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Who said: “Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.”
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Home > Category Index for Science Quotations > Category Index F > Category: Faculty

Faculty Quotes (72 quotes)

In primis, hominis est propria VERI inquisitio atque investigato. Itaque cum sumus negotiis necessariis, curisque vacui, tum avemus aliquid videre, audire, ac dicere, cognitionemque rerum, aut occultarum aut admirabilium, ad benè beatéque vivendum necessariam ducimus; —ex quo intelligitur, quod VERUM, simplex, sincerumque sit, id esse naturæ hominis aptissimum. Huic veri videndi cupiditati adjuncta est appetitio quædam principatûs, ut nemini parere animus benè a naturâ informatus velit, nisi præcipienti, aut docenti, aut utilitatis causâ justè et legitimè imperanti: ex quo animi magnitudo existit, et humanarum rerum contemtio.
Before all other things, man is distinguished by his pursuit and investigation of TRUTH. And hence, when free from needful business and cares, we delight to see, to hear, and to communicate, and consider a knowledge of many admirable and abstruse things necessary to the good conduct and happiness of our lives: whence it is clear that whatsoever is TRUE, simple, and direct, the same is most congenial to our nature as men. Closely allied with this earnest longing to see and know the truth, is a kind of dignified and princely sentiment which forbids a mind, naturally well constituted, to submit its faculties to any but those who announce it in precept or in doctrine, or to yield obedience to any orders but such as are at once just, lawful, and founded on utility. From this source spring greatness of mind and contempt of worldly advantages and troubles.
In De Officiis, Book 1. Sect. 13. As given in epigraph to John Frederick William Herschel, A Preliminary Discourse on the Study of Natural Philosophy (1830), viii.
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The Word Reason in the English Language has different Significances: sometimes it is taken for true, and clear Principles: Sometimes for clear, and fair deductions from those Principles: and sometimes for Cause, and particularly the final Cause: but the Consideration I shall have of it here, is in a Signification different from all these; and that is, as it stands for a Faculty of Man, That Faculty, whereby Man is supposed to be distinguished from Beasts; and wherein it is evident he much surpasses them.
In 'Of Reason', Essay Concerning Humane Understanding (1690), Book 4, Ch. 17, Sec. 1, 341.
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A great discovery solves a great problem, but there is a grain of discovery in the solution of any problem. Your problem may be modest, but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.
From Preface to the first printing, reprinted in How to Solve It: A New Aspect of Mathematical Method (2004), v.
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Alphonse of Castile is reported to have said that if he had had the making of the universe he would have done it much better. And I think so too. Instead of making a man go through the degradation of faculties and death, he should continually improve with age, and then be translated from this world to a superior planet, where he should begin life with the knowledge gained here, and so on. That would be to my mind, as an old man, a more satisfactory way of conducting affairs
Address, in 'Report to the Chemical Society's Jubilee', Nature (26 Mar 1891), 43, 493.
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André Weil suggested that there is a logarithmic law at work: first-rate people attract other first-rate people, but second-rate people tend to hire third-raters, and third-rate people hire fifth-raters. If a dean or a president is genuinely interested in building and maintaining a high-quality university (and some of them are), then he must not grant complete self-determination to a second-rate department; he must, instead, use his administrative powers to intervene and set things right. That’s one of the proper functions of deans and presidents, and pity the poor university in which a large proportion of both the faculty and the administration are second-raters; it is doomed to diverge to minus infinity.
In I Want to be a Mathematician: an Automathography (1985), 123.
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Apprehension by the senses supplies, directly or indirectly, the material of all human knowledge; or, at least, the stimulus necessary to develop every inborn faculty of the mind.
In 'The Theory of Vision', collected in Science and Culture: Popular and Philosophical Essays (), 127.
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As an exercise of the reasoning faculty, pure mathematics is an admirable exercise, because it consists of reasoning alone, and does not encumber the student with an exercise of judgment: and it is well to begin with learning one thing at a time, and to defer a combination of mental exercises to a later period.
In Annotations to Bacon’s Essays (1873), Essay 1, 493.
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As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to stimulate the faculty of invention.
In 'A Plea for the Mathematician', Nature, 1, 261 in Collected Mathematical Papers, Vol. 2 (1908), 717.
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But since the brain, as well as the cerebellum, is composed of many parts, variously figured, it is possible, that nature, which never works in vain, has destined those parts to various uses, so that the various faculties of the mind seem to require different portions of the cerebrum and cerebellum for their production.
A Dissertation on the Functions of the Nervous System (1784), trans. and ed. Thomas Laycock (1851), 446.
