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

Today in Science History - Quickie Quiz
Who said: “I was going to record talking... the foil was put on; I then shouted 'Mary had a little lamb',... and the machine reproduced it perfectly.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index F > Category: Fruitful

Fruitful Quotes (58 quotes)
Fruitfully Quotes

Agri non omnes frugiferi sunt.
Not all fields are fruitful.
From Tusculanae Disputationes (Tusculan Disputations) (45 BC), book 2, chap. 5, line 13. As translated in epigraph in Hagen Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets (2009), 1368. Cicero uses this as a metaphor, to illustrate that all men are not equally susceptible of improvement.
Science quotes on:  |  All (4108)  |  Field (364)  |  Fruit (102)

[Recalling Professor Ira Remsen's remarks (1895) to a group of his graduate students about to go out with their degrees into the world beyond the university:]
He talked to us for an hour on what was ahead of us; cautioned us against giving up the desire to push ahead by continued study and work. He warned us against allowing our present accomplishments to be the high spot in our lives. He urged us not to wait for a brilliant idea before beginning independent research, and emphasized the fact the Lavoisier's first contribution to chemistry was the analysis of a sample of gypsum. He told us that the fields in which the great masters had worked were still fruitful; the ground had only been scratched and the gleaner could be sure of ample reward.
Quoted in Frederick Hutton Getman, The Life of Ira Remsen (1980), 73.
Science quotes on:  |   (2863)  |  Accomplishment (93)  |  Against (332)  |  Ample (4)  |  Analysis (233)  |  Beginning (305)  |  Beyond (308)  |  Brilliance (13)  |  Brilliant (53)  |  Caution (24)  |  Chemist (156)  |  Chemistry (353)  |  Contribution (89)  |  Degree (276)  |  Desire (204)  |  Fact (1210)  |  Field (364)  |  First (1283)  |  Graduate (29)  |  Graduate Student (11)  |  Graduation (6)  |  Great (1574)  |  Ground (217)  |  Gypsum (2)  |  High (362)  |  Hour (186)  |  Idea (843)  |  Independent (67)  |  Antoine-Laurent Lavoisier (40)  |  Live (628)  |  Master (178)  |  Present (619)  |  Professor (128)  |  Push (62)  |  Ira Remsen (6)  |  Research (664)  |  Reward (68)  |  Sample (19)  |  Scratch (13)  |  Still (613)  |  Student (300)  |  Study (653)  |  University (121)  |  Work (1351)  |  World (1774)

A living organism must be studied from two distinct aspects. One of these is the causal-analytic aspect which is so fruitfully applicable to ontogeny. The other is the historical descriptive aspect which is unravelling lines of phylogeny with ever-increasing precision. Each of these aspects may make suggestions concerning the possible significance of events seen under the other, but does not explain or translate them into simpler terms.
'Embryology and Evolution', in G. R. de Beer (ed.), Evolution: Essays on Aspects of Evolutionary Biology presented to Professor E. S. Goodrich on his Seventieth Birthday (1938), 76-7.
Science quotes on:  |  Applicable (31)  |  Aspect (124)  |  Descriptive (17)  |  Distinct (97)  |  Embryology (17)  |  Event (216)  |  Evolution (590)  |  Explain (322)  |  Historical (70)  |  Living (491)  |  Must (1526)  |  Ontogeny (10)  |  Organism (220)  |  Other (2236)  |  Phylogeny (10)  |  Possible (552)  |  Precision (68)  |  Significance (113)  |  Suggestion (46)  |  Term (349)  |  Terms (184)  |  Translate (19)  |  Two (937)  |  Unraveling (3)

A subtle thought that is in error may yet give rise to fruitful inquiry that can establish truths of great value.
In Steven D. Price, 1001 Smartest Things Ever Said (2005), 163.
Science quotes on:  |  Enquiry (87)  |  Error (321)  |  Great (1574)  |  Inquiry (78)  |  Rise (166)  |  Thought (953)  |  Truth (1057)  |  Value (365)

