for mathematical studies. Many more, of course, can be drilled into a fair knowledge of elementary mathematics, but only this small proportion possess the natural faculty which renders it possible for them ever to rank high as mathematicians, to take any pleasure in it, or to do any original mathematical work.]
In Darwinism, chap. 15.
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Technique and ability alone do not get you to the top; it is the willpower that is the most important. This willpower you cannot buy with money or be given by others...it rises from your heart.
…...
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That ability to impart knowledge … what does it consist of? … a deep belief in the interest and importance of the thing taught, a concern about it amounting to a sort of passion. A man who knows a subject thoroughly, a man so soaked in it that he eats it, sleeps it and dreams it—this man can always teach it with success, no matter how little he knows of technical pedagogy. That is because there is enthusiasm in him, and because enthusiasm is almost as contagious as fear or the barber’s itch. An enthusiast is willing to go to any trouble to impart the glad news bubbling within him. He thinks that it is important and valuable for to know; given the slightest glow of interest in a pupil to start with, he will fan that glow to a flame. No hollow formalism cripples him and slows him down. He drags his best pupils along as fast as they can go, and he is so full of the thing that he never tires of expounding its elements to the dullest.
This passion, so unordered and yet so potent, explains the capacity for teaching that one frequently observes in scientific men of high attainments in their specialties—for example, Huxley, Ostwald, Karl Ludwig, Virchow, Billroth, Jowett, William G. Sumner, Halsted and Osler—men who knew nothing whatever about the so-called science of pedagogy, and would have derided its alleged principles if they had heard them stated.
In Prejudices: third series (1922), 241-2.
For a longer excerpt, see H.L. Mencken on Teaching, Enthusiasm and Pedagogy.
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The ability of a cell to sense these broken ends, to direct them towards each other, and then to unite them so that the union of the two DNA strands is correctly oriented, is a particularly revealing example of the sensitivity of cells to all that is going on within them. They make wise decisions and act on them.
(8 Dec 1983) The Significance of Responses of the Genome to Challenge, Nobel Lecture
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The ability of the genes to vary and, when they vary (mutate), to reproduce themselves in their new form, confers on these cell elements, as Muller has so convincingly pointed out, the properties of the building blocks required by the process of evolution. Thus, the cell, robbed of its noblest prerogative, was no longer the ultimate unit of life. This title was now conferred on the genes, subcellular elements, of which the cell nucleus contained many thousands and, more precisely, like Noah’s ark, two of each kind.
Nucleo-cytoplasmic Relations in Micro-Organisms: Their Bearing on Cell Heredity and Differentiation (1953), 2-3.
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The ability to imagine relations is one of the most indispensable conditions of all precise thinking. No subject can be named, in the investigation of which it is not imperatively needed; but it can be nowhere else so thoroughly acquired as in the study of mathematics.
In Darwinism and other Essays (1893), 296.
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The ability to learn faster than your competitors may be the only sustainable competitive advantage.
In 'Planning as Learning', Harvard Business Review (Mar-Apr 1988), 66, No. 2, 71.
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The ability to play is one of the principal criteria of mental health.
In 'Childhood’s Promises', Television & Children (1980), 3, No. 3, 17.
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The Anglo-Dane appears to possess an aptitude for mathematics which is not shared by the native of any other English district as a whole, and it is in the exact sciences that the Anglo-Dane triumphs.
In A Study of British Genius (1904), 69. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 131. Moritz adds an editorial footnote: “The mathematical tendencies of Cambridge are due to the fact that Cambridge drains the ability of nearly the whole Anglo-Danish district.”
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The cosmogonist has finished his task when he has described to the best of his ability the inevitable sequence of changes which constitute the history of the material universe. But the picture which he draws opens questions of the widest interest not only to science, but also to humanity. What is the significance of the vast processes it portrays? What is the meaning, if any there be which is intelligible to us, of the vast accumulations of matter which appear, on our present interpretations of space and time, to have been created only in order that they may destroy themselves.
In Astronomy and Cosmogony (1961).
