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Home > Dictionary of Science Quotations > Scientist Names Index D > Augustus De Morgan Quotes

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Augustus De Morgan
(27 Jun 1806 - 18 Mar 1871)

English mathematician and logician who did important work in abstract symbolic logic, the theory of relations, and formulated De Morgan's laws.

Science Quotes by Augustus De Morgan (25 quotes)

>> Click for Augustus De Morgan Quotes on | Mathematics |

[About Francis Baily] The history of the astronomy of the nineteenth century will be incomplete without a catalogue of his labours. He was one of the founders of the Astronomical Society, and his attention to its affairs was as accurate and minute as if it had been a firm of which he was the chief clerk, with expectation of being taken into partnership.
— Augustus De Morgan
In Supplement to the Penny Cyclopaedia. Quoted in Sophia Elizabeth De Morgan, Memoir of Augustus De Morgan (1882), 46
Science quotes on:  |  19th Century (22)  |  Accurate (21)  |  Affair (25)  |  Astronomy (180)  |  Attention (85)  |  Catalogue (2)  |  Chief (25)  |  Clerk (3)  |  Expectation (47)  |  Firm (20)  |  Founder (12)  |  History (314)  |  Incomplete (14)  |  Labour (36)  |  Minute (32)  |  Partnership (4)

As to writing another book on geometry [to replace Euclid] the middle ages would have as soon thought of composing another New Testament.
— Augustus De Morgan
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 130.
Science quotes on:  |  Euclid (28)  |  Geometry (100)

Common integration is only the memory of differentiation...
— Augustus De Morgan
Science quotes on:  |  Differentiation (17)  |  Integration (14)  |  Mathematics (597)

Considerable obstacles generally present themselves to the beginner, in studying the elements of Solid Geometry, from the practice which has hitherto uniformly prevailed in this country, of never submitting to the eye of the student, the figures on whose properties he is reasoning, but of drawing perspective representations of them upon a plane. ...I hope that I shall never be obliged to have recourse to a perspective drawing of any figure whose parts are not in the same plane.
— Augustus De Morgan
Quoted in Adrian Rice, 'What Makes a Great Mathematics Teacher?' The American Mathematical Monthly, (June-July 1999), 540.
Science quotes on:  |  Art (217)  |  Geometry (100)

During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical. The question now is, not whether this or that hypothesis is better or worse to the pure thought, but whether it accords with observed phenomena in those consequences which can be shown necessarily to follow from it, if it be true
— Augustus De Morgan
In Augustus De Morgan and Sophia Elizabeth De Morgan (ed.), A Budget of Paradoxes (1872), 2.
Science quotes on:  |  Accord (22)  |  Basis (66)  |  Better (146)  |  Century (103)  |  Consequence (81)  |  Follow (79)  |  Hypothesis (231)  |  Knowledge (1148)  |  Mathematics (597)  |  Necessity (125)  |  Observation (421)  |  Phenomenon (223)  |  Physical Science (56)  |  Pure (63)  |  Question (327)  |  Thought (400)  |  Truth (764)  |  Worse (17)

Every science that has thriven has thriven upon its own symbols: logic, the only science which is admitted to have made no improvements in century after century, is the only one which has grown no symbols.
— Augustus De Morgan
Transactions Cambridge Philosophical Society, vol. X, 1864, p.184
Science quotes on:  |  Logic (190)  |  Symbol (37)

Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn have, greater fleas to go on;
While these again have greater still, and greater still, and so on.
[He was imitating: 'So, naturalists observe, a flea Has smaller fleas that on him prey; And these have smaller still to bite 'em; And so proceed ad infinitum.' Poetry, a Rhapsody, by Jonathan Swift.]
— Augustus De Morgan
A Budget of Paradoxes (1915), first published 1872, Vol. 2, 191.
Science quotes on:  |  Poem (86)

I don't quite hear what you say, but I beg to differ entirely with you.
— Augustus De Morgan
Science quotes on:  |  Quip (76)

