Celebrating 19 Years on the Web
TODAY IN SCIENCE HISTORY ®
Find science on or your birthday

Today in Science History - Quickie Quiz
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.”
more quiz questions >>
Home > Dictionary of Science Quotations > Scientist Names Index D > Augustus De Morgan Quotes

Thumbnail of Augustus De Morgan (source)
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 (42 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 (27)  |  Accurate (35)  |  Affair (29)  |  Astronomy (204)  |  Attention (121)  |  Catalogue (4)  |  Chief (38)  |  Clerk (3)  |  Expectation (55)  |  Firm (24)  |  Founder (16)  |  History (369)  |  Incomplete (15)  |  Labour (47)  |  Minute (44)  |  Partnership (4)

A few days afterwards, I went to him [the same actuary referred to in another quote] and very gravely told him that I had discovered the law of human mortality in the Carlisle Table, of which he thought very highly. I told him that the law was involved in this circumstance. Take the table of the expectation of life, choose any age, take its expectation and make the nearest integer a new age, do the same with that, and so on; begin at what age you like, you are sure to end at the place where the age past is equal, or most nearly equal, to the expectation to come. “You don’t mean that this always happens?”—“Try it.” He did try, again and again; and found it as I said. “This is, indeed, a curious thing; this is a discovery!” I might have sent him about trumpeting the law of life: but I contented myself with informing him that the same thing would happen with any table whatsoever in which the first column goes up and the second goes down.
— Augustus De Morgan
In Budget of Paradoxes (1872), 172.
Science quotes on:  |  Age (178)  |  Begin (108)  |  Choose (60)  |  Circumstance (66)  |  Column (15)  |  Content (69)  |  Curious (43)  |  Discover (199)  |  Discovery (680)  |  Down (86)  |  End (195)  |  Equal (83)  |  Expectation (55)  |  Find (408)  |  Gravely (2)  |  Happen (82)  |  Highly (16)  |  Human (550)  |  Inform (16)  |  Integer (10)  |  Involve (48)  |  Law (515)  |  Life (1131)  |  Mathematicians and Anecdotes (141)  |  Mean (101)  |  Mortality (15)  |  Nearly (26)  |  New Age (5)  |  Past (152)  |  Place (175)  |  Send (22)  |  Table (36)  |  Tell (110)  |  Thought (546)  |  Trumpet (2)  |  Try (141)  |  Up (5)

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 (54)  |  Geometry (232)

Bacon himself was very ignorant of all that had been done by mathematics; and, strange to say, he especially objected to astronomy being handed over to the mathematicians. Leverrier and Adams, calculating an unknown planet into a visible existence by enormous heaps of algebra, furnish the last comment of note on this specimen of the goodness of Bacon’s view… . Mathematics was beginning to be the great instrument of exact inquiry: Bacon threw the science aside, from ignorance, just at the time when his enormous sagacity, applied to knowledge, would have made him see the part it was to play. If Newton had taken Bacon for his master, not he, but somebody else, would have been Newton.
— Augustus De Morgan
In Budget of Paradoxes (1872), 53-54.
Science quotes on:  |  Algebra (104)  |  Apply (77)  |  Astronomy (204)  |  Sir Francis Bacon (181)  |  Begin (108)  |  Calculate (33)  |  Comment (11)  |  Enormous (41)  |  Exact (68)  |  Existence (299)  |  Furnish (42)  |  Goodness (14)  |  Great (534)  |  Heap (14)  |  Ignorance (213)  |  Ignorant (40)  |  Inquiry (45)  |  Instrument (95)  |  Knowledge (1306)  |  LeVerrier_Urbain (3)  |  Master (98)  |  Mathematician (384)  |  Mathematicians and Anecdotes (141)  |  Mathematics (1205)  |  Sir Isaac Newton (333)  |  Note (34)  |  Part (222)  |  Planet (263)  |  Play (112)  |  Sagacity (8)  |  Science (2067)  |  See (369)  |  Specimen (18)  |  Throw (43)  |  Time (595)  |  Unknown (107)  |  View (171)  |  Visible (38)

Common integration is only the memory of differentiation...
— Augustus De Morgan
Science quotes on:  |  Differentiation (18)  |  Integration (17)  |  Mathematics (1205)

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 (294)  |  Geometry (232)