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The education explosion is producing a vast number of people who want to live significant, important lives but lack the ability to satisfy this craving for importance by individual achievement. The country is being swamped with nobodies who want to be somebodies.
From address to employees of the Phillips Petroleum Co. In Bartlesville, Oklahoma, excerpted in the Franklin, Indiana, The Daily Journal (23 Jan 1978), 2.
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The enthusiasm of Sylvester for his own work, which manifests itself here as always, indicates one of his characteristic qualities: a high degree of subjectivity in his productions and publications. Sylvester was so fully possessed by the matter which for the time being engaged his attention, that it appeared to him and was designated by him as the summit of all that is important, remarkable and full of future promise. It would excite his phantasy and power of imagination in even a greater measure than his power of reflection, so much so that he could never marshal the ability to master his subject-matter, much less to present it in an orderly manner.
Considering that he was also somewhat of a poet, it will be easier to overlook the poetic flights which pervade his writing, often bombastic, sometimes furnishing apt illustrations; more damaging is the complete lack of form and orderliness of his publications and their sketchlike character, … which must be accredited at least as much to lack of objectivity as to a superfluity of ideas. Again, the text is permeated with associated emotional expressions, bizarre utterances and paradoxes and is everywhere accompanied by notes, which constitute an essential part of Sylvester’s method of presentation, embodying relations, whether proximate or remote, which momentarily suggested themselves. These notes, full of inspiration and occasional flashes of genius, are the more stimulating owing to their incompleteness. But none of his works manifest a desire to penetrate the subject from all sides and to allow it to mature; each mere surmise, conceptions which arose during publication, immature thoughts and even errors were ushered into publicity at the moment of their inception, with utmost carelessness, and always with complete unfamiliarity of the literature of the subject. Nowhere is there the least trace of self-criticism. No one can be expected to read the treatises entire, for in the form in which they are available they fail to give a clear view of the matter under contemplation.
Sylvester’s was not a harmoniously gifted or well-balanced mind, but rather an instinctively active and creative mind, free from egotism. His reasoning moved in generalizations, was frequently influenced by analysis and at times was guided even by mystical numerical relations. His reasoning consists less frequently of pure intelligible conclusions than of inductions, or rather conjectures incited by individual observations and verifications. In this he was guided by an algebraic sense, developed through long occupation with processes of forms, and this led him luckily to general fundamental truths which in some instances remain veiled. His lack of system is here offset by the advantage of freedom from purely mechanical logical activity.
The exponents of his essential characteristics are an intuitive talent and a faculty of invention to which we owe a series of ideas of lasting value and bearing the germs of fruitful methods. To no one more fittingly than to Sylvester can be applied one of the mottos of the Philosophic Magazine:
“Admiratio generat quaestionem, quaestio investigationem investigatio inventionem.”
In Mathematische Annalen (1898), 50, 155-160. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 176-178.
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The fact that all normal children acquire essentially comparable grammars of great complexity with remarkable rapidity suggests that human beings are somehow specially designed to do this, with data-handling or 'hypothesis-formulating' ability of unknown character and complexity.
A review of B. F. Skinner, Verbal Behavior (1957). In Language: Journal of the Linguistic Society of America, 1959, 35, 57.
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The game of chess has always fascinated mathematicians, and there is reason to suppose that the possession of great powers of playing that game is in many features very much like the possession of great mathematical ability. There are the different pieces to learn, the pawns, the knights, the bishops, the castles, and the queen and king. The board possesses certain possible combinations of squares, as in rows, diagonals, etc. The pieces are subject to certain rules by which their motions are governed, and there are other rules governing the players. … One has only to increase the number of pieces, to enlarge the field of the board, and to produce new rules which are to govern either the pieces or the player, to have a pretty good idea of what mathematics consists.
In Book review, 'What is Mathematics?', Bulletin American Mathematical Society (May 1912), 18, 386-387.
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The Gombe Stream chimpanzees … in their ability to modify a twig or stick to make it suitable for a definite purpose, provide the first examples of free-ranging nonhuman primates actually making very crude tools.
