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Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Home > Category Index for Science Quotations > Category Index M > Category: Mastery

Mastery Quotes (34 quotes)

All the human culture, all the results of art, science and technology that we see before us today, are almost exclusively the creative product of the Aryan. This very fact admits of the not unfounded inference that he alone was the founder of all higher humanity, therefore representing the prototype of all that we understand by the word 'man.' He is the Prometheus of mankind from whose shining brow the divine spark of genius has sprung at all times, forever kindling anew that fire of knowledge which illuminated the night of silent mysteries and thus caused man to climb the path to mastery over the other beings of the earth ... It was he who laid the foundations and erected the walls of every great structure in human culture.
Mein Kampf (1925-26), American Edition (1943), 290. In William Lawrence Shirer, The Rise and Fall of the Third Reich (1990), 86-87.
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Besides a mathematical inclination, an exceptionally good mastery of one’s native tongue is the most vital asset of a competent programmer.
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Creating a new theory is not like destroying an old barn and erecting a skyscraper in its place. It is rather like climbing a mountain, gaining new and wider views, discovering unexpected connections between our starting point and its rich environment. But the point from which we started out still exists and can be seen, although it appears smaller and forms a tiny part of our broad view gained by the mastery of the obstacles on our adventurous way up.
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Education is like a diamond with many facets: It includes the basic mastery of numbers and letters that give us access to the treasury of human knowledge, accumulated and refined through the ages; it includes technical and vocational training as well as instruction in science, higher mathematics, and humane letters.
In Proclamation 5463, for Education Day (19 Apr 1986). Collected in Public Papers of the Presidents of the United States: Ronald Reagan, 1986 (1988), 490.
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First, as concerns the success of teaching mathematics. No instruction in the high schools is as difficult as that of mathematics, since the large majority of students are at first decidedly disinclined to be harnessed into the rigid framework of logical conclusions. The interest of young people is won much more easily, if sense-objects are made the starting point and the transition to abstract formulation is brought about gradually. For this reason it is psychologically quite correct to follow this course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.
In Ueber den Mathematischen Unterricht an den hoheren Schulen; Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 11, 131.
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From the freedom to explore comes the joy of learning. From knowledge acquired by personal initiative arises the desire for more knowledge. And from mastery of the novel and beautiful world awaiting every child comes self-confidence.
In The Creation: An Appeal to Save Life on Earth (2010), 147.
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I also maintain that clear knowledge of natural science must be acquired, in the first instance, through mastery of medicine alone.
In Fielding Hudson Garrison, An Introduction to the History of Medicine (1929), 14.
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I trust ... I have succeeded in convincing you that modern chemistry is not, as it has so long appeared, an ever-growing accumulation of isolated facts, as impossible for a single intellect to co-ordinate as for a single memory to grasp.
The intricate formulae that hang upon these walls, and the boundless variety of phenomena they illustrate, are beginning to be for us as a labyrinth once impassable, but to which we have at length discovered the clue. A sense of mastery and power succeeds in our minds to the sort of weary despair with which we at first contemplated their formidable array. For now, by the aid of a few general principles, we find ourselves able to unravel the complexities of these formulae, to marshal the compounds which they represent in orderly series; nay, even to multiply their numbers at our will, and in a great measure to forecast their nature ere we have called them into existence. It is the great movement of modern chemistry that we have thus, for an hour, seen passing before us. It is a movement as of light spreading itself over a waste of obscurity, as of law diffusing order throughout a wilderness of confusion, and there is surely in its contemplation something of the pleasure which attends the spectacle of a beautiful daybreak, something of the grandeur belonging to the conception of a world created out of chaos.
Concluding remark for paper presented at the Friday Discourse of the the Royal Institution (7 Apr 1865). 'On the Combining Power of Atoms', Proceedings of the Royal Institution (1865), 4, No. 42, 416.
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If there be an order in which the human race has mastered its various kinds of knowledge, there will arise in every child an aptitude to acquire these kinds of knowledge in the same order. So that even were the order intrinsically indifferent, it would facilitate education to lead the individual mind through the steps traversed by the general mind. But the order is not intrinsically indifferent; and hence the fundamental reason why education should be a repetition of civilization in little.
Education: Intellectual, Moral and Physical (1861), 76.
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It is not an easy paper to follow, for the items that require retention throughout the analysis are many, and it is fatal to one's understanding to lose track of any of them. Mastery of this paper, however, can give one the strong feeling of being ableto master anything else [one] might have to wrestle within biology.
Describing the paper 'A Correlation of Cytological and Genetic Crossings-over in Zea mays' published by Barbara McClintock and her student Harriet Creighton in the Proceedings of the National Academy of Sciences (1931).
Classic Papers in Genetics (1959), 156.
