TODAY IN SCIENCE HISTORY ®  •  TODAYINSCI ®
Celebrating 24 Years on the Web
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “The path towards sustainable energy sources will be long and sometimes difficult. But America cannot resist this transition, we must lead it... That is how we will preserve our planet, commanded to our care by God. That�s what will lend meaning to the creed our fathers once declared.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index F > Category: Frequent

Frequent Quotes (26 quotes)

...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.
I Want to be a Mathematician: an Automathography in Three Parts (1985), 324.
Science quotes on:  |  Case (102)  |  Concept (242)  |  Concrete (55)  |  Essence (85)  |  Example (98)  |  Generality (45)  |  Great (1610)  |  Instance (33)  |  Mathematics (1395)  |  Seeming (10)  |  Seemingly (28)  |  Small (489)  |  Source (101)  |  Special (188)  |  Special Case (9)

[Benjamin Peirce's] lectures were not easy to follow. They were never carefully prepared. The work with which he rapidly covered the blackboard was very illegible, marred with frequent erasures, and not infrequent mistakes (he worked too fast for accuracy). He was always ready to digress from the straight path and explore some sidetrack that had suddenly attracted his attention, but which was likely to have led nowhere when the college bell announced the close of the hour and we filed out, leaving him abstractedly staring at his work, still with chalk and eraser in his hands, entirely oblivious of his departing class.
Writing as a Professor Emeritus at Harvard University, a former student of Peirce, in 'Benjamin Peirce: II. Reminiscences', The American Mathematical Monthly (Jan 1925), 32, No. 1, 6.
Science quotes on:  |  Accuracy (81)  |  Attention (196)  |  Attracted (3)  |  Bell (35)  |  Blackboard (11)  |  Carefully (65)  |  Chalk (9)  |  Class (168)  |  Close (77)  |  College (71)  |  Covered (5)  |  Departing (2)  |  Easy (213)  |  Eraser (2)  |  Fast (49)  |  Follow (389)  |  Hour (192)  |  Infrequent (2)  |  Lecture (111)  |  Marred (3)  |  Mistake (180)  |  Never (1089)  |  Oblivious (9)  |  Path (159)  |  Prepared (5)  |  Rapidly (67)  |  Staring (3)  |  Still (614)  |  Straight (75)  |  Suddenly (91)  |  Work (1402)

[J.J.] Sylvester’s methods! He had none. “Three lectures will be delivered on a New Universal Algebra,” he would say; then, “The course must be extended to twelve.” It did last all the rest of that year. The following year the course was to be Substitutions-Théorie, by Netto. We all got the text. He lectured about three times, following the text closely and stopping sharp at the end of the hour. Then he began to think about matrices again. “I must give one lecture a week on those,” he said. He could not confine himself to the hour, nor to the one lecture a week. Two weeks were passed, and Netto was forgotten entirely and never mentioned again. Statements like the following were not unfrequent in his lectures: “I haven’t proved this, but I am as sure as I can be of anything that it must be so. From this it will follow, etc.” At the next lecture it turned out that what he was so sure of was false. Never mind, he kept on forever guessing and trying, and presently a wonderful discovery followed, then another and another. Afterward he would go back and work it all over again, and surprise us with all sorts of side lights. He then made another leap in the dark, more treasures were discovered, and so on forever.
As quoted by Florian Cajori, in Teaching and History of Mathematics in the United States (1890), 265-266.
Science quotes on:  |  Algebra (117)  |  Back (395)  |  Confine (26)  |  Course (413)  |  Dark (145)  |  Deliver (30)  |  Discover (571)  |  Discovery (837)  |  End (603)  |  Extend (129)  |  False (105)  |  Follow (389)  |  Forever (111)  |  Forget (125)  |  Forgotten (53)  |  Go Back (4)  |  Guess (67)  |  Himself (461)  |  Hour (192)  |  Keep (104)  |  Last (425)  |  Leap (57)  |  Lecture (111)  |  Light (635)  |  Mathematicians and Anecdotes (141)  |  Matrix (14)  |  Mention (84)  |  Mentioned (3)  |  Method (531)  |  Mind (1377)  |  More (2558)  |  Must (1525)  |  Never (1089)  |  New (1273)  |  Next (238)  |  Pass (241)  |  Prove (261)  |  Rest (287)  |  Say (989)  |  Side (236)  |  Statement (148)  |  Surprise (91)  |  James Joseph Sylvester (58)  |  Think (1122)  |  Time (1911)  |  Treasure (59)  |  Trying (144)  |  Turn (454)  |  Turn Out (9)  |  Two (936)  |  Universal (198)  |  Week (73)  |  Will (2350)  |  Wonderful (155)  |  Work (1402)  |  Year (963)