In 'Chimpanzees of the Gombe Stream Reserve', collected in Primate Behavior: Field Studies of Monkeys and Apes (1965), 473.
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The human organism inherits so delicate an adjustment to climate that, in spite of man's boasted ability to live anywhere, the strain of the frozen North eliminates the more nervous and active types of mind.
The Red Man's Continent: A Chronicle of Aboriginal America (1919), 20.
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The meaning of human life and the destiny of man cannot be separable from the meaning and destiny of life in general. 'What is man?' is a special case of 'What is life?' Probably the human species is not intelligent enough to answer either question fully, but even such glimmerings as are within our powers must be precious to us. The extent to which we can hope to understand ourselves and to plan our future depends in some measure on our ability to read the riddles of the past. The present, for all its awesome importance to us who chance to dwell in it, is only a random point in the long flow of time. Terrestrial life is one and continuous in space and time. Any true comprehension of it requires the attempt to view it whole and not in the artificial limits of any one place or epoch. The processes of life can be adequately displayed only in the course of life throughout the long ages of its existence.
The Meaning of Evolution: A Study of the History of Life and of its Significance for Man (1949), 9.
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The microbial global brain—gifted with long-range transport, data trading, genetic variants … and the ability to reinvent genomes—began its operations some 91 trillion bacterial generations before the birth of the Internet. Ancient bacteria, if they functioned like those today, had mastered the art of worldwide information exchange. … The earliest microorganisms would have used planet-sweeping currents of wind and water to carry the scraps of genetic code…
In 'Creative Nets in the Precambrian Era', Global Brain: The Evolution of Mass Mind from the Big Bang to the 21st Century (2000), 18-19.
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The most striking characteristic of the written language of algebra and of the higher forms of the calculus is the sharpness of definition, by which we are enabled to reason upon the symbols by the mere laws of verbal logic, discharging our minds entirely of the meaning of the symbols, until we have reached a stage of the process where we desire to interpret our results. The ability to attend to the symbols, and to perform the verbal, visible changes in the position of them permitted by the logical rules of the science, without allowing the mind to be perplexed with the meaning of the symbols until the result is reached which you wish to interpret, is a fundamental part of what is called analytical power. Many students find themselves perplexed by a perpetual attempt to interpret not only the result, but each step of the process. They thus lose much of the benefit of the labor-saving machinery of the calculus and are, indeed, frequently incapacitated for using it.
In 'Uses of Mathesis', Bibliotheca Sacra (Jul 1875), 32, 505.
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THE OATH. I swear by Apollo [the healing God], the physician and Aesclepius [son of Apollo], and Health [Hygeia], and All-heal [Panacea], and all the gods and goddesses, that, according to my ability and judgment, I will keep this Oath and this stipulation—to reckon him who taught me this Art equally dear to me as my parents, to share my substance with him, and relieve his necessities if required; to look upon his offspring in the same footing as my own brothers, and to teach them this art, if they shall wish to learn it, without fee or stipulation; and that by precept, lecture, and every other mode of instruction, I will impart a knowledge of the Art to my own sons, and those of my teachers, and to disciples bound by a stipulation and oath according to the law of medicine, but to none others. I will follow that system of regimen which, according to my ability and judgment, I consider for the benefit of my patients, and abstain from whatever is deleterious and mischievous. I will give no deadly medicine to any one if asked, nor suggest any such counsel; and in like manner I will not give to a woman a pessary to produce abortion. With purity and with holiness I will pass my life and practice my Art. I will not cut persons laboring under the stone, but will leave this to be done by men who are practitioners of this work. Into whatever houses I enter, I will go into them for the benefit of the sick, and will abstain from every voluntary act of mischief and corruption; and, further, from the seduction of females or males, of freemen and slaves. Whatever, in connection with my professional practice or not, in connection with it, I see or hear, in the life of men, which ought not to be spoken of abroad, I will not divulge, as reckoning that all such should be kept secret. While I continue to keep this Oath unviolated, may it be granted to me to enjoy life and the practice of the art, respected by all men, in all times! But should I trespass and violate this Oath, may the reverse be my lot!