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 (36)  |  Basis (91)  |  Better (192)  |  Century (131)  |  Consequence (114)  |  Follow (124)  |  Hypothesis (252)  |  Knowledge (1306)  |  Mathematics (1205)  |  Necessity (143)  |  Observation (450)  |  Phenomenon (278)  |  Physical Science (66)  |  Pure (103)  |  Question (404)  |  Thought (546)  |  Truth (928)  |  Worse (24)

Euler was a believer in God, downright and straightforward. The following story is told by Thiebault, in his Souvenirs de vingt ans de séjour à Berlin, … Thiebault says that he has no personal knowledge of the truth of the story, but that it was believed throughout the whole of the north of Europe. Diderot paid a visit to the Russian Court at the invitation of the Empress. He conversed very freely, and gave the younger members of the Court circle a good deal of lively atheism. The Empress was much amused, but some of her counsellors suggested that it might be desirable to check these expositions of doctrine. The Empress did not like to put a direct muzzle on her guest’s tongue, so the following plot was contrived. Diderot was informed that a learned mathematician was in possession of an algebraical demonstration of the existence of God, and would give it him before all the Court, if he desired to hear it. Diderot gladly consented: though the name of the mathematician is not given, it was Euler. He advanced toward Diderot, and said gravely, and in a tone of perfect conviction:
Monsieur, (a + bn) / n = x, donc Dieu existe; repondez!

Diderot, to whom algebra was Hebrew, was embarrassed and disconcerted; while peals of laughter rose on all sides. He asked permission to return to France at once, which was granted.
— Augustus De Morgan
In Budget of Paradoxes (1878), 251. [The declaration in French expresses, “therefore God exists; please answer!” This Euler-Diderot anecdote, as embellished by De Morgan, is generally regarded as entirely fictional. Diderot before he became an encyclopedist was an accomplished mathematician and fully capable of recognizing—and responding to—the absurdity of an algebraic expression in proving the existence of God. See B.H. Brown, 'The Euler-Diderot Anecdote', The American Mathematical Monthly (May 1942), 49, No. 5, 392-303. —Webmaster.]
Science quotes on:  |  Advance (165)  |  Algebra (104)  |  Amused (3)  |  Atheism (8)  |  Belief (504)  |  Believer (11)  |  Check (24)  |  Circle (56)  |  Consent (10)  |  Contrive (6)  |  Converse (7)  |  Conviction (71)  |  Court (20)  |  Deal (49)  |  Demonstration (86)  |  Desirable (11)  |  Desire (142)  |  Denis Diderot (6)  |  Direct (84)  |  Doctrine (75)  |  Leonhard Euler (35)  |  Europe (43)  |  Existence (299)  |  Exposition (15)  |  Follow (124)  |  France (27)  |  Freely (13)  |  Gladly (2)  |  God (535)  |  Good (345)  |  Grant (32)  |  Gravely (2)  |  Guest (5)  |  Hear (63)  |  Hebrew (7)  |  Inform (16)  |  Invitation (10)  |  Knowledge (1306)  |  Laughter (23)  |  Learn (288)  |  Lively (7)  |  Mathematician (384)  |  Mathematicians and Anecdotes (141)  |  Member (40)  |  Name (170)  |  North (11)  |  Peal (2)  |  Perfect (89)  |  Permission (7)  |  Personal (66)  |  Plot (10)  |  Possession (46)  |  Return (55)  |  Russia (13)  |  Story (73)  |  Straightforward (7)  |  Suggest (33)  |  Tell (110)  |  Tone (11)  |  Tongue (19)  |  Toward (45)  |  Truth (928)  |  Visit (26)  |  Whole (192)  |  Young (100)

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 (260)  |  Symbol (73)

Geometrical reasoning, and arithmetical process, have each its own office: to mix the two in elementary instruction, is injurious to the proper acquisition of both.
— Augustus De Morgan
In Trigonometry and Double Algebra (1849), 92.
Science quotes on:  |  Acquisition (42)  |  Arithmetical (11)  |  Both (81)  |  Elementary (45)  |  Geometrical (10)  |  Injurious (4)  |  Instruction (73)  |  Mix (19)  |  Office (22)  |  Process (267)  |  Proper (38)  |  Reason (471)  |  Teaching of Mathematics (39)

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 (92)

I don't quite hear what you say, but I beg to differ entirely with you.
— Augustus De Morgan
Science quotes on:  |  Quip (80)

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 (260)  |  Symbol (73)

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 (232)  |  Mathematics (1205)

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 (10)  |  Mathematics (1205)

Is there anyone whose name cannot be twisted into either praise or satire? I have had given to me,
Thomas Babington Macaulay
Mouths big: a Cantab anomaly.