A frequent misunderstanding of my vision of Gaia is that I champion complacence, that I claim feedback will always protect the environment from any serious harm that humans might do. It is sometimes more crudely put as “Lovelock’s Gaia gives industry the green light to pollute at will.” The truth is almost diametrically opposite. Gaia, as I see her, is no doting mother tolerant of misdemeanors, nor is she some fragile and delicate damsel in danger from brutal mankind. She is stern and tough, always keeping the world warm and comfortable for those who obey the rules, but ruthless in her destruction of those who transgress. Her unconscious goal is a planet fit for life. If humans stand in the way of this, we shall be eliminated with as little pity as would be shown by the micro-brain of an intercontinental ballistic nuclear missile in full flight to its target.
In The Ages of Gaia: A Biography of Our Living Earth (1999), 199.
Science quotes on:  |  Brain (281)  |  Brutal (3)  |  Champion (6)  |  Claim (154)  |  Comfortable (13)  |  Complacent (7)  |  Danger (127)  |  Delicate (45)  |  Destruction (135)  |  Diametrical (2)  |  Dote (2)  |  Eliminate (25)  |  Environment (239)  |  Feedback (10)  |  Fit (139)  |  Flight (101)  |  Fragile (26)  |  Gaia (15)  |  Goal (155)  |  Harm (43)  |  Human (1512)  |  Industry (159)  |  Life (1870)  |  Little (717)  |  Mankind (356)  |  Misdemeanor (2)  |  Misunderstanding (13)  |  Mother (116)  |  Nuclear Missile (2)  |  Obey (46)  |  Opposite (110)  |  Pity (16)  |  Planet (402)  |  Pollution (53)  |  Protect (65)  |  Rule (307)  |  Ruthless (12)  |  Serious (98)  |  Show (353)  |  Stand (284)  |  Stern (6)  |  Target (13)  |  Tolerant (4)  |  Tough (22)  |  Truth (1109)  |  Unconscious (24)  |  Vision (127)  |  Warm (74)  |  World (1850)

A superficial knowledge of mathematics may lead to the belief that this subject can be taught incidentally, and that exercises akin to counting the petals of flowers or the legs of a grasshopper are mathematical. Such work ignores the fundamental idea out of which quantitative reasoning grows—the equality of magnitudes. It leaves the pupil unaware of that relativity which is the essence of mathematical science. Numerical statements are frequently required in the study of natural history, but to repeat these as a drill upon numbers will scarcely lend charm to these studies, and certainly will not result in mathematical knowledge.
In Primary Arithmetic: First Year, for the Use of Teachers (1897), 26-27.
Science quotes on:  |  Belief (615)  |  Certain (557)  |  Certainly (185)  |  Charm (54)  |  Count (107)  |  Counting (26)  |  Drill (12)  |  Equality (34)  |  Essence (85)  |  Exercise (113)  |  Flower (112)  |  Fundamental (264)  |  Grasshopper (8)  |  Grow (247)  |  History (716)  |  Idea (881)  |  Ignore (52)  |  Incidental (15)  |  Knowledge (1647)  |  Lead (391)  |  Leave (138)  |  Leg (35)  |  Lend (4)  |  Magnitude (88)  |  Mathematics (1395)  |  Natural (810)  |  Natural History (77)  |  Number (710)  |  Numerical (39)  |  Petal (4)  |  Pupil (62)  |  Quantitative (31)  |  Reason (766)  |  Reasoning (212)  |  Relativity (91)  |  Repeat (44)  |  Require (229)  |  Required (108)  |  Result (700)  |  Scarce (11)  |  Scarcely (75)  |  Statement (148)  |  Study (701)  |  Subject (543)  |  Superficial (12)  |  Teach (299)  |  Teaching of Mathematics (39)  |  Unaware (6)  |  Will (2350)  |  Work (1402)