All knowledge is profitable; profitable in its ennobling effect on the character, in the pleasure it imparts in its acquisition, as well as in the power it gives over the operations of mind and of matter. All knowledge is useful; every part of this complex system of nature is connected with every other. Nothing is isolated. The discovery of to-day, which appears unconnected with any useful process, may, in the course of a few years, become the fruitful source of a thousand inventions.
In 'Report of the Secretary', Sixth Annual Report of the Board of Regents of the Smithsonian Institution for 1851 (1852), 10.
Science quotes on:  |  Acquisition (45)  |  All (4108)  |  Become (815)  |  Character (243)  |  Complex (188)  |  Connect (125)  |  Course (409)  |  Discovery (780)  |  Effect (393)  |  Ennoble (8)  |  Impart (23)  |  Invention (369)  |  Isolated (14)  |  Knowledge (1529)  |  Matter (798)  |  Mind (1338)  |  Nature (1926)  |  Nothing (966)  |  Operation (213)  |  Operations (107)  |  Other (2236)  |  Pleasure (178)  |  Power (746)  |  Process (423)  |  Profitable (28)  |  Source (93)  |  System (537)  |  Thousand (331)  |  Unconnected (10)  |  Useful (250)  |  Year (933)

An increase in knowledge acquired too quickly and with too little participation on one’s own part is not very fruitful: erudition can produce foliage without bearing fruit.
Aphorism 26 in Notebook C (1772-1773), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 36.
Science quotes on:  |   (2863)  |  Acquired (78)  |  Bearing (9)  |  Erudition (6)  |  Foliage (5)  |  Fruit (102)  |  Increase (210)  |  Knowledge (1529)  |  Little (707)  |  Participation (15)  |  Quickly (18)

Analysis and natural philosophy owe their most important discoveries to this fruitful means, which is called induction. Newton was indebted to it for his theorem of the binomial and the principle of universal gravity.
In Frederick Wilson Truscott (trans.) and Frederick Lincoln Emory (trans.), A Philosophical Essay on Probabilities (1902), 176.
Science quotes on:  |  Analysis (233)  |  Binomial (6)  |  Binomial Theorem (5)  |  Call (769)  |  Discovery (780)  |  Gravity (132)  |  Important (209)  |  Indebted (7)  |  Induction (77)  |  Law Of Gravitation (22)  |  Mean (809)  |  Means (579)  |  Most (1731)  |  Natural (796)  |  Natural Philosophy (52)  |  Nature Of Mathematics (80)  |  Sir Isaac Newton (333)  |  Owe (71)  |  Philosophy (380)  |  Principle (507)  |  Theorem (112)  |  Universal (189)

And yet surely to alchemy this right is due, that it may be compared to the husbandman whereof Æsop makes the fable, that when he died he told his sons that he had left unto them gold buried under the ground in his vineyard: and they digged over the ground, gold they found none, but by reason of their stirring and digging the mould about the roots of their vines, they had a great vintage the year following: so assuredly the search and stir to make gold hath brought to light a great number of good and fruitful inventions and experiments, as well for the disclosing of nature as for the use of man's life.
The Advancement of Learning (1605, 1712), Vol. 1, 15.
Science quotes on:  |   (2863)  |  Alchemy (30)  |  Digging (11)  |  Due (141)  |  Experiment (695)  |  Fable (12)  |  Gold (97)  |  Good (889)  |  Great (1574)  |  Ground (217)  |  Invention (369)  |  Knowledge (1529)  |  Life (1795)  |  Light (607)  |  Man (2251)  |  Nature (1926)  |  Number (699)  |  Reason (744)  |  Right (452)  |  Root (120)  |  Search (162)  |  Stir (21)  |  Surely (101)  |  Use (766)  |  Year (933)