— Augustus De Morgan
In Budget of Paradoxes (1872), 83. [Macaulay’s full name is followed by an anagram of it. —Webmaster]
Science quotes on:  |  Anagram (9)  |  Anomaly (8)  |  Anyone (35)  |  Big (48)  |  Give (201)  |  Mathematicians and Anecdotes (141)  |  Mouth (21)  |  Name (170)  |  Praise (26)  |  Satire (3)  |  Twist (3)

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 (93)  |  Diminutive (3)  |  Health (156)  |  Infant (15)  |  Sir Isaac Newton (333)  |  Pendant (2)  |  Story (73)  |  Tooth (26)  |  Vigour (13)

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.
— Augustus De Morgan
In On the Study and Difficulties of Mathematics (1898), chap. 1.
Science quotes on:  |  Absolutely (39)  |  Actual (48)  |  Adapt (28)  |  Adjective (2)  |  Admit (45)  |  Adverb (2)  |  Algebra (104)  |  Alike (22)  |  Alone (106)  |  Arithmetical (11)  |  Art (294)  |  Ascertain (15)  |  Attain (45)  |  Attempt (126)  |  Authority (66)  |  Avoid (55)  |  Calculation (100)  |  Certainty (131)  |  Child (252)  |  Choose (60)  |  Common (122)  |  Competent (20)  |  Conclusion (160)  |  Confidence (41)  |  Confound (14)  |  Degree (82)  |  Demonstration (86)  |  Derive (33)  |  Desirable (11)  |  Develop (107)  |  Difference (246)  |  Discovery (680)  |  Distinction (46)  |  Distinctly (5)  |  Education (347)  |  Employ (35)  |  Entirely (33)  |  Evident (29)  |  Exert (14)  |  Existence (299)  |  Expect (44)  |  Experience (342)  |  Explain (107)  |  Express (65)  |  Faculty (70)  |  False (99)  |  Falsehood (26)  |  Far (154)  |  Fence (9)  |  Find Out (20)  |  Finish (25)  |  First (314)  |  Follow (124)  |  General (160)  |  Geometry (232)  |  Give (201)  |  Grant (32)  |  Ground (90)  |  Guide (65)  |  Idea (580)  |  Independent (67)  |  Instructor (5)  |  Know (556)  |  Language (228)  |  Learn (288)  |  Lodestone (6)  |  Logical (55)  |  Manifest (21)  |  Mathematics (1205)  |  Matter (343)  |  Mean (101)  |  Meanings (5)  |  Means (176)  |  Measurement (161)  |  Mind (760)  |  Natural History (50)  |  Nature (1223)  |  Necessary (154)  |  New (496)  |  Nothing (395)  |  Object (175)  |  Observation (450)  |  Obtain (45)  |  Ocular (3)  |  Opinion (176)  |  Order (242)  |  Passage (20)  |  Peculiarly (4)  |  Port (2)  |  Power (366)  |  Principle (292)  |  Probability (106)  |  Property (126)  |  Provide (69)  |  Pupil (36)  |  Purpose (194)  |  Rarely (20)  |  Reason (471)  |  Rely (11)  |  Require (85)  |  Rest (93)  |  Result (389)  |  Safe (28)  |  Same (156)  |  Say (228)  |  Self-Evident (12)  |  Sort (49)  |  Stand (108)  |  Strictly (13)  |  Study (476)  |  Swim (16)  |  Tell (110)  |  Term (122)  |  Thought (546)  |  Total (36)  |  True (208)  |  Trust (49)  |  Truth (928)  |  Value Of Mathematics (60)  |  Verify (17)  |  Voyage (11)  |  Word (302)  |  Work (635)

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 (384)

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 (384)