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Cayley was singularly learned in the work of other men, and catholic in his range of knowledge. Yet he did not read a memoir completely through: his custom was to read only so much as would enable him to grasp the meaning of the symbols and understand its scope. The main result would then become to him a subject of investigation: he would establish it (or test it) by algebraic analysis and, not infrequently, develop it so to obtain other results. This faculty of grasping and testing rapidly the work of others, together with his great knowledge, made him an invaluable referee; his services in this capacity were used through a long series of years by a number of societies to which he was almost in the position of standing mathematical advisor.
In Proceedings of London Royal Society (1895), 58, 11-12.
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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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Doubtless the reasoning faculty, the mind, is the leading and characteristic attribute of the human race. By the exercise of this, man arrives at the properties of the natural bodies. This is science, properly and emphatically so called. It is the science of pure mathematics; and in the high branches of this science lies the truly sublime of human acquisition. If any attainment deserves that epithet, it is the knowledge, which, from the mensuration of the minutest dust of the balance, proceeds on the rising scale of material bodies, everywhere weighing, everywhere measuring, everywhere detecting and explaining the laws of force and motion, penetrating into the secret principles which hold the universe of God together, and balancing worlds against worlds, and system against system. When we seek to accompany those who pursue studies at once so high, so vast, and so exact; when we arrive at the discoveries of Newton, which pour in day on the works of God, as if a second fiat had gone forth from his own mouth; when, further, we attempt to follow those who set out where Newton paused, making his goal their starting-place, and, proceeding with demonstration upon demonstration, and discovery upon discovery, bring new worlds and new systems of worlds within the limits of the known universe, failing to learn all only because all is infinite; however we may say of man, in admiration of his physical structure, that “in form and moving he is express and admirable,” it is here, and here without irreverence, we may exclaim, “In apprehension how like a god!” The study of the pure mathematics will of course not be extensively pursued in an institution, which, like this [Boston Mechanics’ Institute], has a direct practical tendency and aim. But it is still to be remembered, that pure mathematics lie at the foundation of mechanical philosophy, and that it is ignorance only which can speak or think of that sublime science as useless research or barren speculation.
In Works (1872), Vol. 1, 180.
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Enlist a great mathematician and a distinguished Grecian; your problem will be solved. Such men can teach in a dwelling-house as well as in a palace. Part of the apparatus they will bring; part we will furnish.
Advice given to the Trustees of Johns Hopkins University on the choice of a professorial staff. In Report of the President of Johns Hopkins University (1888), 29. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 122.
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From whence it is obvious to conclude that, since our Faculties are not fitted to penetrate into the internal Fabrick and real Essences of Bodies; but yet plainly discover to us the Being of a GOD, and the Knowledge of our selves, enough to lead us into a full and clear discovery of our Duty, and great Concernment, it will become us, as rational Creatures, to imploy those Faculties we have about what they are most adapted to, and follow the direction of Nature, where it seems to point us out the way.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 4, Chapter 12, Section 11, 646.
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Genius, in truth, means little more than the faculty of perceiving in an unhabitual way.
In Psychology (1904), 328.
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He that believes, without having any Reason for believing, may be in love with his own Fancies; but neither seeks Truth as he ought, nor pays the Obedience due to his Maker, who would have him use those discerning Faculties he has given him, to keep him out of Mistake and Errour.
In 'Of Reason', Essay Concerning Humane Understanding (1690), Book 4, Ch. 17, Sec. 24, 347.
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Holding then to science with one hand—the left hand—we give the right hand to religion, and cry: ‘Open Thou mine eyes, that I may behold wondrous things, more wondrous than the shining worlds can tell.’ Obedient to the promise, religion does awaken faculties within us, does teach our eyes to the beholding of more wonderful things. Those great worlds blazing like suns die like feeble stars in the glory of the morning, in the presence of this new light. The soul knows that an infinite sea of love is all about it, throbbing through it, everlasting arms of affection lift it, and it bathes itself in the clear consciousness of a Father’s love.
…...
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I know, indeed, and can conceive of no pursuit so antagonistic to the cultivation of the oratorical faculty … as the study of Mathematics. An eloquent mathematician must, from the nature of things, ever remain as rare a phenomenon as a talking fish, and it is certain that the more anyone gives himself up to the study of oratorical effect the less will he find himself in a fit state to mathematicize.
In Address (22 Feb 1877) for Commemoration Day at Johns Hopkins University. Published as a pamphlet, and reprinted in The Collected Mathematical Papers of James Joseph Sylvester: (1870-1883) (1909), Vol. 3, 72. https://books.google.com/books?id=wgVbAAAAQAAJ James Joseph Sylvester - 1877
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I never guess. It is a shocking habit—destructive to the logical faculty.