As language-using organisms, we participate in the evolution of the Universe most fruitfully through interpretation. We understand the world by drawing pictures, telling stories, conversing. These are our special contributions to existence. It is our immense good fortune and grave responsibility to sing the songs of the Cosmos.
Epigraph, without citation, in Michael Dowd, Thank God for Evolution: How the Marriage of Science and Religion Will Transform Your Life and Our World (2008), 103.
Science quotes on:  |  Contribution (89)  |  Converse (8)  |  Cosmos (63)  |  Draw (137)  |  Drawing (56)  |  Evolution (590)  |  Existence (456)  |  Fortune (49)  |  Good (889)  |  Grave (52)  |  Immense (86)  |  Interpretation (85)  |  Language (293)  |  Most (1731)  |  Organism (220)  |  Picture (143)  |  Responsibility (66)  |  Sing (26)  |  Song (37)  |  Special (184)  |  Story (118)  |  Tell (340)  |  Through (849)  |  Understand (606)  |  Universe (857)  |  World (1774)

As long as museums and universities send out expeditions to bring to light new forms of living and extinct animals and new data illustrating the interrelations of organisms and their environments, as long as anatomists desire a broad comparative basis human for anatomy, as long as even a few students feel a strong curiosity to learn about the course of evolution and relationships of animals, the old problems of taxonomy, phylogeny and evolution will gradually reassert themselves even in competition with brilliant and highly fruitful laboratory studies in cytology, genetics and physiological chemistry.
'Genetics Versus Paleontology', The American Naturalist, 1917, 51, 623.
Science quotes on:  |  Anatomist (23)  |  Anatomy (69)  |  Animal (617)  |  Basis (173)  |  Brilliant (53)  |  Chemistry (353)  |  Competition (39)  |  Course (409)  |  Curiosity (128)  |  Cytology (7)  |  Data (156)  |  Desire (204)  |  Environment (216)  |  Evolution (590)  |  Expedition (8)  |  Extinct (21)  |  Feel (367)  |  Form (959)  |  Genetic (108)  |  Genetics (101)  |  Gradually (102)  |  Human (1468)  |  Laboratory (196)  |  Learn (629)  |  Light (607)  |  Living (491)  |  Long (790)  |  Museum (31)  |  New (1216)  |  Old (481)  |  Organism (220)  |  Paleontologist (19)  |  Phylogeny (10)  |  Physiological (62)  |  Problem (676)  |  Relationship (104)  |  Strong (174)  |  Student (300)  |  Taxonomy (18)  |  Themselves (433)  |  Will (2355)

Be fruitful and multiply, and then fill the earth and subdue it.
Bible
(circa 725 B.C.)
Science quotes on:  |  Earth (996)  |  Fill (61)  |  Multiply (37)  |  Reproduction (72)  |  Subdue (7)

Each science and law is … prospective and fruitful. Astronomy is not yet astronomy, whilst it only counts the stars in the sky. It must come nearer, and be related to men and their life.
From Notes to 'Progress of Culture' in The Complete Works of Ralph Waldo Emerson: Letters and Social Aims (1875, 1904), Vol. 8, 409.
Science quotes on:  |  Astronomy (229)  |  Count (105)  |  Law (894)  |  Life (1795)  |  Must (1526)  |  Nearer (45)  |  Prospective (7)  |  Related (5)  |  Science (3879)  |  Sky (161)  |  Star (427)  |  Stars (304)

Everything that we call Invention or Discovery in the higher sense of the word is the serious exercise and activity of an original feeling for truth, which, after a long course of silent cultivation, suddenly flashes out into fruitful knowledge.
In The Maxims and Reflections of Goethe (1906), 193.
Science quotes on:  |  Activity (210)  |  Call (769)  |  Course (409)  |  Cultivation (35)  |  Discovery (780)  |  Everything (476)  |  Exercise (110)  |  Feeling (250)  |  Flash (49)  |  Invention (369)  |  Knowledge (1529)  |  Long (790)  |  Original (58)  |  Sense (770)  |  Serious (91)  |  Silent (29)  |  Suddenly (88)  |  Truth (1057)  |  Word (619)