Kepler’s suggestion of gravitation with the inverse distance, and Bouillaud’s proposed substitution of the inverse square of the distance, are things which Newton knew better than his modern readers. I have discovered two anagrams on his name, which are quite conclusive: the notion of gravitation was not new; but Newton went on.
— Augustus De Morgan
In Budget of Paradoxes (1872), 82.
Science quotes on:  |  Anagram (9)  |  Better (192)  |  Conclusive (7)  |  Discover (199)  |  Distance (77)  |  Gravitation (38)  |  Inverse (7)  |  Johannes Kepler (91)  |  Know (556)  |  Mathematicians and Anecdotes (141)  |  Modern (162)  |  Name (170)  |  New (496)  |  Sir Isaac Newton (333)  |  Notion (59)  |  Propose (23)  |  Reader (40)  |  Square (24)  |  Substitution (13)  |  Suggestion (30)

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 (26)  |  Mathematics (1205)

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 (26)  |  Go (6)  |  Ignorance (213)  |  Key (50)  |  Knowledge (1306)  |  Learn (288)  |  Lock (12)  |  Metaphysics (36)  |  Science (2067)

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 (69)  |  Discovery (680)  |  Discussion (48)  |  Explain (107)  |  Fact (733)  |  Find (408)  |  Hypothesis (252)  |  Modern (162)  |  Nature (1223)  |  Result (389)  |  Supposition (37)  |  Truth (928)

Of my own age I may say … I was x years old in the year x × x. … I dare say Professor De Morgan, or some of your mathematical correspondents, will be able to find my age.
— Augustus De Morgan
In Notes and Queries: Volume Twelve: July—December 1855 (4 Aug 1855), Vol. 12 No. 301, 94. The reply is signed as by M. However De Morgan is identified as author in C.O. Tuckey, 'Noughts and Crosses', The Mathematical Gazette (Dec 1929), 14, No. 204, 577, which points out: M “contributed other replies that were certainly from the pen of De Morgan.” Furthermore, De Morgan, mathematician, born in 1806, was 43 in the year 1849 (43 × 43, which is the only reasonable solution for an adult writing in 1855 since 42² = 1764).
Science quotes on:  |  Age (178)  |  Mathematics (1205)  |  Puzzle (35)  |  Square (24)

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 (92)

Remember this, the rule for giving an extempore lecture is—let the the mind rest from the subject entirely for an interval preceding the lecture, after the notes are prepared; the thoughts will ferment without your knowing it, and enter into new combinations; but if you keep the mind active upon the subject up to the moment, the subject will not ferment but stupefy.
— Augustus De Morgan
In Letter (10 Jul 1854) to William Rowan Hamilton, collected in Robert Perceval Graves, Life of Sir William Rowan Hamilton (1882-89), Vol. 3, 487.
Science quotes on:  |  Active (25)  |  Combination (91)  |  Enter (32)  |  Entirely (33)  |  Ferment (5)  |  Give (201)  |  Interval (13)  |  Keep (100)  |  Know (556)  |  Lecture (68)  |  Let (61)  |  Mind (760)  |  Moment (107)  |  New (496)  |  Note (34)  |  Precede (23)  |  Prepare (35)  |  Remember (82)  |  Rest (93)  |  Rule (177)  |  Subject (240)  |  Teaching of Mathematics (39)  |  Thought (546)

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 (204)  |  Poem (92)

The examples which a beginner should choose for practice should be simple and should not contain very large numbers. The powers of the mind cannot be directed to two things at once; if the complexity of the numbers used requires all the student’s attention, he cannot observe the principle of the rule which he is following.
— Augustus De Morgan
In Study and Difficulties of Mathematics (1902), chap. 3.
Science quotes on:  |  Attention (121)  |  Beginner (9)  |  Choose (60)  |  Complexity (91)  |  Contain (67)  |  Direct (84)  |  Example (94)  |  Follow (124)  |  Large (130)  |  Mind (760)  |  Number (282)  |  Observe (76)  |  Power (366)  |  Practice (94)  |  Principle (292)  |  Require (85)  |  Rule (177)  |  Simple (178)  |  Student (203)  |  Study And Research In Mathematics (61)

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 (1205)

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
In '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 (248)  |  Clumsiness (2)  |  Design (115)  |  Detail (87)  |  Difficulty (146)  |  Leonhard Euler (35)  |  Genius (249)  |  Instrument (95)  |  Investigation (176)  |  Count Joseph-Louis de Lagrange (26)  |  Pierre-Simon Laplace (62)  |  Mathematics (1205)  |  Obstacle (31)  |  Power (366)  |  Result (389)  |  Simplicity (147)  |  Sledge Hammer (3)  |  Student (203)  |  Symmetry (37)

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 (1205)