Spoken by fictitious character Sherlock Holmes in The Sign of Four (1890), 17.
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I thought it was a miracle that I got this faculty appointment and was so happy to be there for a few years that I just wanted to follow what was exciting for me. I didn’t have expectations of getting tenure. So this was an aspect of gender inequality that was extremely positive. It allowed me to be fearless.
As quoted in Anna Azvolinsky, 'Fearless About Folding', The Scientist (Jan 2016).
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I [do not know] when the end of science will come. ... What I do know is that our species is dumber than we normally admit to ourselves. This limit of our mental faculties, and not necessarily of science itself, ensures to me that we have only just begun to figure out the universe.
In Death by Black Hole: And Other Cosmic Quandaries (2007), 17.
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If we may believe our logicians, man is distinguished from all other creatures by the faculty of laughter.
In The Spectator (26 Sep 1712), No. 494, as collected in Vol. 7 (1729, 10th ed.), 84.
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In mathematics two ends are constantly kept in view: First, stimulation of the inventive faculty, exercise of judgment, development of logical reasoning, and the habit of concise statement; second, the association of the branches of pure mathematics with each other and with applied science, that the pupil may see clearly the true relations of principles and things.
In 'Aim of the Mathematical Instruction', International Commission on Teaching of Mathematics, American Report: United States Bureau of Education: Bulletin 1912, No. 4, 7.
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In no case may we interpret an action [of an animal] as the outcome of the exercise of a higher psychical faculty, if it can be interpreted as the outcome of the exercise of one which stands lower in the psychological scale.
[Morgan's canon, the principle of parsimony in animal research.]
An Introduction to Comparative Psychology (1894), 53.
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In the mathematics I can report no deficience, except that it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it. So that as tennis is a game of no use in itself, but of great use in respect it maketh a quick eye and a body ready to put itself into all postures; so in the mathematics, that use which is collateral and intervenient is no less worthy than that which is principal and intended.
As translated in John Fauvel and Jeremy Gray (eds.) A History of Mathematics: A Reader (1987), 290-291. From De Augmentis, Book 3, The Advancement of Learning (1605), Book 2. Reprinted in The Two Books of Francis Bacon: Of the Proficience and Advancement of Learning, Divine and Human (2009), 97.
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Indeed, the aim of teaching [mathematics] should be rather to strengthen his [the pupil’s] faculties, and to supply a method of reasoning applicable to other subjects, than to furnish him with an instrument for solving practical problems.
In John Perry (ed.), Discussion on the Teaching of Mathematics (1901), 84. The discussion took place on 14 Sep 1901 at the British Association at Glasgow, during a joint meeting of the mathematics and physics sections with the education section. The proceedings began with an address by John Perry. Magnus spoke in the Discussion that followed.
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It goes so heavily with my disposition that this goodly frame, the earth, seems to me a sterile promontory. This most excellent canopy the air, look you, this brave o'erhanging, this majestic roof fretted with golden fire—why, it appears no other thing to me than a foul and pestilent congregation of vapours. What a piece of work is a man. How noble in reason, how infinite in faculty, in form and moving, how express and admirable, in action, how like an angel! in apprehension, how like a god—the beauty of the world, the paragon of animals! And yet to me, what is this quintessence of dust? Man delights not me—no, nor woman neither, though by your smiling you seem to say so.
Hamlet (1601), II, ii.
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It is a happy world after all. The air, the earth, the water teem with delighted existence. In a spring noon, or a summer evening, on whichever side I turn my eyes, myriads of happy beings crowd upon my view. “The insect youth are on the wing.” Swarms of new-born flies are trying their pinions in the air. Their sportive motions, their wanton mazes, their gratuitous activity testify their joy and the exultation they feel in their lately discovered faculties … The whole winged insect tribe, it is probable, are equally intent upon their proper employments, and under every variety of constitution, gratified, and perhaps equally gratified, by the offices which the author of their nature has assigned to them.
Natural Theology: or, Evidences of the Existence and Attributes of The Deity, Collected from the Appearances of Nature (1802), 490-1.
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It is admitted by all that a finished or even a competent reasoner is not the work of nature alone; the experience of every day makes it evident that education develops faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided it can be reasoned upon with certainty. The properties of mind or matter, or the study of languages, mathematics, or natural history, may be chosen for this purpose. Now of all these, it is desirable to choose the one which admits of the reasoning being verified, that is, in which we can find out by other means, such as measurement and ocular demonstration of all sorts, whether the results are true or not. When the guiding property of the loadstone was first ascertained, and it was necessary to learn how to use this new discovery, and to find out how far it might be relied on, it would have been thought advisable to make many passages between ports that were well known before attempting a voyage of discovery. So it is with our reasoning faculties: it is desirable that their powers should be exerted upon objects of such a nature, that we can tell by other means whether the results which we obtain are true or false, and this before it is safe to trust entirely to reason. Now the mathematics are peculiarly well adapted for this purpose, on the following grounds:
1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing.