The Genuine Works of Hippocrates, trans. Francis Adams (1886), Vol. 2, 344-5.
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The profound mathematical ability of Bolyai János showed itself physically not only in his handling of the violin, where he was a master, but also of arms, where he was unapproachable.
In János Bolyai, Science Absolute of Space, translated from the Latin by George Bruce Halsted (1896), Translator's Introduction, xxix. [Bolyai was the victor in many duels. —Webmaster]
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The responsibility which rests upon man is proportional to the ability which he possesses and the opportunity which he faces. Perhaps that responsibility is no greater for him than was that of Notharctus or Eohippus or a trilobite, each in his own day, but because of man’s unique abilities it is the greatest responsibility that has ever rested upon any of the earth’s offspring.
In Sons of the Earth: The Geologist’s View of History (1930), 258.
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The Royal Navy’s unique ability to combat scurvy was said by one naval physician to have doubled its performance and contributed directly to Britain’s eventual defeat of the French and Spanish fleets at Trafalgar in 1805. (It also meant that British sailors became known as “limeys.”)
In A History of the World in 6 Glasses (2005, 2009), 110.
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The scientist knows very well that he is approaching ultimate truth only in an asymptotic curve and is barred from ever reaching it; but at the same time he is proudly aware of being indeed able to determine whether a statement is a nearer or a less near approach to the truth.
In On Aggression (1966, 2002), 279.
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The scientist takes off from the manifold observations of predecessors, and shows his intelligence, if any, by his ability to discriminate between the important and the negligible, by selecting here and there the significant steppingstones that will lead across the difficulties to new understanding. The one who places the last stone and steps across to the terra firma of accomplished discovery gets all the credit.
In As I Remember Him (1940).
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The test of a first-rate intelligence is the ability to hold two opposed ideas in mind at the same time and still retain the ability to function.
The Crack-Up (1936, 1993), 69.
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The test of a theory is its ability to cope with all the relevant phenomena, not its a priori 'reasonableness'. The latter would have proved a poor guide in the development of science, which often makes progress by its encounter with the totally unexpected and initially extremely puzzling.
'From DAMTP [Department of Applied Mathematics and Theoretical Physics] to Westcott House', Cambridge Review (1981), 103, 61.
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The tools we use have a profound (and devious!) influence on our thinking habits, and, therefore, on our thinking abilities.
…...
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The unavoidable conclusion is that the unprecedented meekness of the majority is responsible for the increase in violence. Social stability is the product of an equilibrium between a vigorous majority and violent minorities. Disorder does not come from an increased inner pressure or from the interaction of explosive ingredients. There is no reason to believe that the nature of the violent minorities is now greatly different from what it was in the past. What has changed is the will and ability of the majority to react.
In 'Thoughts on the Present', First Things, Last Things (1971), 110.
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There are, as we have seen, a number of different modes of technological innovation. Before the seventeenth century inventions (empirical or scientific) were diffused by imitation and adaption while improvement was established by the survival of the fittest. Now, technology has become a complex but consciously directed group of social activities involving a wide range of skills, exemplified by scientific research, managerial expertise, and practical and inventive abilities. The powers of technology appear to be unlimited. If some of the dangers may be great, the potential rewards are greater still. This is not simply a matter of material benefits for, as we have seen, major changes in thought have, in the past, occurred as consequences of technological advances.
Concluding paragraph of "Technology," in Dictionary of the History of Ideas (1973), Vol. 4, 364.
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There can be but one opinion as to the beauty and utility of this analysis of Laplace; but the manner in which it has been hitherto presented has seemed repulsive to the ablest mathematicians, and difficult to ordinary mathematical students.[Co-author with Peter Guthrie Tait.]
In William Thomson Baron Kelvin, Peter Guthrie Tait, Treatise on Natural Philosophy (1879), Vol. 1, Preface, vii.
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There has never been just 'coach class' health care, but with these amenities you are seeing people get priorities according to your ability to pay. It's one thing to say you get perks; it's another to say you can buy your way to the head of the line.