The invention of what we may call primary or fundamental notation has been but little indebted to analogy, evidently owing to the small extent of ideas in which comparison can be made useful. But at the same time analogy should be attended to, even if for no other reason than that, by making the invention of notation an art, the exertion of individual caprice ceases to be allowable. Nothing is more easy than the invention of notation, and nothing of worse example and consequence than the confusion of mathematical expressions by unknown symbols. If new notation be advisable, permanently or temporarily, it should carry with it some mark of distinction from that which is already in use, unless it be a demonstrable extension of the latter.
— Augustus De Morgan
In 'Calculus of Functions', Encyclopaedia of Pure Mathematics (1847), Addition to Article 26, 388.
Science quotes on:  |  Allowable (2)  |  Analogy (60)  |  Art (294)  |  Caprice (5)  |  Cease (39)  |  Comparison (64)  |  Confusion (42)  |  Consequence (114)  |  Distinction (46)  |  Easy (102)  |  Evidently (3)  |  Example (94)  |  Exertion (15)  |  Expression (110)  |  Extension (31)  |  Fundamental (164)  |  Idea (580)  |  Individual (221)  |  Invention (324)  |  Mathematics (1205)  |  Mathematics As A Language (20)  |  New (496)  |  Notation (23)  |  Nothing (395)  |  Permanent (29)  |  Primary (41)  |  Same (156)  |  Symbol (73)  |  Temporary (17)  |  Unknown (107)  |  Useful (100)  |  Worse (24)

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 (275)  |  Mathematics (1205)

The number of mathematical students … would be much augmented if those who hold the highest rank in science would condescend to give more effective assistance in clearing the elements of the difficulties which they present.
— Augustus De Morgan
In Study and Difficulties of Mathematics (1902), Preface.
Science quotes on:  |  Assistance (10)  |  Augment (5)  |  Clear (98)  |  Condescend (2)  |  Difficulty (146)  |  Effective (30)  |  Element (162)  |  Give (201)  |  Highest (18)  |  Hold (94)  |  Mathematics (1205)  |  Number (282)  |  Present (176)  |  Rank (32)  |  Science (2067)  |  Student (203)  |  Teaching of Mathematics (39)

The sacred writings excepted, no Greek has been so much read and so variously translated as Euclid.
— Augustus De Morgan
In Article 'Eucleides', in Smith, Dictionary of Greek and Roman Biology and Mythology (1902). A footnote adds: Riccardi, Bibliografia Euclidea (1887), lists nearly two thousand editions.
Science quotes on:  |  Edition (5)  |  Euclid (54)  |  Greek (73)  |  Mathematicians and Anecdotes (141)  |  Read (145)  |  Sacred (18)  |  Thousand (152)  |  Translate (8)  |  Variously (2)  |  Writings (6)

The student should not lose any opportunity of exercising himself in numerical calculation and particularly in the use of logarithmic tables. His power of applying mathematics to questions of practical utility is in direct proportion to the facility which he possesses in computation.
— Augustus De Morgan
In Study and Difficulties of Mathematics (1902), chap. 12.
Science quotes on:  |  Apply (77)  |  Calculation (100)  |  Computation (18)  |  Direct (84)  |  Exercise (69)  |  Facility (11)  |  Logarithmic (5)  |  Lose (94)  |  Mathematics (1205)  |  Numerical (15)  |  Opportunity (63)  |  Particularly (21)  |  Possess (56)  |  Power (366)  |  Practical (133)  |  Proportion (72)  |  Question (404)  |  Student (203)  |  Study And Research In Mathematics (61)  |  Table (36)  |  Utility (33)

The thirteen books of Euclid must have been a tremendous advance, probably even greater than that contained in the Principia of Newton.
— Augustus De Morgan
In Article 'Eucleides', in Smith, Dictionary of Greek and Roman Biology and Mythology (1902).
Science quotes on:  |  Advance (165)  |  Book (257)  |  Contain (67)  |  Euclid (54)  |  Great (534)  |  Mathematicians and Anecdotes (141)  |  Sir Isaac Newton (333)  |  Principia (10)  |  Probably (48)  |  Tremendous (17)

This mysterious 3.141592..., which comes in at every door and window, and down every chimney.
— Augustus De Morgan
Science quotes on:  |  Pi (9)

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 (12)  |  Mathematician (384)