From time immemorial, the infinite has stirred men's emotions more than any other question. Hardly any other idea has stimulated the mind so fruitfully. Yet, no other concept needs clarification more than it does.
In address (4 Jun 1925), at a congress of the Westphalian Mathematical Society in Munster, in honor of Karl Weierstrass. First published in Mathematische Annalen (1926), 95, 161-190. Translated by Erna Putnam and Gerald J. Massey as 'On the Infinite', collected in Paul Benacerraf (ed.) Philosophy of Mathematics: Selected Readings (1983), 185. Compare another translation elsewhere on this page, beginning, “The Infinite!…”.
Science quotes on:  |   (2863)  |  Clarification (7)  |  Concept (221)  |  Emotion (100)  |  Idea (843)  |  Immemorial (3)  |  Infinite (231)  |  Mind (1338)  |  More (2559)  |  Need (290)  |  Other (2236)  |  Question (621)  |  Stimulate (18)  |  Stirred (3)  |  Time (1877)

Give me a fruitful error any time, full of seeds, bursting with its own corrections. You can keep your sterile truth for yourself.
Pareto’s comment on Kepler. In John Bartlett, Familiar Quotations (12th ed. 1949), 1198. Also in Francis Crick, The Astonishing Hypothesis: the Scientific Search for the Soul (1995), 231.
Science quotes on:  |  Correction (40)  |  Error (321)  |  Keep (101)  |  Seed (93)  |  Sterile (21)  |  Time (1877)  |  Truth (1057)

I am acutely aware of the fact that the marriage between mathematics and physics, which was so enormously fruitful in past centuries, has recently ended in divorce.
From 'Missed Opportunities', Josiah Willard Gibbs Lecture (17 Jan 1972), as published in Bulletin of the American Mathematical Society (Sep 1972), 78, No. 5. Collected in Jong-Ping Hsu and Dana Fine (eds.), 100 Years of Gravity and Accelerated Frames: The Deepest Insights of Einstein and Yang-Mills (2005), 347.
Science quotes on:  |  Divorce (6)  |  End (590)  |  Fact (1210)  |  Marriage (39)  |  Mathematics (1328)  |  Past (337)  |  Physic (517)  |  Physics (533)

I found the best ideas usually came, not when one was actively striving for them, but when one was in a more relaxed state… I used to take long solitary walks on Sundays, during which I tended to review the current situation in a leisurely way. Such occasions often proved fruitful, even though (or perhaps, because) the primary purpose of the walk was relaxation and not research.
'Methods in Theoretical Physics', From A Life of Physics: Evening Lectures at the International Centre for Theoretical Physics, Trieste, Italy. A Special Supplement of the IAEA Bulletin (1968), 24.
Science quotes on:  |  Autobiography (56)  |  Best (459)  |  Current (118)  |  Idea (843)  |  Long (790)  |  More (2559)  |  Occasion (85)  |  Primary (80)  |  Purpose (317)  |  Research (664)  |  Review (26)  |  Situation (113)  |  State (491)  |  Tend (124)  |  Usually (176)  |  Walk (124)  |  Way (1217)

I respect Kirkpatrick both for his sponges and for his numinous nummulosphere. It is easy to dismiss a crazy theory with laughter that debars any attempt to understand a man’s motivation–and the nummulosphere is a crazy theory. I find that few men of imagination are not worth my attention. Their ideas may be wrong, even foolish, but their methods often repay a close study ... The different drummer often beats a fruitful tempo.
…...
Science quotes on:  |   (2863)  |  Attempt (251)  |  Attention (190)  |  Beat (41)  |  Both (493)  |  Close (69)  |  Crazy (26)  |  Debar (2)  |  Different (577)  |  Dismiss (10)  |  Drummer (3)  |  Easy (204)  |  Find (998)  |  Foolish (40)  |  Idea (843)  |  Imagination (328)  |  Laughter (31)  |  Man (2251)  |  Method (505)  |  Methods (204)  |  Motivation (27)  |  Often (106)  |  Repay (3)  |  Respect (207)  |  Sponge (9)  |  Study (653)  |  Tempo (3)  |  Theory (970)  |  Understand (606)  |  Worth (169)  |  Wrong (234)