Quoted in Nancy S. Tilghman, 'Southampton Hospital Drops V.I.P. Idea', New York Times (27 Jun 2004), L13.
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There is no more convincing proof of the truth of a comprehensive theory than its power of absorbing and finding a place for new facts, and its capability of interpreting phenomena which had been previously looked upon as unaccountable anomalies. It is thus that the law of universal gravitation and the undulatory theory of light have become established and universally accepted by men of science. Fact after fact has been brought forward as being apparently inconsistent with them, and one alter another these very facts have been shown to be the consequences of the laws they were at first supposed to disprove. A false theory will never stand this test. Advancing knowledge brings to light whole groups of facts which it cannot deal with, and its advocates steadily decrease in numbers, notwithstanding the ability and scientific skill with which it may have been supported.
From a review of four books on the subject 'Mimicry, and Other Protective Resemblances Among Animals', in The Westminster Review (Jul 1867), 88, 1. Wallace is identified as the author in the article as reprinted in William Beebe, The Book of Naturalists: An Anthology of the Best Natural History (1988), 108.
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There’s no question in my mind that the capability of [the space shuttle] to put 65,000 pounds in low earth orbit—to put payloads up there cheaper than we’ve been able to do it before, not having to throw away the booster—will absolutely revolutionize the way we do business here on earth in ways that we just can’t imagine. It will help develop science and technology. With the space shuttle—when we get it operational—we’ll be able to do in 5 or 10 years what it would take us 20 to 30 years to do otherwise in science and technology development.
Interview for U.S. News & World Report (13 Apr 1981), 56.
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These specimens, which I could easily multiply, may suffice to justify a profound distrust of Auguste Comte, wherever he may venture to speak as a mathematician. But his vast general ability, and that personal intimacy with the great Fourier, which I most willingly take his own word for having enjoyed, must always give an interest to his views on any subject of pure or applied mathematics.
In R. Graves, Life of W. R. Hamilton (1882-89), Vol. 3, 475.
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This ability to incorporate the past gives the sharpest diagnostic tool, if one asks whether a body of knowledge is a science or not. Do present practitioners have to go back to an original work of the past? Or has it been incorporated? … Science is cumulative, and embodies its past.
'The Case of Leavis and the Serious Case’, Times Literary Supplement (9 Jul 1970), 737-740. Collected in Public Affairs (1971), 95.
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Through most of his existence man’s survival depended on his ability to cope with nature. If the mind evolved as an aid in human survival it was primarily as an instrument for the mastery of nature. The mind is still at its best when tinkering with the mathematics that rule nature.
In Before the Sabbath (1979), 26.
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Thus died Negro Tom [Thomas Fuller], this untaught arithmetician, this untutored scholar. Had his opportunities of improvement been equal to those of thousands of his fellow-men, neither the Royal Society of London, the Academy of Science at Paris, nor even a Newton himself need have been ashamed to acknowledge him a brother in science.
[Thomas Fuller (1710-1790), although enslaved from Africa at age 14, was an arithmetical prodigy. He was known as the Virginia Calculator because of his exceptional ability with arithmetic calculations. His intellectual accomplishments were related by Dr. Benjamin Rush in a letter read to the Pennsylvania Society for the Abolition of Slavery.]
Obituary
From obituary in the Boston Columbian Centinal (29 Dec 1790), 14, No. 31. In George Washington Williams, History of the Negro Race in America from 1619 to 1880 (1882), Vol. 1, 400
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To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess.
In I Want to be a Mathematician: An Automathography (1985), 400.
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To make still bigger telescopes will be useless, for the light absorption and temperature variations of the earth’s atmosphere are what now limits the ability to see fine detail. If bigger telescopes are to be built, it will have to be for use in an airless observatory, perhaps an observatory on the moon.
(1965). In Isaac Asimov’s Book of Science and Nature Quotations (1988), 284.
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To mean understandings, it is sufficient honour to be numbered amongst the lowest labourers of learning; but different abilities must find different tasks. To hew stone, would have been unworthy of Palladio; and to have rambled in search of shells and flowers, had but ill suited with the capacity of Newton.