What distinguishes the straight line and circle more than anything else, and properly separates them for the purpose of elementary geometry? Their self-similarity. Every inch of a straight line coincides with every other inch, and of a circle with every other of the same circle. Where, then, did Euclid fail? In not introducing the third curve, which has the same property—the screw. The right line, the circle, the screw—the representations of translation, rotation, and the two combined—ought to have been the instruments of geometry. With a screw we should never have heard of the impossibility of trisecting an angle, squaring the circle, etc.
— Augustus De Morgan
From Letter (15 Feb 1852) to W.R. Hamilton, collected in Robert Perceval Graves, Life of W.R. Hamilton (1889), Vol. 3, 343.
Science quotes on:  |  Angle (20)  |  Circle (56)  |  Coincide (5)  |  Combine (35)  |  Curve (33)  |  Distinguish (64)  |  Elementary (45)  |  Euclid (54)  |  Fail (58)  |  Geometry (232)  |  Impossible (113)  |  Instrument (95)  |  Introduce (42)  |  Line (90)  |  Property (126)  |  Representation (36)  |  Rotation (7)  |  Screw (7)  |  Similar (35)  |  Square (24)  |  Straight Line (17)  |  Translation (15)

[De Morgan relates that some person had made up 800 anagrams on his name, of which he had seen about 650. Commenting on these he says:]
Two of these I have joined in the title-page:
[Ut agendo surgamus arguendo gustamus.]
A few of the others are personal remarks.
Great gun! do us a sum!
is a sneer at my pursuit; but,
Go! great sum! [integral of a to the power u to the power n with respect to u] is more dignified. …
Adsum, nugator, suge!
is addressed to a student who continues talking after the lecture has commenced: …
Graduatus sum! nego
applies to one who declined to subscribe for an M.A. degree.
— Augustus De Morgan
In Budget of Paradoxes (1872), 82. [The Latin phrases translate as, respectively, “Such action will start arguing with taste”, “Here babbler suck!” and “I graduate! I reject.” —Webmaster]
Science quotes on:  |  Address (12)  |  Anagram (9)  |  Apply (77)  |  Argue (23)  |  Babble (2)  |  Commence (5)  |  Comment (11)  |  Continue (65)  |  Decline (17)  |  Degree (82)  |  Augustus De Morgan (45)  |  Dignified (4)  |  Graduate (13)  |  Great (534)  |  Gun (9)  |  Integral (15)  |  Join (25)  |  Lecture (68)  |  Mathematicians and Anecdotes (141)  |  Name (170)  |  Page (30)  |  Person (154)  |  Personal (66)  |  Power (366)  |  Pursuit (79)  |  Relate (20)  |  Remark (27)  |  Say (228)  |  See (369)  |  Sneer (6)  |  Student (203)  |  Subscribe (2)  |  Suck (5)  |  Sum (41)  |  Talk (100)  |  Title (18)



Quotes by others about Augustus De Morgan (3)

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?”
In Mathematical Recreations and Problems (1896), 180; See also De Morgan’s Budget of Paradoxes (1872), 172.
Science quotes on:  |  Acquaintance (23)  |  Alive (49)  |  Anecdote (20)  |  Answer (249)  |  Chance (160)  |  Circle (56)  |  Circumference (16)  |  Death (302)  |  Delusion (22)  |  Diameter (10)  |  Exclaim (4)  |  Explanation (177)  |  Formula (80)  |  Group (72)  |  Interest (237)  |  Interrupt (6)  |  Mathematicians and Anecdotes (141)  |  Number (282)  |  Pi (9)  |  Proportion (72)  |  Question (404)  |  Ratio (19)