2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general.
3. The demonstration is strictly logical, taking nothing for granted except self-evident first principles, resting nothing upon probability, and entirely independent of authority and opinion.
4. When the conclusion is obtained by reasoning, its truth or falsehood can be ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if, as was said before, reason is not to be the instructor, but the pupil.
5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded. Between the meaning of terms there is no distinction, except a total distinction, and all adjectives and adverbs expressing difference of degrees are avoided.
In On the Study and Difficulties of Mathematics (1898), chap. 1.
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It is not, indeed, strange that the Greeks and Romans should not have carried ... any ... experimental science, so far as it has been carried in our time; for the experimental sciences are generally in a state of progression. They were better understood in the seventeenth century than in the sixteenth, and in the eighteenth century than in the seventeenth. But this constant improvement, this natural growth of knowledge, will not altogether account for the immense superiority of the modern writers. The difference is a difference not in degree, but of kind. It is not merely that new principles have been discovered, but that new faculties seem to be exerted. It is not that at one time the human intellect should have made but small progress, and at another time have advanced far; but that at one time it should have been stationary, and at another time constantly proceeding. In taste and imagination, in the graces of style, in the arts of persuasion, in the magnificence of public works, the ancients were at least our equals. They reasoned as justly as ourselves on subjects which required pure demonstration.
History (May 1828). In Samuel Austin Allibone, Prose Quotations from Socrates to Macaulay (1880), 36.
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Its [mathematical analysis] chief attribute is clearness; it has no means for expressing confused ideas. It compares the most diverse phenomena and discovers the secret analogies which unite them. If matter escapes us, as that of air and light because of its extreme tenuity, if bodies are placed far from us in the immensity of space, if man wishes to know the aspect of the heavens at successive periods separated by many centuries, if gravity and heat act in the interior of the solid earth at depths which will forever be inaccessible, mathematical analysis is still able to trace the laws of these phenomena. It renders them present and measurable, and appears to be the faculty of the human mind destined to supplement the brevity of life and the imperfection of the senses, and what is even more remarkable, it follows the same course in the study of all phenomena; it explains them in the same language, as if in witness to the unity and simplicity of the plan of the universe, and to make more manifest the unchangeable order which presides over all natural causes.
From Théorie Analytique de la Chaleur (1822), Discours Préliminaire, xiv, (Theory of Heat, Introduction), as translated by Alexander Freeman in The Analytical Theory of Heat (1878), 7.
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I’ve often been quoted as saying I would rather be governed by the first two thousand people listed in the Boston telephone directory than by the two thousand people on the faculty of Harvard University.
On NBC TV Meet The Press (17 Oct 1965), as quoted and cited in Ralph Keyes, The Quote Verifier: Who Said What, Where, and When (2006), 82-83.
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John Bahcall, an astronomer on the Institute of Advanced Study faculty since 1970 likes to tell the story of his first faculty dinner, when he found himself seated across from Kurt Gödel, … a man dedicated to logic and the clean certainties of mathematical abstraction. Bahcall introduced himself and mentioned that he was a physicist. Gödel replied, “I don’t believe in natural science.”
As stated in Adam Begley, 'The Lonely Genius Club', New York Magazine (30 Jan 1995), 63.
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Logic teaches us that on such and such a road we are sure of not meeting an obstacle; it does not tell us which is the road that leads to the desired end. For this, it is necessary to see the end from afar, and the faculty which teaches us to see is intuition. Without it, the geometrician would be like a writer well up in grammar but destitute of ideas.
…...
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Mathematics gives the young man a clear idea of demonstration and habituates him to form long trains of thought and reasoning methodically connected and sustained by the final certainty of the result; and it has the further advantage, from a purely moral point of view, of inspiring an absolute and fanatical respect for truth. In addition to all this, mathematics, and chiefly algebra and infinitesimal calculus, excite to a high degree the conception of the signs and symbols—necessary instruments to extend the power and reach of the human mind by summarizing an aggregate of relations in a condensed form and in a kind of mechanical way. These auxiliaries are of special value in mathematics because they are there adequate to their definitions, a characteristic which they do not possess to the same degree in the physical and mathematical [natural?] sciences.
There are, in fact, a mass of mental and moral faculties that can be put in full play only by instruction in mathematics; and they would be made still more available if the teaching was directed so as to leave free play to the personal work of the student.