An experiment is an observation that can be repeated, isolated and varied. The more frequently you can repeat an observation, the more likely are you to see clearly what is there and to describe accurately what you have seen. The more strictly you can isolate an observation, the easier does your task of observation become, and the less danger is there of your being led astray by irrelevant circumstances, or of placing emphasis on the wrong point. The more widely you can vary an observation, the more clearly will the uniformity of experience stand out, and the better is your chance of discovering laws.
In A Text-Book of Psychology (1909), 20.
Science quotes on:  |  Accurate (88)  |  Astray (13)  |  Become (821)  |  Being (1276)  |  Better (493)  |  Chance (244)  |  Circumstance (139)  |  Circumstances (108)  |  Clear (111)  |  Danger (127)  |  Describe (132)  |  Description (89)  |  Discovery (837)  |  Easier (53)  |  Emphasis (18)  |  Experience (494)  |  Experiment (736)  |  Irrelevant (11)  |  Isolate (24)  |  Isolated (15)  |  Law (913)  |  Likely (36)  |  More (2558)  |  Observation (593)  |  Point (584)  |  Repeat (44)  |  See (1094)  |  Stand (284)  |  Stand Out (5)  |  Strict (20)  |  Task (152)  |  Uniformity (38)  |  Variation (93)  |  Will (2350)  |  Wrong (246)

As a general scientific principle, it is undesirable to depend crucially on what is unobservable to explain what is observable, as happens frequently in Big Bang cosmology.
In Arp, H.C., G. Burbidge, F. Hoyle, J.V. Narlikar, and N.C. Wickramasinghe, 'The Extragalactic Universe: An Alternative View,' Nature (30 Aug 1990), 346, No. 6287, 812.
Science quotes on:  |  Bang (29)  |  Big Bang (45)  |  Cosmology (26)  |  Crucial (10)  |  Depend (238)  |  Explain (334)  |  Explanation (246)  |  General (521)  |  Happen (282)  |  Observable (21)  |  Principle (530)  |  Scientific (955)  |  Undesirable (3)

Bacteria are highly adaptable. They frequently change both morphologically and functionally. Their virulence is also an essentially fluctuating property, that increases or diminishes according to the conditions to which the pathogenic organism is subjected.
In Studies in Immunity (1909), 1.
Science quotes on:  |  According (236)  |  Adaptability (7)  |  Bacteria (50)  |  Both (496)  |  Change (639)  |  Condition (362)  |  Decrease (16)  |  Essential (210)  |  Fluctuation (15)  |  Function (235)  |  Increase (225)  |  Morphology (22)  |  Organism (231)  |  Pathogen (5)  |  Property (177)  |  Subject (543)  |  Virulence (3)

For the sake of our children and our future, we must do more to combat climate change. Now, it’s true that no single event makes a trend. But the fact is the 12 hottest years on record have all come in the last 15. Heat waves, droughts, wildfires, floods—all are now more frequent and more intense. We can choose to believe that Superstorm Sandy, and the most severe drought in decades, and the worst wildfires some states have ever seen were all just a freak coincidence. Or we can choose to believe in the overwhelming judgment of science—and act before it’s too late.
From second State of the Union Address (12 Feb 2013) at the U.S. Capitol.
Science quotes on:  |  Act (278)  |  Belief (615)  |  Change (639)  |  Children (201)  |  Choose (116)  |  Climate (102)  |  Climate Change (76)  |  Coincidence (20)  |  Combat (16)  |  Decade (66)  |  Do (1905)  |  Drought (14)  |  Event (222)  |  Fact (1257)  |  Flood (52)  |  Freak (6)  |  Future (467)  |  Heat (180)  |  Hottest (2)  |  Intense (22)  |  Judgment (140)  |  Last (425)  |  Late (119)  |  More (2558)  |  Most (1728)  |  Must (1525)  |  Overwhelming (30)  |  Record (161)  |  Sake (61)  |  Sandy (3)  |  Severe (17)  |  Single (365)  |  State (505)  |  Trend (23)  |  Wave (112)  |  Worst (57)  |  Year (963)