The history of mathematics may be instructive as well as agreeable; it may not only remind us of what we have, but may also teach us to increase our store. Says De Morgan, “The early history of the mind of men with regards to mathematics leads us to point out our own errors; and in this respect it is well to pay attention to the history of mathematics.” It warns us against hasty conclusions; it points out the importance of a good notation upon the progress of the science; it discourages excessive specialization on the part of the investigator, by showing how apparently distinct branches have been found to possess unexpected connecting links; it saves the student from wasting time and energy upon problems which were, perhaps, solved long since; it discourages him from attacking an unsolved problem by the same method which has led other mathematicians to failure; it teaches that fortifications can be taken by other ways than by direct attack, that when repulsed from a direct assault it is well to reconnoiter and occupy the surrounding ground and to discover the secret paths by which the apparently unconquerable position can be taken.
In History of Mathematics (1897), 1-2.
Science quotes on:  |  Agreeable (9)  |  Apparently (19)  |  Assault (11)  |  Attack (41)  |  Attention (121)  |  Branch (107)  |  Conclusion (160)  |  Connect (33)  |  Direct (84)  |  Discourage (9)  |  Discover (199)  |  Distinct (46)  |  Early (62)  |  Energy (214)  |  Error (277)  |  Excessive (10)  |  Failure (138)  |  Find (408)  |  Fortification (6)  |  Good (345)  |  Ground (90)  |  Hasty (6)  |  History (369)  |  History Of Mathematics (7)  |  Importance (218)  |  Increase (146)  |  Instruction (73)  |  Investigator (35)  |  Lead (160)  |  Link (42)  |  Long (174)  |  Mathematician (384)  |  Mathematics (1205)  |  Method (239)  |  Mind (760)  |  Notation (23)  |  Occupy (27)  |  Part (222)  |  Path (84)  |  Pay (43)  |  Point (123)  |  Point Out (8)  |  Position (76)  |  Possess (56)  |  Problem (497)  |  Progress (368)  |  Reconnoitre (2)  |  Regard (95)  |  Remind (13)  |  Repulse (2)  |  Respect (86)  |  Save (56)  |  Say (228)  |  Science (2067)  |  Secret (131)  |  Show (93)  |  Solve (78)  |  Specialization (17)  |  Store (21)  |  Student (203)  |  Study And Research In Mathematics (61)  |  Surround (29)  |  Teach (188)  |  Time (595)  |  Unconquerable (3)  |  Unexpected (36)  |  Unsolved (10)  |  Warn (5)  |  Waste (65)

[De Morgan relates that some person had made up 800 anagrams on his name, of which he had seen about 650. Commenting on these he says:]
Two of these I have joined in the title-page:
[Ut agendo surgamus arguendo gustamus.]
A few of the others are personal remarks.
Great gun! do us a sum!
is a sneer at my pursuit; but,
Go! great sum! [integral of a to the power u to the power n with respect to u] is more dignified. …
Adsum, nugator, suge!
is addressed to a student who continues talking after the lecture has commenced: …
Graduatus sum! nego
applies to one who declined to subscribe for an M.A. degree.
In Budget of Paradoxes (1872), 82. [The Latin phrases translate as, respectively, “Such action will start arguing with taste”, “Here babbler suck!” and “I graduate! I reject.” —Webmaster]
Science quotes on:  |  Address (12)  |  Anagram (9)  |  Apply (77)  |  Argue (23)  |  Babble (2)  |  Commence (5)  |  Comment (11)  |  Continue (65)  |  Decline (17)  |  Degree (82)  |  Dignified (4)  |  Graduate (13)  |  Great (534)  |  Gun (9)  |  Integral (15)  |  Join (25)  |  Lecture (68)  |  Mathematicians and Anecdotes (141)  |  Name (170)  |  Page (30)  |  Person (154)  |  Personal (66)  |  Power (366)  |  Pursuit (79)  |  Relate (20)  |  Remark (27)  |  Say (228)  |  See (369)  |  Sneer (6)  |  Student (203)  |  Subscribe (2)  |  Suck (5)  |  Sum (41)  |  Talk (100)  |  Title (18)


See also:

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)

Quotations about:Atomic  BombBiologyChemistryDeforestationEngineeringAnatomyAstronomyBacteriaBiochemistryBotanyConservationDinosaurEnvironmentFractalGeneticsGeologyHistory of ScienceInventionJupiterKnowledgeLoveMathematicsMeasurementMedicineNatural ResourceOrganic ChemistryPhysicsPhysicianQuantum TheoryResearchScience and ArtTeacherTechnologyUniverseVolcanoVirusWind PowerWomen ScientistsX-RaysYouthZoology  ... (more topics)
Sitewide search within all Today In Science History pages:
Visit our Science and Scientist Quotations index for more Science Quotes from archaeologists, biologists, chemists, geologists, inventors and inventions, mathematicians, physicists, pioneers in medicine, science events and technology.

Names index: | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

Categories index: | 1 | 2 | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

- 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



who invites your feedback
Thank you for sharing.
Today in Science History
Sign up for Newsletter
with quiz, quotes and more.