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It is the triumph of civilization that at last communities have obtained such a mastery over natural laws that they drive and control them. The winds, the water, electricity, all aliens that in their wild form were dangerous, are now controlled by human will, and are made useful servants.
In Tryon Edwards, A Dictionary of Thoughts (1908), 75.
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Man is a rational animal—so at least I have been told. … Aristotle, so far as I know, was the first man to proclaim explicitly that man is a rational animal. His reason for this view was … that some people can do sums. … It is in virtue of the intellect that man is a rational animal. The intellect is shown in various ways, but most emphatically by mastery of arithmetic. The Greek system of numerals was very bad, so that the multiplication table was quite difficult, and complicated calculations could only be made by very clever people.
From An Outline of Intellectual Rubbish (1937, 1943), 5. Collected in The Basic Writings of Bertrand Russell (2009), 45.
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Only by following out the injunction of our great predecessor [William Harvey] to search out and study the secrets of Nature by way of experiment, can we hope to attain to a comprehension of 'the wisdom of the body and the understanding of the heart,' and thereby to the mastery of disease and pain, which will enable us to relieve the burden of mankind.
'The Wisdom of the Body', The Lancet (1923), 205, 870.
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Only one who devotes himself to a cause with his whole strength and soul can be a true master. For this reason mastery demands all of a person.
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Science is not about control. It is about cultivating a perpetual sense of wonder in the face of something that forever grows one step richer and subtler than our latest theory about it. It is about reverence, not mastery.
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Science offers us complete mastery over our environment and our own destiny, yet instead of rejoicing we feel deeply afraid. Why should this be?
From transcript of BBC radio Reith Lecture (12 Nov 1967), 'A Runaway World', on the bbc.co.uk website.
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Science will never be able to reduce the value of a sunset to arithmetic. Nor can it reduce friendship or statesmanship to a formula. Laughter and love, pain and loneliness, the challenge of beauty and truth: these will always surpass the scientific mastery of nature.
Louis Orr
As President, American Medical Association. From Commencement address at Emory University, Atlanta, 6 Jun 60
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Some see a clear line between genetic enhancement and other ways that people seek improvement in their children and themselves. Genetic manipulation seems somehow worse - more intrusive, more sinister - than other ways of enhancing performance and seeking success. But, morally speaking, the difference is less significant than it seems. Bioengineering gives us reason to question the low-tech, high-pressure child-rearing practices we commonly accept. The hyperparenting familiar in our time represents an anxious excess of mastery and dominion that misses the sense of life as a gift. This draws it disturbingly close to eugenics... Was the old eugenics objectionable only insofar as it was coercive? Or is there something inherently wrong with the resolve to deliberately design our progeny's traits... But removing coercion does not vindicate eugenics. The problem with eugenics and genetic engineering is that they represent a one-sided triumph of willfulness over giftedness, of dominion over reverence, of molding over beholding.
Michael J. Sandel, 'The Case Against Perfection', The Atlantic Monthly (Apr 2004).
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Technical skill is mastery of complexity while creativity is mastery of simplicity.
In Catastrophe Theory: selected papers, 1972-1977 (1977).
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The central task of science is to arrive, stage by stage, at a clearer comprehension of nature, but this does not mean, as it is sometimes claimed to mean, a search for mastery over nature.
In Late Night Thoughts on Listening to Mahler's Ninth Symphony(1984), 153.
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The professor may choose familiar topics as a starting point. The students collect material, work problems, observe regularities, frame hypotheses, discover and prove theorems for themselves. … the student knows what he is doing and where he is going; he is secure in his mastery of the subject, strengthened in confidence of himself. He has had the experience of discovering mathematics. He no longer thinks of mathematics as static dogma learned by rote. He sees mathematics as something growing and developing, mathematical concepts as something continually revised and enriched in the light of new knowledge. The course may have covered a very limited region, but it should leave the student ready to explore further on his own.
In A Concrete Approach to Abstract Algebra (1959), 1-2.
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The progressive development of man is vitally dependent on invention. It is the most important product of his creative brain. Its ultimate purpose is the complete mastery of mind over the material world, the harnessing of the forces of nature to human needs.
Opening lines of 'My Inventions', Electrical Experimenter (1919). Reprinted in My Inventions: The Autobiography of Nikola Tesla (2011), 4.
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The science [of mathematics] has grown to such vast proportion that probably no living mathematician can claim to have achieved its mastery as a whole.
In An Introduction to Mathematics (1911), 262.
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The solution of problems is one of the lowest forms of mathematical research, … yet its educational value cannot be overestimated. It is the ladder by which the mind ascends into higher fields of original research and investigation. Many dormant minds have been aroused into activity through the mastery of a single problem.
With co-editor J. M. Colaw, Editorial introducing the first issue of The American Mathematical Monthly (Jan 1894), 1, No. 1, 2.