I completed my formal education having been one of the first students in geophysics at three great universities. By today’s standards my studies were extremely casual, but I had learned to work hard, taking courses which it turned out were often irrelevant, old-fashioned, and frequently wrong. Nevertheless, the very casualness encouraged independence in thought and action.
In 'Early Days in University Geophysics', Annual Review of Earth and Planetary Sciences (1982), 10, 7.
Science quotes on:  |  Action (342)  |  Casual (9)  |  Course (413)  |  Education (423)  |  Encourage (43)  |  First (1302)  |  Geophysics (5)  |  Great (1610)  |  Independence (37)  |  Irrelevant (11)  |  Learn (672)  |  Often (109)  |  Old-Fashioned (9)  |  Standard (64)  |  Student (317)  |  Study (701)  |  Thought (995)  |  Today (321)  |  Turned Out (5)  |  University (130)  |  Work Hard (14)  |  Wrong (246)

In general the position as regards all such new calculi is this That one cannot accomplish by them anything that could not be accomplished without them. However, the advantage is, that, provided such a calculus corresponds to the inmost nature of frequent needs, anyone who masters it thoroughly is able—without the unconscious inspiration of genius which no one can command—to solve the respective problems, yea, to solve them mechanically in complicated cases in which, without such aid, even genius becomes powerless. Such is the case with the invention of general algebra, with the differential calculus, and in a more limited region with Lagrange’s calculus of variations, with my calculus of congruences, and with Möbius’s calculus. Such conceptions unite, as it were, into an organic whole countless problems which otherwise would remain isolated and require for their separate solution more or less application of inventive genius.
Letter (15 May 1843) to Schumacher, collected in Carl Friedrich Gauss Werke (1866), Vol. 8, 298, as translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914), 197-198. From the original German, “Überhaupt verhält es sich mit allen solchen neuen Calculs so, dass man durch sie nichts leisten kann, was nicht auch ohne sie zu leisten wäre; der Vortheil ist aber der, dass, wenn ein solcher Calcul dem innersten Wesen vielfach vorkommender Bedürfnisse correspondirt, jeder, der sich ihn ganz angeeignet hat, auch ohne die gleichsam unbewussten Inspirationen des Genies, die niemand erzwingen kann, die dahin gehörigen Aufgaben lösen, ja selbst in so verwickelten Fällen gleichsam mechanisch lösen kann, wo ohne eine solche Hülfe auch das Genie ohnmächtig wird. So ist es mit der Erfindung der Buchstabenrechnung überhaupt; so mit der Differentialrechnung gewesen; so ist es auch (wenn auch in partielleren Sphären) mit Lagranges Variationsrechnung, mit meiner Congruenzenrechnung und mit Möbius' Calcul. Es werden durch solche Conceptionen unzählige Aufgaben, die sonst vereinzelt stehen, und jedesmal neue Efforts (kleinere oder grössere) des Erfindungsgeistes erfordern, gleichsam zu einem organischen Reiche.”
Science quotes on:  |  Accomplishment (102)  |  Advantage (144)  |  Aid (101)  |  Algebra (117)  |  Application (257)  |  Become (821)  |  Calculus (65)  |  Command (60)  |  Complicated (117)  |  Conception (160)  |  Congruence (3)  |  Countless (39)  |  Differential Calculus (11)  |  General (521)  |  Genius (301)  |  Inmost (2)  |  Inspiration (80)  |  Invention (400)  |  Inventive (10)  |  Isolate (24)  |  Count Joseph-Louis de Lagrange (26)  |  Limit (294)  |  Limited (102)  |  Master (182)  |  Mathematics As A Language (20)  |  Mechanical (145)  |  August Möbius (2)  |  More (2558)  |  More Or Less (71)  |  Nature (2017)  |  Need (320)  |  New (1273)  |  Organic (161)  |  Position (83)  |  Powerless (7)  |  Problem (731)  |  Regard (312)  |  Region (40)  |  Remain (355)  |  Require (229)  |  Respective (2)  |  Separate (151)  |  Solution (282)  |  Solve (145)  |  Thorough (40)  |  Thoroughly (67)  |  Unconscious (24)  |  Unite (43)  |  Variation (93)  |  Whole (756)