I strongly reject any conceptual scheme that places our options on a line, and holds that the only alternative to a pair of extreme positions lies somewhere between them. More fruitful perspectives often require that we step off the line to a site outside the dichotomy.
…...
Science quotes on:  |  Alternative (29)  |  Conceptual (10)  |  Dichotomy (4)  |  Extreme (75)  |  Hold (95)  |  Lie (364)  |  Line (91)  |  More (2559)  |  Often (106)  |  Option (9)  |  Outside (141)  |  Pair (9)  |  Perspective (28)  |  Place (177)  |  Position (77)  |  Reject (63)  |  Require (219)  |  Scheme (57)  |  Site (14)  |  Step (231)  |  Strongly (9)

If entomologists have things backward, their errors have spawned a host of others central to modern evolutionary science. … E.O. Wilson is … the founder of a rich and fruitful discipline—sociobiology. And sociobiology has … helped lay the groundwork for the dogma of the “selfish gene.”
In 'The Embryonic Meme', Global Brain: The Evolution of Mass Mind from the Big Bang to the 21st Century (2000), 34.
Science quotes on:  |  Central (80)  |  Discipline (77)  |  Dogma (48)  |  Entomologist (6)  |  Error (321)  |  Evolution (590)  |  Founder (26)  |  Gene (98)  |  Groundwork (4)  |  Modern (385)  |  Other (2236)  |  Rich (62)  |  Science (3879)  |  Selfish (11)  |  Sociobiology (5)  |  Spawn (2)  |  Thing (1915)  |  Edward O. Wilson (65)

In every case the awakening touch has been the mathematical spirit, the attempt to count, to measure, or to calculate. What to the poet or the seer may appear to be the very death of all his poetry and all his visions—the cold touch of the calculating mind,—this has proved to be the spell by which knowledge has been born, by which new sciences have been created, and hundreds of definite problems put before the minds and into the hands of diligent students. It is the geometrical figure, the dry algebraical formula, which transforms the vague reasoning of the philosopher into a tangible and manageable conception; which represents, though it does not fully describe, which corresponds to, though it does not explain, the things and processes of nature: this clothes the fruitful, but otherwise indefinite, ideas in such a form that the strict logical methods of thought can be applied, that the human mind can in its inner chamber evolve a train of reasoning the result of which corresponds to the phenomena of the outer world.
In A History of European Thought in the Nineteenth Century (1896), Vol. 1, 314.
Science quotes on:  |  Algebra (113)  |  All (4108)  |  Appear (118)  |  Applied (177)  |  Apply (160)  |  Attempt (251)  |  Awaken (15)  |  Awakening (11)  |  Born (33)  |  Calculate (54)  |  Chamber (7)  |  Cold (112)  |  Conception (154)  |  Correspond (9)  |  Count (105)  |  Create (235)  |  Death (388)  |  Definite (110)  |  Describe (128)  |  Diligent (19)  |  Dry (57)  |  Estimates of Mathematics (30)  |  Evolution (590)  |  Explain (322)  |  Figure (160)  |  Form (959)  |  Formula (98)  |  Geometry (255)  |  Human (1468)  |  Human Mind (128)  |  Hundred (229)  |  Idea (843)  |  Indefinite (20)  |  Inner (71)  |  Knowledge (1529)  |  Logical (55)  |  Mathematics (1328)  |  Measure (232)  |  Method (505)  |  Methods (204)  |  Mind (1338)  |  Nature (1926)  |  New (1216)  |  Otherwise (24)  |  Phenomenon (318)  |  Philosopher (258)  |  Poet (83)  |  Poetry (143)  |  Problem (676)  |  Process (423)  |  Prove (250)  |  Reasoning (207)  |  Represent (155)  |  Result (677)  |  Science (3879)  |  Seer (4)  |  Spell (9)  |  Spirit (265)  |  Strict (17)  |  Student (300)  |  Tangible (15)  |  Thing (1915)  |  Thought (953)  |  Touch (141)  |  Train (114)  |  Transform (73)  |  Vague (47)  |  Vision (123)  |  World (1774)