I end with a word on the new symbols which I have employed. Most writers on logic strongly object to all symbols. ... I should advise the reader not to make up his mind on this point until he has well weighed two facts which nobody disputes, both separately and in connexion. First, logic is the only science which has made no progress since the revival of letters; secondly, logic is the only science which has produced no growth of symbols.
— Augustus De Morgan
Science quotes on:  |  Logic (190)  |  Symbol (37)

I was x years old in the year x2.
When asked about his age (43).
— Augustus De Morgan
Quoted in H. Eves, In Mathematical Circles (1969).
Science quotes on:  |  Biography (228)  |  Mathematics (597)

Imagine a person with a gift of ridicule [He might say] First that a negative quantity has no logarithm; secondly that a negative quantity has no square root; thirdly that the first non-existent is to the second as the circumference of a circle is to the diameter.
— Augustus De Morgan
Science quotes on:  |  Logarithm (4)  |  Mathematics (597)

Isaac Newton was born at Woolsthorpe, near Grantham, in Lincolnshire, on Christmas Day, 1642: a weakly and diminutive infant, of whom it is related that, at his birth, he might have found room in a quart mug. He died on March the 20th, 1727, after more than eighty-four years of more than average bodily health and vigour; it is a proper pendant to the story of the quart mug to state that he never lost more than one of his second teeth.
— Augustus De Morgan
In Essays on the life and work of Newton (), 4.
Science quotes on:  |  Birth (87)  |  Diminutive (3)  |  Health (141)  |  Infant (13)  |  Sir Isaac Newton (261)  |  Pendant (2)  |  Story (62)  |  Tooth (23)  |  Vigour (9)

It is easier to square the circle than to get round a mathematician.
— Augustus De Morgan
In Budget of Paradoxes (1872), 90.
Science quotes on:  |  Mathematician (178)

It was long before I got at the maxim, that in reading an old mathematician you will not read his riddle unless you plough with his heifer; you must see with his light, if you want to know how much he saw.
— Augustus De Morgan
Letter to W. R. Hamilton, 27 January 1853. In R. P. Graves (ed.), A Life of Sir W. R. Hamilton (1889), Vol. 3, 438.
Science quotes on:  |  Mathematician (178)

Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty (of the parallel axiom). He went so far as to write a paper, which he took with him to the Institute, and began to read it. But in the first paragraph something struck him that he had not observed: he muttered: 'Il faut que j'y songe encore', and put the paper in his pocket.' [I must think about it again]
— Augustus De Morgan
Budget of Paradoxes (1872), 173.
Science quotes on:  |  Count Joseph-Louis de Lagrange (11)  |  Mathematics (597)

Metaphysics. The science to which ignorance goes to learn its knowledge, and knowledge to learn its ignorance. On which all men agree that it is the key, but no two upon how it is to be put into the lock.
— Augustus De Morgan
Lest remark in letter to Dr. Whewell (25 May 1850), collected in Sophia Elizabeth De Morgan (ed.), Memoir of Augustus De Morgan (1882), 210.
Science quotes on:  |  Agree (20)  |  Go (6)  |  Ignorance (194)  |  Key (40)  |  Knowledge (1148)  |  Learn (193)  |  Lock (10)  |  Metaphysics (30)  |  Science (1741)

Modern discoveries have not been made by large collections of facts, with subsequent discussion, separation, and resulting deduction of a truth thus rendered perceptible. A few facts have suggested an hypothesis, which means a supposition, proper to explain them. The necessary results of this supposition are worked out, and then, and not till then, other facts are examined to see if their ulterior results are found in Nature.
— Augustus De Morgan
In A Budget of Paradoxes (1872), 55.
Science quotes on:  |  Deduction (51)  |  Discovery (601)  |  Discussion (40)  |  Explain (71)  |  Fact (628)  |  Find (297)  |  Hypothesis (231)  |  Modern (110)  |  Nature (1081)  |  Result (267)  |  Supposition (34)  |  Truth (764)

One day at least in every week,
The sects of every kind
Their doctrines here are sure to seek,
And just as sure to find.
— Augustus De Morgan
From Matter to Spirit, Preface.
Science quotes on:  |  Poem (86)