In my opinion, there is absolutely no trustworthy proof that talents have been improved by their exercise through the course of a long series of generations. The Bach family shows that musical talent, and the Bernoulli family that mathematical power, can be transmitted from generation to generation, but this teaches us nothing as to the origin of such talents. In both families the high-watermark of talent lies, not at the end of the series of generations, as it should do if the results of practice are transmitted, but in the middle. Again, talents frequently appear in some member of a family which has not been previously distinguished.
In 'On Heredity', Essays upon Heredity and Kindred Biological Problems (1889), Vol. 1, 95-96.
Science quotes on:  |  Appear (122)  |  Bach (7)  |  Bach_Johann (2)  |  Jacob Bernoulli (6)  |  Both (496)  |  Course (413)  |  Distinguish (168)  |  Distinguished (84)  |  Do (1905)  |  End (603)  |  Exercise (113)  |  Family (101)  |  Generation (256)  |  High (370)  |  Improve (64)  |  Lie (370)  |  Long (778)  |  Mathematics (1395)  |  Member (42)  |  Middle (19)  |  Musical (10)  |  Nothing (1000)  |  Opinion (291)  |  Origin (250)  |  Power (771)  |  Practice (212)  |  Previous (17)  |  Proof (304)  |  Result (700)  |  Series (153)  |  Show (353)  |  Talent (99)  |  Teach (299)  |  Through (846)  |  Transmit (12)  |  Trustworthy (14)

It frequently happens that two persons, reasoning right on a mechanical subject, think alike and invent the same thing without any communication with each other.
As quoted by Coleman Sellers, Jr., in his Lecture (20 Nov 1885) delivered at the Franklin Institute. Printed in Coleman Sellers, Jr., 'Oliver Evans and his Inventions', Journal of the Franklin Institute (Jul 1886), 122, No. 1, 15.
Science quotes on:  |  Alike (60)  |  Communication (101)  |  Happen (282)  |  Invent (57)  |  Mechanical (145)  |  Other (2233)  |  Person (366)  |  Reasoning (212)  |  Right (473)  |  Same (166)  |  Subject (543)  |  Thing (1914)  |  Think (1122)  |  Two (936)

It seems to me, that if statesmen had a little more arithmetic, or were accustomed to calculation, wars would be much less frequent.
Letter to his sister, Mrs. Jane Mecom (1787) just after the close of the Constitutional Convention. In Jared Sparks (ed.) The Works of Benjamin Franklin (1840), Vol. 10, 445.
Science quotes on:  |  Accustom (52)  |  Accustomed (46)  |  Arithmetic (144)  |  Calculation (134)  |  Less (105)  |  Little (717)  |  More (2558)  |  Seem (150)  |  Statesman (20)  |  War (233)

Just as the musician is able to form an acoustic image of a composition which he has never heard played by merely looking at its score, so the equation of a curve, which he has never seen, furnishes the mathematician with a complete picture of its course. Yea, even more: as the score frequently reveals to the musician niceties which would escape his ear because of the complication and rapid change of the auditory impressions, so the insight which the mathematician gains from the equation of a curve is much deeper than that which is brought about by a mere inspection of the curve.
In Jahresbericht der Deutschen Mathematiker Vereiningung, 13, 864. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 190
Science quotes on:  |  Acoustic (3)  |  Auditory (2)  |  Change (639)  |  Complete (209)  |  Complication (30)  |  Composition (86)  |  Course (413)  |  Curve (49)  |  Deep (241)  |  Ear (69)  |  Equation (138)  |  Escape (85)  |  Form (976)  |  Gain (146)  |  Hear (144)  |  Image (97)  |  Impression (118)  |  Insight (107)  |  Inspection (7)  |  Looking (191)  |  Mathematician (407)  |  Mathematics As A Fine Art (23)  |  Mere (86)  |  Merely (315)  |  More (2558)  |  Musician (23)  |  Never (1089)  |  Nice (15)  |  Picture (148)  |  Play (116)  |  Rapid (37)  |  Reveal (152)  |  Score (8)