In 'Science as an Instrument of Education', Popular Science Monthly (1897), 253.
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Mathematics make the mind attentive to the objects which it considers. This they do by entertaining it with a great variety of truths, which are delightful and evident, but not obvious. Truth is the same thing to the understanding as music to the ear and beauty to the eye. The pursuit of it does really as much gratify a natural faculty implanted in us by our wise Creator as the pleasing of our senses: only in the former case, as the object and faculty are more spiritual, the delight is more pure, free from regret, turpitude, lassitude, and intemperance that commonly attend sensual pleasures.
In An Essay on the Usefulness of Mathematical Learning (1701), 3-4.
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Nature never makes excellent things, for mean or no uses: and it is hardly to be conceived, that our infinitely wise Creator, should make so admirable a Faculty, as the power of Thinking, that Faculty which comes nearest the Excellency of his own incomprehensible Being, to be so idlely and uselesly employ’d, at least 1/4 part of its time here, as to think constantly, without remembering any of those Thoughts, without doing any good to it self or others, or being anyway useful to any other part of Creation.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 2, Chapter 1, Section 15, 113.
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Of all the intellectual faculties, judgment is the last to arrive at maturity. The child should give its attention either to subjects where no error is possible at all, such as mathematics, or to those in which there is no particular danger in making a mistake, such as languages, natural science, history, and so on.
In Arthur Schopenhauer and T. Bailey (ed., trans.) Essays of Arthur Schopenhauer (1902), 67.
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Organs, faculties, powers, capacities, or whatever else we call them; grow by use and diminish from disuse, it is inferred that they will continue to do so. And if this inference is unquestionable, then is the one above deduced from it—that humanity must in the end become completely adapted to its conditions—unquestionable also. Progress, therefore, is not an accident, but a necessity.
Social Statics: Or, The Conditions Essential to Human Happiness Specified, and the First of them Developed (1851), 65.
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Psychology is a part of the science of life or biology. … As the physiologist inquires into the way in which the so-called “functions” of the body are performed, so the psychologist studies the so-called “faculties” of the mind.
In Hume (1879), 50.
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Science quickens and cultivates directly the faculty of observation, which in very many persons lies almost dormant through life, the power of accurate and rapid generalizations, and the mental habit of method and arrangement; it accustoms young persons to trace the sequence of cause and effect; it familiarizes then with a kind of reasoning which interests them, and which they can promptly comprehend; and it is perhaps the best corrective for that indolence which is the vice of half-awakened minds, and which shrinks from any exertion that is not, like an effort of memory, merely mechanical.
Anonymous
Report of the Royal Commission on Education (1861), Parliamentary Papers (1864), Vol 20, 32-33, as cited in Paul White, Thomas Huxley: Making the "Man of Science" (2003), 77, footnote. Also quoted in John Lubbock, The Pleasures of Life (1887, 2007), 63.
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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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That mathematics “do not cultivate the power of generalization,”; … will be admitted by no person of competent knowledge, except in a very qualified sense. The generalizations of mathematics, are, no doubt, a different thing from the generalizations of physical science; but in the difficulty of seizing them, and the mental tension they require, they are no contemptible preparation for the most arduous efforts of the scientific mind. Even the fundamental notions of the higher mathematics, from those of the differential calculus upwards are products of a very high abstraction. … To perceive the mathematical laws common to the results of many mathematical operations, even in so simple a case as that of the binomial theorem, involves a vigorous exercise of the same faculty which gave us Kepler’s laws, and rose through those laws to the theory of universal gravitation. Every process of what has been called Universal Geometry—the great creation of Descartes and his successors, in which a single train of reasoning solves whole classes of problems at once, and others common to large groups of them—is a practical lesson in the management of wide generalizations, and abstraction of the points of agreement from those of difference among objects of great and confusing diversity, to which the purely inductive sciences cannot furnish many superior. Even so elementary an operation as that of abstracting from the particular configuration of the triangles or other figures, and the relative situation of the particular lines or points, in the diagram which aids the apprehension of a common geometrical demonstration, is a very useful, and far from being always an easy, exercise of the faculty of generalization so strangely imagined to have no place or part in the processes of mathematics.
In An Examination of Sir William Hamilton’s Philosophy (1878), 612-13.
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The child asks, “What is the moon, and why does it shine?” “What is this water and where does it run?” “What is this wind?” “What makes the waves of the sea?” “Where does this animal live, and what is the use of this plant?” And if not snubbed and stunted by being told not to ask foolish questions, there is no limit to the intellectual craving of a young child; nor any bounds to the slow, but solid, accretion of knowledge and development of the thinking faculty in this way. To all such questions, answers which are necessarily incomplete, though true as far as they go, may be given by any teacher whose ideas represent real knowledge and not mere book learning; and a panoramic view of Nature, accompanied by a strong infusion of the scientific habit of mind, may thus be placed within the reach of every child of nine or ten.