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The student of medicine can no more hope to advance in the mastery of his subject with a loose and careless mind than the student of mathematics. If the laws of abstract truth require such rigid precision from those who study them, we cannot believe the laws of nature require less. On the contrary, they would seem to require more; for the facts are obscure, the means of inquiry imperfect, and in every exercise of the mind there are peculiar facilities to err.
From Address (Oct 1874) delivered at Guy’s Hospital, 'On The Study of Medicine', printed in British Medical journal (1874), 2, 425. Collected in Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), 6.
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The training which mathematics gives in working with symbols is an excellent preparation for other sciences; … the world’s work requires constant mastery of symbols.
In Teaching of Mathematics in the Elementary and the Secondary School (1906), 42.
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There is a moral as well as an intellectual objection to the custom, frequent in these times, of making education consist in a mere smattering of twenty different things, instead of in the mastery of five or six.
As quoted in Tryon Edwards, A Dictionary of Thoughts: Being a Cyclopedia of Laconic Quotations (1891), 266, attributed in the body of the text, with the single name, “Chadwick,” then, in the prefatory material, the 'Index of Authors' lists only “Chadwick, Erwin”. HOWEVER, another quote in this book (“The education of the intellect…”), also attributed in the body of the text to the single name “Chadwick”, has been definitely identified by Webmaster to be from a sermon by clergyman, John White Chadwick. This quote also seems to be more likely from a sermon, than from the pen of Edwin Chadwick, an urban health reformer. Having found no primary source to verify which person authored the quote, Webmaster—tentatively—places this quote under John W. Chadwick. If you know the primary source, please contact Webmaster.
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There is only one subject matter for education, and that is Life in all its manifestations. Instead of this single unity, we offer children—Algebra, from which nothing follows; Geometry, from which nothing follows; Science, from which nothing follows; History, from which nothing follows; a Couple of Languages, never mastered; and lastly, most dreary of all, Literature, represented by plays of Shakespeare, with philological notes and short analyses of plot and character to be in substance committed to memory.
In 'The Aims of Education', The Aims of Education: & Other Essays (1917), 10.
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This quality of genius is, sometimes, difficult to be distinguished from talent, because high genius includes talent. It is talent, and something more. The usual distinction between genius and talent is, that one represents creative thought, the other practical skill: one invents, the other applies. But the truth is, that high genius applies its own inventions better than talent alone can do. A man who has mastered the higher mathematics, does not, on that account, lose his knowledge of arithmetic. Hannibal, Napoleon, Shakespeare, Newton, Scott, Burke, Arkwright, were they not men of talent as well as men of genius?
In 'Genius', Wellman’s Miscellany (Dec 1871), 4, No. 6, 203.
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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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Throughout the last four hundred years, during which the growth of science had gradually shown men how to acquire knowledge of the ways of nature and mastery over natural forces, the clergy have fought a losing battle against science, in astronomy and geology, in anatomy and physiology, in biology and psychology and sociology. Ousted from one position, they have taken up another. After being worsted in astronomy, they did their best to prevent the rise of geology; they fought against Darwin in biology, and at the present time they fight against scientific theories of psychology and education. At each stage, they try to make the public forget their earlier obscurantism, in order that their present obscurantism may not be recognized for what it is.
From An Outline of Intellectual Rubbish (1937, 1943), 6. Collected in The Basic Writings of Bertrand Russell (2009), 47.
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To be worthy of the name, an experimenter must be at once theorist and practitioner. While he must completely master the art of establishing experimental facts, which are the materials of science, he must also clearly understand the scientific principles which guide his reasoning through the varied experimental study of natural phenomena. We cannot separate these two things: head and hand. An able hand, without a head to direct it, is a blind tool; the head is powerless without its executive hand.
In Claude Bernard and Henry Copley Greene (trans.), An Introduction to the Study of Experimental Medicine (1927, 1957), 3.
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We often observe in lawyers, who as Quicquid agunt homines is the matter of law suits, are sometimes obliged to pick up a temporary knowledge of an art or science, of which they understood nothing till their brief was delivered, and appear to be much masters of it.
In The Life of Samuel Johnson (1820), Vol. 1, 218. The Latin phrase translates as “what people do.”
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[Understanding] dispels superstition, and it gives you a feeling of mastery which you can’t have any other way.
In interview, Rushworth M. Kidder, 'Grounded in Space Science', Christian Science Monitor (22 Dec 1989).
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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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- 90 -
Antoine Lavoisier
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Charles Babbage
Ibn Khaldun
Euclid
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Winston Churchill
- 80 -
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Bible
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- 70 -
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- 60 -
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- 50 -
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- 40 -
Pierre Fermat
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- 30 -
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- 20 -
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