In physics we deal with states of affairs much simpler than those of psychology and yet we again and again learn that our task is not to investigate the essence of things—we do not at all know what this would mean&mash;but to develop those concepts that allow us to speak with each other about the events of nature in a fruitful manner.
Letter to H.P.E. Hansen (20 Jul 1935), Niels Bohr Archive. In Jan Faye, Henry J. Folse, Niels Bohr and Contemporary Philosophy (1994), 83.
Science quotes on:  |  Affair (29)  |  Again (3)  |  All (4108)  |  Allow (45)  |  Concept (221)  |  Deal (188)  |  Dealing (10)  |  Develop (268)  |  Development (422)  |  Do (1908)  |  Essence (82)  |  Event (216)  |  Investigate (103)  |  Investigation (230)  |  Know (1518)  |  Knowledge (1529)  |  Learn (629)  |  Learning (274)  |  Manner (58)  |  Mean (809)  |  Meaning (233)  |  Nature (1926)  |  Other (2236)  |  Physic (517)  |  Physics (533)  |  Psychology (154)  |  Simplicity (167)  |  Speak (232)  |  Speaking (119)  |  State (491)  |  Task (147)  |  Thing (1915)

In scientific thought we adopt the simplest theory which will explain all the facts under consideration and enable us to predict new facts of the same kind. The catch in this criterion lies in the world “simplest.” It is really an aesthetic canon such as we find implicit in our criticisms of poetry or painting. The layman finds such a law as dx/dt = κ(d²x/dy²) much less simple than “it oozes,” of which it is the mathematical statement. The physicist reverses this judgment, and his statement is certainly the more fruitful of the two, so far as prediction is concerned. It is, however, a statement about something very unfamiliar to the plain man, namely the rate of change of a rate of change.
In 'Science and Theology as Art-Forms', Possible Worlds (1927), 227.
Science quotes on:  |  Adopt (19)  |  Aesthetic (46)  |  All (4108)  |  Catch (31)  |  Certainly (185)  |  Change (593)  |  Concern (228)  |  Consideration (139)  |  Criterion (27)  |  Criticism (78)  |  Differential Equation (18)  |  Enable (119)  |  Explain (322)  |  Fact (1210)  |  Facts (553)  |  Find (998)  |  Implicit (12)  |  Judgment (132)  |  Kind (557)  |  Law (894)  |  Layman (21)  |  Lie (364)  |  Man (2251)  |  Mathematics (1328)  |  More (2559)  |  New (1216)  |  Ooze (2)  |  Painting (44)  |  Physicist (259)  |  Poetry (143)  |  Predict (79)  |  Prediction (82)  |  Reverse (33)  |  Scientific (941)  |  Scientific Thought (17)  |  Simple (406)  |  Simplest (10)  |  Something (719)  |  Statement (142)  |  Theory (970)  |  Thought (953)  |  Two (937)  |  Unfamiliar (16)  |  Will (2355)  |  World (1774)

In the world of human thought generally, and in physical science particularly, the most important and fruitful concepts are those to which it is impossible to attach a well-defined meaning.
In M. Dresen, H. A. Kramers: Between Tradition and Revolution (1987), 539. In Magdolna Hargittai, In Our Own Image (2000), 3.
Science quotes on:  |  Attach (56)  |  Concept (221)  |  Definition (221)  |  Human (1468)  |  Important (209)  |  Impossible (251)  |  Meaning (233)  |  Most (1731)  |  Physical (508)  |  Physical Science (101)  |  Science (3879)  |  Thought (953)  |  Well-Defined (8)  |  World (1774)