From 'Numb. 83, Tuesday, January 1, 1750', The Rambler (1756), Vol. 2, 154. (Italian architect Palladio, 1509-80, is widely considered the most influential in the history of Western architecture.)
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To most ... of us, Russia was as mysterious and remote as the other side of the moon and not much more productive when it came to really new ideas or inventions. A common joke of the time [mid 1940s] said that the Russians could not surreptitiously introduce nuclear bombs in suitcases into the United States because they had not yet been able to perfect a suitcase.
In Richard Rhodes, The Making of the Atomic Bomb (1986), 760.
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To stay young requires unceasing cultivation of the ability to unlearn old falsehoods.
In Time Enough For Love (1973), 263. In Carl C. Gaither, Mathematically Speaking (1998), 347.
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We can’t all be Einstein (because we don’t all play the violin). At the very least we need a sort of street-smart science: the ability to recognize evidence gather it assess it and act on it.
In Light Elements: Essays in Science from Gravity to Levity (1991), 14.
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We do not know of any enzymes or other chemical defined organic substances having specifically acting auto-catalytic properties such as to enable them to construct replicas of themselves. Neither was there a general principle known that would result in pattern-copying; if there were, the basis of life would be easier to come by. Moreover, there was no evidence to show that the enzymes were not products of hereditary determiners or genes, rather than these genes themselves, and they might even be products removed by several or many steps from the genes, just as many other known substances in the cell must be. However, the determiners or genes themselves must conduct, or at least guide, their own replication, so as to lead to the formation of genes just like themselves, in such wise that even their own mutations become .incorporated in the replicas. And this would probably take place by some kind of copying of pattern similar to that postulated by Troland for the enzymes, but requiring some distinctive chemical structure to make it possible. By virtue of this ability of theirs to replicate, these genes–or, if you prefer, genetic material–contained in the nuclear chromosomes and in whatever other portion of the cell manifests this property, such as the chloroplastids of plants, must form the basis of all the complexities of living matter that have arisen subsequent to their own appearance on the scene, in the whole course of biological evolution. That is, this genetic material must underlie all evolution based on mutation and selective multiplication.
'Genetic Nucleic Acid', Perspectives in Biology and Medicine (1961), 5, 6-7.
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We need to be realistic. There is very little we can do now to stop the ice from disappearing from the North Pole in the Summer. And we probably cannot prevent the melting of the permafrost and the resulting release of methane. In addition, I fear that we may be too late to help the oceans maintain their ability to absorb carbon dioxide. But there is something we can do—and it could make the whole difference and buy us time to develop the necessary low carbon economies. We can halt the destruction of the world’s rainforests—and even restore parts of them—in order to ensure that the forests do what they are so good at—in other words storing carbon naturally. This is a far easier, cheaper and quicker option than imagining we can rely on as yet unproven technology to capture carbon at a cost of some $50 per tonne or, for that matter, imagining we can achieve what is necessary through plantation timber.
Presidential Lecture (3 Nov 2008) at the Presidential Palace, Jakarta, Indonesia. On the Prince of Wales website.
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What, then, is it in particular that can be learned from teachers of special distinction? Above all, what they teach is high standards. We measure everything, including ourselves, by comparisons; and in the absence of someone with outstanding ability there is a risk that we easily come to believe that we are excellent and much better than the next man. Mediocre people may appear big to themselves (and to others) if they are surrounded by small circumstances. By the same token, big people feel dwarfed in the company of giants, and this is a most useful feeling. So what the giants of science teach us is to see ourselves modestly and not to overrate ourselves.
Reminiscences and Reflections (1981), 175.
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When I think of vision, I have in mind the ability to see above and beyond the majority.
…...
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When physicists speak of “beauty” in their theories, they really mean that their theory possesses at least two essential features: 1. A unifying symmetry 2. The ability to explain vast amounts of experimental data with the most economical mathematical expressions.
In 'Quantum Heresy', Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension (1995), 127.