Long before I ever saw the desert I was aware of the mystical overtones which the observation of nature made audible to me. But I have never been more frequently or more vividly aware of them than in connection with the desert phenomena.
The Voice of the Desert, a Naturalist’s Interpretation (1955, 1975), 216.
Science quotes on:  |  Audible (4)  |  Connection (171)  |  Desert (59)  |  Long (778)  |  More (2558)  |  Mystery (188)  |  Nature (2017)  |  Never (1089)  |  Observation (593)  |  Overtone (3)  |  Saw (160)  |  Vivid (25)  |  Vividly (11)

Newton lectured now and then to the few students who chose to hear him; and it is recorded that very frequently he came to the lecture-room and found it empty. On such occasions he would remain fifteen minutes, and then, if no one came, return to his apartments.
In 'Sir Isaac Newton', People’s Book of Biography: Or, Short Lives of the Most Interesting Persons of All Ages and Countries (1868), 250.
Science quotes on:  |  Apartment (4)  |  Choose (116)  |  Empty (82)  |  Hear (144)  |  Lecture (111)  |  Mathematicians and Anecdotes (141)  |  Minute (129)  |  Sir Isaac Newton (363)  |  Occasion (87)  |  Record (161)  |  Remain (355)  |  Return (133)  |  Student (317)

Science is a method of logical analysis of nature’s operations. It has lessened human anxiety about the cosmos by demonstrating the materiality of nature’s forces, and their frequent predictability.
In Sexual Personae: Art and Decadence from Nefertiti to Emily Dickinson (1990), 5.
Science quotes on:  |  Analysis (244)  |  Anxiety (30)  |  Cosmos (64)  |  Force (497)  |  Human (1512)  |  Lessen (6)  |  Logic (311)  |  Materiality (2)  |  Method (531)  |  Nature (2017)  |  Operation (221)  |  Operations (107)  |  Predictability (7)

The actual evolution of mathematical theories proceeds by a process of induction strictly analogous to the method of induction employed in building up the physical sciences; observation, comparison, classification, trial, and generalisation are essential in both cases. Not only are special results, obtained independently of one another, frequently seen to be really included in some generalisation, but branches of the subject which have been developed quite independently of one another are sometimes found to have connections which enable them to be synthesised in one single body of doctrine. The essential nature of mathematical thought manifests itself in the discernment of fundamental identity in the mathematical aspects of what are superficially very different domains. A striking example of this species of immanent identity of mathematical form was exhibited by the discovery of that distinguished mathematician … Major MacMahon, that all possible Latin squares are capable of enumeration by the consideration of certain differential operators. Here we have a case in which an enumeration, which appears to be not amenable to direct treatment, can actually be carried out in a simple manner when the underlying identity of the operation is recognised with that involved in certain operations due to differential operators, the calculus of which belongs superficially to a wholly different region of thought from that relating to Latin squares.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A, Nature (1 Sep 1910), 84, 290.
Science quotes on:  |  Actual (118)  |  Actually (27)  |  Amenable (4)  |  Analogous (7)  |  Appear (122)  |  Aspect (129)  |  Belong (168)  |  Body (557)  |  Both (496)  |  Branch (155)  |  Build (211)  |  Building (158)  |  Calculus (65)  |  Capable (174)  |  Carry (130)  |  Case (102)  |  Certain (557)  |  Classification (102)  |  Comparison (108)  |  Connection (171)  |  Consideration (143)  |  Develop (278)  |  Different (595)  |  Differential (7)  |  Direct (228)  |  Discernment (4)  |  Discovery (837)  |  Distinguish (168)  |  Distinguished (84)  |  Doctrine (81)  |  Domain (72)  |  Due (143)  |  Employ (115)  |  Enable (122)  |  Essential (210)  |  Evolution (635)  |  Example (98)  |  Exhibit (21)  |  Find (1014)  |  Form (976)  |  Fundamental (264)  |  Generalization (61)  |  Identity (19)  |  Include (93)  |  Independent (74)  |  Independently (24)  |  Induction (81)  |  Involve (93)  |  Involved (90)  |  Latin (44)  |  Percy Alexander MacMahon (3)  |  Major (88)  |  Manifest (21)  |  Manner (62)  |  Mathematician (407)  |  Mathematics (1395)  |  Method (531)  |  Nature (2017)  |  Nature Of Mathematics (80)  |  Observation (593)  |  Obtain (164)  |  Operation (221)  |  Operations (107)  |  Operator (4)  |  Physical (518)  |  Physical Science (104)  |  Possible (560)  |  Proceed (134)  |  Process (439)  |  Really (77)  |  Recognise (14)  |  Region (40)  |  Relate (26)  |  Result (700)  |  Simple (426)  |  Single (365)  |  Sometimes (46)  |  Special (188)  |  Species (435)  |  Square (73)  |  Strictly (13)  |  Strike (72)  |  Striking (48)  |  Subject (543)  |  Superficial (12)  |  Synthesis (58)  |  Synthesize (3)  |  Theory (1015)  |  Thought (995)  |  Treatment (135)  |  Trial (59)  |  Underlying (33)  |  Wholly (88)