Inventions and discoveries are of two kinds. The one which we owe to chance, such as those of the mariner’s compass, gunpowder, and in general almost all the discoveries we have made in the arts. The other which we owe to genius: and here we ought to understand by the word discovery, a new combination, or a new relation perceived between certain objects or ideas. A person obtains the title of a man of genius, if the ideas which result from this combination form one grand whole, are fruitful in truths, and are of importance with respect to mankind.
From the original French, “Les inventions ou les découvertes sont de deux espèces. Il en est que nous devons au hazard; telles sont la boussole, la poudre à canon, & généralement presque toutes les découvertes que nous avons faites dans les arts. Il en est d'autres que nous devons au génie: &, par ce mot de découverte, on doit alors entendre une nouvelle combinaison, un rapport nouveau aperçu entre certains objets ou certaines idées. On obtient le titre d'homme de génie, si les idées qui résultent de ce rapport forment un grand ensemble, sont fécondes en vérités & intéressantes pour l'humanité,” in 'Du Génie', L’Esprit (1758), Discourse 4, 476. English version from Claude Adrien Helvétius and William Mudford (trans.), 'Of Genius', De l’Esprit or, Essays on the Mind and its several Faculties (1759), Essay 4, Chap. 1, 241-242.
Science quotes on:  |   (2863)  |  All (4108)  |  Art (657)  |  Certain (550)  |  Chance (239)  |  Combination (144)  |  Compass (34)  |  Discovery (780)  |  Form (959)  |  General (511)  |  Genius (284)  |  Gunpowder (16)  |  Idea (843)  |  Importance (286)  |  Invention (369)  |  Kind (557)  |  Man (2251)  |  Mankind (339)  |  Mariner (11)  |  New (1216)  |  Object (422)  |  Obtain (163)  |  Other (2236)  |  Owe (71)  |  Perceive (40)  |  Person (363)  |  Relation (157)  |  Respect (207)  |  Result (677)  |  Title (18)  |  Truth (1057)  |  Two (937)  |  Understand (606)  |  Whole (738)  |  Word (619)

It is an open secret to the few who know it, but a mystery and stumbling block to the many, that Science and Poetry are own sisters; insomuch that in those branches of scientific inquiry which are most abstract, most formal, and most remote from the grasp of the ordinary sensible imagination, a higher power of imagination akin to the creative insight of the poet is most needed and most fruitful of lasting work.
From Introduction written for William Kingdon Clifford, Clifford’s Lectures and Essays (1879), Vol. 1, 1.
Science quotes on:  |  Abstract (124)  |  Branch (150)  |  Creative (137)  |  Formal (33)  |  Grasp (61)  |  Imagination (328)  |  Inquiry (78)  |  Insight (102)  |  Know (1518)  |  Mathematics As A Fine Art (23)  |  Most (1731)  |  Mystery (177)  |  Need (290)  |  Open (274)  |  Ordinary (160)  |  Poet (83)  |  Poetry (143)  |  Power (746)  |  Remote (83)  |  Science (3879)  |  Science And Poetry (14)  |  Scientific (941)  |  Secret (194)  |  Sensible (27)  |  Sister (8)  |  Stumbling Block (6)  |  Work (1351)

It is possible for a mathematician to be “too strong” for a given occasion. He forces through, where another might be driven to a different, and possible more fruitful, approach. (So a rock climber might force a dreadful crack, instead of finding a subtle and delicate route.)
In A Mathematician's Miscellany (1953). Reissued as Béla Bollobás (ed.), Littlewood’s Miscellany (1986), 144.
Science quotes on:  |  Approach (108)  |  Climber (7)  |  Crack (15)  |  Delicate (43)  |  Different (577)  |  Dreadful (14)  |  Find (998)  |  Force (487)  |  Mathematician (387)  |  More (2559)  |  Occasion (85)  |  Possible (552)  |  Rock (161)  |  Route (15)  |  Strong (174)  |  Subtle (35)  |  Through (849)