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When the ability to have movement across social class becomes virtually impossible, I think it is the beginning of the end of a country. And because education is so critical to success in this country, if we don't figure out a way to create greater mobility across social class, I do think it will be the beginning of the end.
In a segment from PBS TV program, Newshour (9 Sep 2013).
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When the war finally came to an end, 1 was at a loss as to what to do. ... I took stock of my qualifications. A not-very-good degree, redeemed somewhat by my achievements at the Admiralty. A knowledge of certain restricted parts of magnetism and hydrodynamics, neither of them subjects for which I felt the least bit of enthusiasm.
No published papers at all … [Only gradually did I realize that this lack of qualification could be an advantage. By the time most scientists have reached age thirty they are trapped by their own expertise. They have invested so much effort in one particular field that it is often extremely difficult, at that time in their careers, to make a radical change. I, on the other hand, knew nothing, except for a basic training in somewhat old-fashioned physics and mathematics and an ability to turn my hand to new things. … Since I essentially knew nothing, I had an almost completely free choice. …
In What Mad Pursuit (1988).
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When we think of giving a child a mathematical education we are apt to ask whether he has special aptitudes fitting him to receive it. Do we ask any such questions when we talk of teaching him to read and write?
In 'Mathematics for Children', Popular Science Monthly (Oct 1899), 187, citing “translated for the Popular Science Monthly from the Revue Scientifique. Also seen paraphrased as “To ask whether a child has an aptitude for mathematics is equivalent to asking whether he has an aptitude for reading and writing,” in William L. Schaaf, 'Memorabilia Mathematica', The Mathematics Teacher (Mar 1957), 50, No. 3, 231.
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Whenever we pride ourselves upon finding a newer, stricter way of thought or exposition; whenever we start insisting too hard upon “operationalism” or symbolic logic or any other of these very essential systems of tramlines, we lose something of the ability to think new thoughts. And equally, of course, whenever we rebel against the sterile rigidity of formal thought and exposition and let our ideas run wild, we likewise lose. As I see it, the advances in scientific thought come from a combination of loose and strict thinking, and this combination is the most precious tool of science.
In 'Culture Contact and Schismogenesis' (1935), in Steps to an Ecology of Mind: Collected Essays in Anthropology, Psychiatry, Evolution, and Epistemology (1972).
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[Charles Kettering] is unique in that he combines in one individual the interest in pure science with the practical ability to apply knowledge in useful devices.
As quoted in book review, T.A. Boyd, 'Charles F. Kettering: Prophet of Progress', Science (30 Jan 1959), 256.
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[Richard Feynman] believed in the primacy of doubt, not as a blemish upon our ability to know but as the essence of knowing. The alternative to uncertainty is authority, against which science has fought for centuries.
In Genius: The Life and Science of Richard Feynman (1992), 371-372.
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[Werhner von Braun] is a human leader whose eyes and thoughts have always been turned toward the stars. It would be foolish to assign rocketry success to one person totally. Components must necessarily be the work of many minds; so must successive stages of development. But because Wernher von Braun joins technical ability, passionate optimism, immense experience and uncanny organizing ability in the elusive power to create a team, he is the greatest human element behind today’s rocketry success
Quoted in 'Reach For The Stars', Time (17 Feb 1958), 71, 25.
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…comparing the capacity of computers to the capacity of the human brain, I’ve often wondered, where does our success come from? The answer is synthesis, the ability to combine creativity and calculation, art and science, into whole that is much greater than the sum of its parts.
In How Life Imitates Chess: Making the Right Moves, from the Board to the Boardroom (2007), 4.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
Quotations by:Albert EinsteinIsaac NewtonLord KelvinCharles DarwinSrinivasa RamanujanCarl SaganFlorence NightingaleThomas EdisonAristotleMarie CurieBenjamin FranklinWinston ChurchillGalileo GalileiSigmund FreudRobert BunsenLouis PasteurTheodore RooseveltAbraham LincolnRonald ReaganLeonardo DaVinciMichio KakuKarl PopperJohann GoetheRobert OppenheimerCharles Kettering  ... (more people)

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- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton



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