In 'Scientific Education', Lay Sermons, Addresses, and Reviews (1870), 71. https://books.google.com/books?id=13cJAAAAIAAJ Thomas Henry Huxley - 1870
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The conditions that direct the order of the whole of the living world around us, are marked by their persistence in improving the birthright of successive generations. They determine, at much cost of individual comfort, that each plant and animal shall, on the general average, be endowed at its birth with more suitable natural faculties than those of its representative in the preceding generation.
In 'The Observed Order of Events', Inquiries Into Human Faculty and Its Development (1882), 229.
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The faculty for remembering is not diminished in proportion to what one has learnt, just as little as the number of moulds in which you cast sand lessens its capacity for being cast in new moulds.
Religion: a Dialogue, and Other Essays (1890), 99.
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The faculty of resolution is possibly much invigorated by mathematical study, and especially by that highest branch of it which, unjustly, merely on account of its retrograde operations, has been called, as if par excellence, analysis.
In The Murders in Rue Morgue.
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The fairest thing we can experience is the mysterious. It is the fundamental emotion which stands at the cradle of true science. He who knows it not, and can no longer wonder, no longer feel amazement, is as good as dead. We all had this priceless talent when we were young. But as time goes by, many of us lose it. The true scientist never loses the faculty of amazement. It is the essence of his being.
Newsweek (31 Mar 1958).
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The great mathematician, like the great poet or naturalist or great administrator, is born. My contention shall be that where the mathematic endowment is found, there will usually be found associated with it, as essential implications in it, other endowments in generous measure, and that the appeal of the science is to the whole mind, direct no doubt to the central powers of thought, but indirectly through sympathy of all, rousing, enlarging, developing, emancipating all, so that the faculties of will, of intellect and feeling learn to respond, each in its appropriate order and degree, like the parts of an orchestra to the “urge and ardor” of its leader and lord.
In Lectures on Science, Philosophy and Art (1908), 22.
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The imagination is … the most precious faculty with which a scientist can be equipped. It is a risky possession, it is true, for it leads him astray a hundred times for once that it conducts him to truth; but without it he has no chance at all of getting at the meaning of the facts he has learned or discovered.
In Respiratory Proteids: Researches in Biological Chemistry (1897), Preface, iv.
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The metaphysical philosopher from his point of view recognizes mathematics as an instrument of education, which strengthens the power of attention, develops the sense of order and the faculty of construction, and enables the mind to grasp under the simple formulae the quantitative differences of physical phenomena.
In Dialogues of Plato (1897), Vol. 2, 78.
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The mind uses its faculty for creating only when experience forces it to do so.
From La Science et l’Hypothèse (1908), 43 as translated by George Bruce Halsted in Science and Hypothesis (1905), 25. From the original French, “L’esprit n’use de sa faculté créatrice que quand l’expérience lui en impose la nécessité”.
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The moral faculties are generally and justly esteemed as of higher value than the intellectual powers. But we should bear in mind that the activity of the mind in vividly recalling past impressions is one of the fundamental though secondary bases of conscience. This affords the strongest argument for educating and stimulating in all possible ways the intellectual faculties of every human being.
…...
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The most beautiful emotion we can experience is the mystical. It is the power of all true art and science. He to whom this emotion is a stranger, who can no longer wonder and stand rapt in awe, is as good as dead. To know that what is impenetrable to us really exists, manifesting itself as the highest wisdom and the most radiant beauty, which our dull faculties can comprehend only in their most primitive forms — this knowledge, this feeling, is at the center of true religiousness. In this sense, and in this sense only, I belong to the rank of devoutly religious men.
As quoted in Philip Frank, Einstein: His Life and Times (1947), chap. 12, sec. 5 - “Einstein’s Attitude Toward Religion.”