The Astronomer’s Drinking Song
Astronomers! What can avail
Those who calumniate us;
Experiment can never fail
With such an apparatus…
— Augustus De Morgan
A Budget of Paradoxes
Science quotes on:  |  Astronomy (180)  |  Poem (86)

The gambling reasoner is incorrigible; if he would but take to the squaring of the circle, what a load of misery would be saved.
— Augustus De Morgan
Quoted in D. MacHale, Comic Sections (1993).
Science quotes on:  |  Mathematics (597)

The genius of Laplace was a perfect sledge hammer in bursting purely mathematical obstacles; but, like that useful instrument, it gave neither finish nor beauty to the results. In truth, in truism if the reader please, Laplace was neither Lagrange nor Euler, as every student is made to feel. The second is power and symmetry, the third power and simplicity; the first is power without either symmetry or simplicity. But, nevertheless, Laplace never attempted investigation of a subject without leaving upon it the marks of difficulties conquered: sometimes clumsily, sometimes indirectly, always without minuteness of design or arrangement of detail; but still, his end is obtained and the difficulty is conquered.
— Augustus De Morgan
'Review of "Théorie Analytique des Probabilites" par M. le Marquis de Laplace, 3eme edition. Paris. 1820', Dublin Review (1837), 2, 348.
Science quotes on:  |  Beauty (200)  |  Clumsiness (2)  |  Design (99)  |  Detail (68)  |  Difficulty (117)  |  Leonhard Euler (10)  |  Genius (194)  |  Instrument (75)  |  Investigation (124)  |  Count Joseph-Louis de Lagrange (11)  |  Pierre-Simon Laplace (50)  |  Mathematics (597)  |  Obstacle (28)  |  Power (286)  |  Result (267)  |  Simplicity (128)  |  Sledge Hammer (2)  |  Student (140)  |  Symmetry (26)

The imaginary expression √(-a) and the negative expression -b, have this resemblance, that either of them occurring as the solution of a problem indicates some inconsistency or absurdity. As far as real meaning is concerned, both are imaginary, since 0 - a is as inconceivable as √(-a).
— Augustus De Morgan
Science quotes on:  |  Mathematics (597)

The moving power of mathematical invention is not reasoning but imagination.
— Augustus De Morgan
Quoted in Robert Perceval Graves, Life of Sir W. R. Hamilton, Vol. 3 (1889), 219.
Science quotes on:  |  Imagination (222)  |  Mathematics (597)

This mysterious 3.141592..., which comes in at every door and window, and down every chimney.
— Augustus De Morgan
Science quotes on:  |  Pi (7)

We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of science are mathematics and logic; the mathematical set puts out the logical eye, the logical set puts out the mathematical eye; each believing that it sees better with one eye than with two.
Note that De Morgan, himself, only had sight with only one eye.
— Augustus De Morgan
Review of a book on geometry in the Athenaeum, 1868, Vol. 2, 71-73.
Science quotes on:  |  Logician (3)  |  Mathematician (178)

Quotes by others about Augustus De Morgan (1)

De Morgan was explaining to an actuary what was the chance that a certain proportion of some group of people would at the end of a given time be alive; and quoted the actuarial formula, involving p [pi], which, in answer to a question, he explained stood for the ratio of the circumference of a circle to its diameter. His acquaintance, who had so far listened to the explanation with interest, interrupted him and exclaimed, 'My dear friend, that must be a delusion, what can a circle have to do with the number of people alive at a given time?'
Mathematical Recreations and Problems (1896), 180; See also De Morgan's Budget of Paradoxes (1872), 172.
Science quotes on:  |  Acquaintance (14)  |  Alive (44)  |  Anecdote (17)  |  Answer (210)  |  Chance (137)  |  Circle (32)  |  Circumference (13)  |  Death (277)  |  Delusion (17)  |  Diameter (9)  |  Exclaim (2)  |  Explanation (165)  |  Formula (51)  |  Group (55)  |  Interest (182)  |  Interrupt (4)  |  Number (188)  |  Pi (7)  |  Proportion (51)  |  Question (327)  |  Ratio (16)

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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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