The Earth is a very small stage in a vast cosmic arena. Think of the rivers of blood spilled by all those generals and emperors, so that, in glory and triumph, they could become the momentary masters of a fraction of a dot. Think of the endless cruelties visited by the inhabitants of one corner of this pixel on the scarcely distinguishable inhabitants of some other corner, how frequent their misunderstandings, how eager they are to kill one another, how fervent their hatreds.
…...
Science quotes on:  |  Arena (4)  |  Become (821)  |  Blood (144)  |  Corner (59)  |  Cosmic (74)  |  Cruelty (24)  |  Distinguishable (2)  |  Dot (18)  |  Eager (17)  |  Earth (1076)  |  Emperor (6)  |  Endless (60)  |  Fervent (6)  |  Fraction (16)  |  General (521)  |  Glory (66)  |  Hatred (21)  |  Inhabitant (50)  |  Kill (100)  |  Master (182)  |  Misunderstanding (13)  |  Momentary (5)  |  Other (2233)  |  Pixel (2)  |  River (140)  |  Scarcely (75)  |  Small (489)  |  Spill (3)  |  Stage (152)  |  Think (1122)  |  Triumph (76)  |  Vast (188)  |  Visit (27)

The present state of the earth and of the organisms now inhabiting it, is but the last stage of a long and uninterrupted series of changes which it has undergone, and consequently, that to endeavour to explain and account for its present condition without any reference to those changes (as has frequently been done) must lead to very imperfect and erroneous conclusions.
In 'On the Law which has regulated the Introduction of New Species', The Annals and Magazine of Natural History (1855), 16, No. 93, 184.
Science quotes on:  |  Account (195)  |  Change (639)  |  Conclusion (266)  |  Condition (362)  |  Consequent (19)  |  Earth (1076)  |  Endeavor (74)  |  Endeavour (63)  |  Erroneous (31)  |  Error (339)  |  Explain (334)  |  Imperfect (46)  |  Inhabit (18)  |  Last (425)  |  Lead (391)  |  Long (778)  |  Must (1525)  |  Organism (231)  |  Present (630)  |  Reference (33)  |  Series (153)  |  Stage (152)  |  State (505)  |  Undergo (18)  |  Uninterrupted (7)

The word “definition” has come to have a dangerously reassuring sound, owing no doubt to its frequent occurrence in logical and mathematical writings.
In 'Two Dogmas of Empiricism', From a Logical Point of View: Nine Logico-Philosophical Essays (1953, 1961), 26.
Science quotes on:  |  Dangerous (108)  |  Definition (238)  |  Doubt (314)  |  Logical (57)  |  Mathematics (1395)  |  Occurrence (53)  |  Owing (39)  |  Reassure (7)  |  Sound (187)  |  Word (650)  |  Writing (192)  |  Writings (6)