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The one who stays in my mind as the ideal man of science is, not Huxley or Tyndall, Hooker or Lubbock, still less my friend, philosopher and guide Herbert Spencer, but Francis Galton, whom I used to observe and listen to—I regret to add, without the least reciprocity—with rapt attention. Even to-day. I can conjure up, from memory’s misty deep, that tall figure with its attitude of perfect physical and mental poise; the clean-shaven face, the thin, compressed mouth with its enigmatical smile; the long upper lip and firm chin, and, as if presiding over the whole personality of the man, the prominent dark eyebrows from beneath which gleamed, with penetrating humour, contemplative grey eyes. Fascinating to me was Francis Galton’s all-embracing but apparently impersonal beneficence. But, to a recent and enthusiastic convert to the scientific method, the most relevant of Galton’s many gifts was the unique contribution of three separate and distinct processes of the intellect; a continuous curiosity about, and rapid apprehension of individual facts, whether common or uncommon; the faculty for ingenious trains of reasoning; and, more admirable than either of these, because the talent was wholly beyond my reach, the capacity for correcting and verifying his own hypotheses, by the statistical handling of masses of data, whether collected by himself or supplied by other students of the problem.
In My Apprenticeship (1926), 134-135.
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The present gigantic development of the mathematical faculty is wholly unexplained by the theory of natural selection, and must be due to some altogether distinct cause.
In Darwinism, chap. 15.
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The problems of the infinite have challenged man’s mind and have fired his imagination as no other single problem in the history of thought. The infinite appears both strange and familiar, at times beyond our grasp, at times easy and natural to understand. In conquering it, man broke the fetters that bound him to earth. All his faculties were required for this conquest—his reasoning powers, his poetic fancy, his desire to know.
With co-author James R Newman, in 'Beyond the Google', Mathematics and the Imagination (1940), 35.
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The scientist, if he is to be more than a plodding gatherer of bits of information, needs to exercise an active imagination. The scientists of the past whom we now recognize as great are those who were gifted with transcendental imaginative powers, and the part played by the imaginative faculty of his daily life is as least as important for the scientist as it is for the worker in any other field—much more important than for most. A good scientist thinks logically and accurately when conditions call for logical and accurate thinking—but so does any other good worker when he has a sufficient number of well-founded facts to serve as the basis for the accurate, logical induction of generalizations and the subsequent deduction of consequences.
‘Imagination in Science’, Tomorrow (Dec 1943), 38-9. Quoted In Barbara Marinacci (ed.), Linus Pauling In His Own Words: Selected Writings, Speeches, and Interviews (1995), 82.
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The student skit at Christmas contained a plaintive line: “Give us Master’s exams that our faculty can pass, or give us a faculty that can pass our Master’s exams.”
In I Want to be a Mathematician: An Automathography (1985), 146.
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The study of mathematics cannot be replaced by any other activity that will train and develop man’s purely logical faculties to the same level of rationality.
In The American Mathematical Monthly (1949), 56, 19. Excerpted in John Ewing (ed,), A Century of Mathematics: Through the Eyes of the Monthly (1996), 186.
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There is no fundamental difference between man and the higher animals in their mental faculties ... The lower animals, like man, manifestly feel pleasure and pain, happiness, and misery.
…...
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There is no study in the world which brings into more harmonious action all the faculties of the mind than [mathematics], … or, like this, seems to raise them, by successive steps of initiation, to higher and higher states of conscious intellectual being.
In Presidential Address to British Association (19 Aug 1869), 'A Plea for the Mathematician', published in Nature (6 Jan 1870), 1, 261.
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There’s a touch of the priesthood in the academic world, a sense that a scholar should not be distracted by the mundane tasks of day-to-day living. I used to have great stretches of time to work. Now I have research thoughts while making peanut butter and jelly sandwiches. Sure it’s impossible to write down ideas while reading “Curious George” to a two-year-old. On the other hand, as my husband was leaving graduate school for his first job, his thesis advisor told him, “You may wonder how a professor gets any research done when one has to teach, advise students, serve on committees, referee papers, write letters of recommendation, interview prospective faculty. Well, I take long showers.”
In 'In Her Own Words: Six Mathematicians Comment on Their Lives and Careers: Susan Landau', Notices of the AMS (Sep 1991), 38, No. 7, 704.
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This [the fact that the pursuit of mathematics brings into harmonious action all the faculties of the human mind] accounts for the extraordinary longevity of all the greatest masters of the Analytic art, the Dii Majores of the mathematical Pantheon. Leibnitz lived to the age of 70; Euler to 76; Lagrange to 77; Laplace to 78; Gauss to 78; Plato, the supposed inventor of the conic sections, who made mathematics his study and delight, who called them the handles or aids to philosophy, the medicine of the soul, and is said never to have let a day go by without inventing some new theorems, lived to 82; Newton, the crown and glory of his race, to 85; Archimedes, the nearest akin, probably, to Newton in genius, was 75, and might have lived on to be 100, for aught we can guess to the contrary, when he was slain by the impatient and ill mannered sergeant, sent to bring him before the Roman general, in the full vigour of his faculties, and in the very act of working out a problem; Pythagoras, in whose school, I believe, the word mathematician (used, however, in a somewhat wider than its present sense) originated, the second founder of geometry, the inventor of the matchless theorem which goes by his name, the pre-cognizer of the undoubtedly mis-called Copernican theory, the discoverer of the regular solids and the musical canon who stands at the very apex of this pyramid of fame, (if we may credit the tradition) after spending 22 years studying in Egypt, and 12 in Babylon, opened school when 56 or 57 years old in Magna Græcia, married a young wife when past 60, and died, carrying on his work with energy unspent to the last, at the age of 99. The mathematician lives long and lives young; the wings of his soul do not early drop off, nor do its pores become clogged with the earthy particles blown from the dusty highways of vulgar life.