There appears to be a total absence of place names [in southern Sudan]; there are indeed names for regions, areas, but all hamlets (there are scarcely any villages) bear the name of their headman or district head…, which is as ephemeral as the existence of the bearer himself in this unquiet country. Furthermore, residences are shifted every few years, in order to have fresh farmland; added to this the frequent wars, many deaths etc. In contrast, all bodies of water, even the most insignificant ditches, are permanently named. These will be the only guides if future travelers follow my path in this country or wish to trace it.
On the diffuse difficulties and contradictions in placing permanent names on the maps was making. In August Petermann, Petermann’s Geographische Mittheilungen (1871), 137. As quoted and cited in Kathrin Fritsch, '"You Have Everything Confused And Mixed Up…!" Georg Schweinfurth, Knowledge And Cartography Of Africa In The 19th Century', History in Africa (2009), 36, 91.
Science quotes on:  |  Absence (21)  |  Area (33)  |  Country (269)  |  Death (406)  |  District (11)  |  Ditch (2)  |  Ephemeral (5)  |  Existence (481)  |  Farmland (2)  |  Follow (389)  |  Fresh (69)  |  Future (467)  |  Guide (107)  |  Hamlet (10)  |  Insignificant (33)  |  Nubian (6)  |  Path (159)  |  Permanent (67)  |  Region (40)  |  Residence (3)  |  Shift (45)  |  Trace (109)  |  Traveler (33)  |  Village (13)  |  War (233)  |  Water (503)  |  Wish (216)

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.
Science quotes on:  |  Consist (223)  |  Custom (44)  |  Different (595)  |  Education (423)  |  Intellectual (258)  |  Making (300)  |  Mastery (36)  |  Mere (86)  |  Moral (203)  |  Objection (34)  |  Smattering (2)  |  Thing (1914)  |  Time (1911)

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.
Science quotes on:  |  Activity (218)  |  Afford (19)  |  Aid (101)  |  Analysis (244)  |  Attention (196)  |  Being (1276)  |  Boundless (28)  |  Call (781)  |  Capable (174)  |  Case (102)  |  Causation (14)  |  Close (77)  |  Closed (38)  |  Comparison (108)  |  Conceive (100)  |  Constantly (27)  |  Continually (17)  |  Correspondence (24)  |  Define (53)  |  Direct (228)  |  Discern (35)  |  Effort (243)  |  Exercise (113)  |  Experiment (736)  |  Experimental (193)  |  Fact (1257)  |  Facts (553)  |  Faculty (76)  |  Fist (3)  |  Form (976)  |  Forth (14)  |  Grasp (65)  |  Hand (149)  |  High (370)  |  Hollow (6)  |  Human (1512)  |  Human Mind (133)  |  Idea (881)  |  Imagination (349)  |  Individual (420)  |  Induction (81)  |  Inherent (43)  |  Inner (72)  |  Introspection (6)  |  Invention (400)  |  Invoke (7)  |  Know (1538)  |  Man (2252)  |  Mathematical Analysis (23)  |  Mathematics (1395)  |  Method (531)  |  Mind (1377)  |  More (2558)  |  Nature Of Mathematics (80)  |  New (1273)  |  New Ideas (17)  |  Nothing (1000)  |  Object (438)  |  Observation (593)  |  Opposite (110)  |  Other (2233)  |  Outer (13)  |  Palm (5)  |  Phenomenon (334)  |  Physical (518)  |  Physical World (30)  |  Power (771)  |  Principal (69)  |  Principle (530)  |  Project (77)  |  Recourse (12)  |  Relation (166)  |  Renew (20)  |  Require (229)  |  Same (166)  |  Scope (44)  |  Shadow (73)  |  Spring (140)  |  Stand (284)  |  Statement (148)  |  Study (701)  |  Tell (344)  |  Think (1122)  |  Thought (995)  |  Trial (59)  |  Unceasingly (2)  |  Vary (27)  |  Verification (32)  |  Weapon (98)  |  Weapons (57)  |  Word (650)  |  World (1850)

When he had a few moments for diversion, he [Napoleon] not unfrequently employed them over a book of logarithms, in which he always found recreation.
In Napoleon Bonaparte (1904), Vol. 1, chap. 10.
Science quotes on:  |  Emperor Napoléon Bonaparte (20)  |  Book (413)  |  Diversion (10)  |  Employ (115)  |  Find (1014)  |  Logarithm (12)  |  Mathematicians and Anecdotes (141)  |  Moment (260)  |  Napoleon (16)  |  Recreation (23)


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 |
Thank you for sharing.
- 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


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