In Presidential Address to the British Association, Collected Mathematical Papers, Vol. 2 (1908), 658.
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Till the fifteenth century little progress appears to have been made in the science or practice of music; but since that era it has advanced with marvelous rapidity, its progress being curiously parallel with that of mathematics, inasmuch as great musical geniuses appeared suddenly among different nations, equal in their possession of this special faculty to any that have since arisen. As with the mathematical so with the musical faculty it is impossible to trace any connection between its possession and survival in the struggle for existence.
In 'Darwinism Applied to Man', Darwinism: An Exposition of the Theory of Natural Selection with Some of Its Applications (1901), Chap. 15, 468.
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To unfold the secret laws and relations of those high faculties of thought by which all beyond the merely perceptive knowledge of the world and of ourselves is attained or matured, is a object which does not stand in need of commendation to a rational mind.
An Investigation of the Laws of Thought (1854), 3.
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We are apt to consider that invention is the result of spontaneous action of some heavenborn genius, whose advent we must patiently wait for, but cannot artificially produce. It is unquestionable, however, that education, legal enactments, and general social conditions have a stupendous influence on the development of the originative faculty present in a nation and determine whether it shall be a fountain of new ideas or become simply a purchaser from others of ready-made inventions.
Epigraph, without citation, in Roger Cullisin, Patents, Inventions and the Dynamics of Innovation: A Multidisciplinary Study (2007), ix.
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We are told that “Mathematics is that study which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation.” I think no statement could have been made more opposite to the facts of the case; that mathematical analysis is constantly invoking the aid of new principles, new ideas, and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activities of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world (to which the inner one in each individual man may, I think, be conceived to stand somewhat in the same relation of correspondence as a shadow to the object from which it is projected, or as the hollow palm of one hand to the closed fist which it grasps of the other), that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of the imagination and invention.
In Presidential Address to British Association, Exeter British Association Report (1869), pp. 1-9, in Collected Mathematical Papers, Vol. 2, 654.
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What Art was to the ancient world, Science is to the modern: the distinctive faculty. In the minds of men the useful has succeeded to the beautiful. … There are great truths to tell, if we had either the courage to announce them or the temper to receive them.
In Coningsby: or the New Generation (1844), Vol. 2, Book 4, Chap. 1, 2.
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Who has studied the works of such men as Euler, Lagrange, Cauchy, Riemann, Sophus Lie, and Weierstrass, can doubt that a great mathematician is a great artist? The faculties possessed by such men, varying greatly in kind and degree with the individual, are analogous with those requisite for constructive art. Not every mathematician possesses in a specially high degree that critical faculty which finds its employment in the perfection of form, in conformity with the ideal of logical completeness; but every great mathematician possesses the rarer faculty of constructive imagination.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A, Nature (1 Sep 1910), 84, 290.
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[E.H.] Moore was presenting a paper on a highly technical topic to a large gathering of faculty and graduate students from all parts of the country. When half way through he discovered what seemed to be an error (though probably no one else in the room observed it). He stopped and re-examined the doubtful step for several minutes and then, convinced of the error, he abruptly dismissed the meeting—to the astonishment of most of the audience. It was an evidence of intellectual courage as well as honesty and doubtless won for him the supreme admiration of every person in the group—an admiration which was in no wise diminished, but rather increased, when at a later meeting he announced that after all he had been able to prove the step to be correct.
In Obituary, 'Eliakim Hastings Moore', The American Mathematical Monthly (Apr 1933), 40, 191.
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[The] humanization of mathematical teaching, the bringing of the matter and the spirit of mathematics to bear not merely upon certain fragmentary faculties of the mind, but upon the whole mind, that this is the greatest desideratum is. I assume, beyond dispute.
Address (28 Mar 1912), Michigan School Masters' Club, Ann Arbor, 'The Humanization of the Teaching of Mathematics. Printed in Science (26 Apr 1912). Collected in The Human Worth of Rigorous Thinking: Essays and Addresses (1916), 62-63.
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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
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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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