It may well be doubted whether, in all the range of Science, there is any field so fascinating to the explorer—so rich in hidden treasures—so fruitful in delightful surprises—as that of Pure Mathematics. The charm lies chiefly, I think, in the absolute certainty of its results: for that is what, beyond all mental treasures, the human intellect craves for. Let us only be sure of something! More light, more light … “And if our fate be death, give light and let us die” This is the cry that, through all the ages, is going up from perplexed Humanity, and Science has little else to offer, that will really meet the demands of its votaries, than the conclusions of Pure Mathematics.
Opening of 'Introduction', A New Theory of Parallels (1890), xv. As a non-fiction work, the author’s name on the title page of this book was Charles Lutwidge Dodgson. Being better known for his works of fiction as Lewis Carroll, all quotes relating to this one person, published under either name, are gathered on this single web page under his pen name.
Science quotes on:  |  Absolute (145)  |  Age (499)  |  All (4108)  |  Beyond (308)  |  Certainty (174)  |  Charm (51)  |  Chiefly (47)  |  Conclusion (254)  |  Crave (9)  |  Cry (29)  |  Death (388)  |  Delightful (17)  |  Demand (123)  |  Die (86)  |  Doubt (304)  |  Estimates of Mathematics (30)  |  Explorer (28)  |  Fascinating (37)  |  Fate (72)  |  Field (364)  |  Give (202)  |  Hide (69)  |  Human (1468)  |  Human Intellect (31)  |  Humanity (169)  |  Intellect (233)  |  Let (61)  |  Lie (364)  |  Light (607)  |  Little (707)  |  Mathematics (1328)  |  Mental (177)  |  More (2559)  |  Offer (141)  |  Pure (291)  |  Pure Mathematics (67)  |  Range (99)  |  Result (677)  |  Rich (62)  |  Science (3879)  |  Something (719)  |  Surprise (86)  |  Think (1086)  |  Through (849)  |  Treasure (57)  |  Votary (3)  |  Will (2355)

It may well be doubted whether, in all the range of science, there is any field so fascinating to the explorer—so rich in hidden treasures—so fruitful in delightful surprises—as that of Pure Mathematics. The charm lies chiefly, I think, in the absolute certainty of its results; for that is what, beyond all mental treasures, the human intellect craves for. Let us only be sure of something! More light, more light!
Written without pseudonym as Charles L. Dodgson. Opening remarks in Introduction to A New Theory of Parallels (1888, 1890), xv.
Science quotes on:  |  Absolute (145)  |  All (4108)  |  Beyond (308)  |  Certainty (174)  |  Charm (51)  |  Chiefly (47)  |  Crave (9)  |  Delightful (17)  |  Doubt (304)  |  Explorer (28)  |  Fascinate (12)  |  Fascinating (37)  |  Field (364)  |  Human (1468)  |  Human Intellect (31)  |  Intellect (233)  |  Knowledge (1529)  |  Lie (364)  |  Light (607)  |  Mathematics (1328)  |  Mental (177)  |  More (2559)  |  Pure (291)  |  Pure Mathematics (67)  |  Range (99)  |  Result (677)  |  Science (3879)  |  Science And Mathematics (10)  |  Something (719)  |  Surprise (86)  |  Think (1086)  |  Treasure (57)

Mathematicians attach great importance to the elegance of their methods and their results. This is not pure dilettantism. What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details. But this is exactly what yields great results, in fact the more we see this aggregate clearly and at a single glance, the better we perceive its analogies with other neighboring objects, consequently the more chances we have of divining the possible generalizations. Elegance may produce the feeling of the unforeseen by the unexpected meeting of objects we are not accustomed to bring together; there again it is fruitful, since it thus unveils for us kinships before unrecognized. It is fruitful even when it results only from the contrast between the simplicity of the means and the complexity of the problem set; it makes us then think of the reason for this contrast and very often makes us see that chance is not the reason; that it is to be found in some unexpected law. In a word, the feeling of mathematical elegance is only the satisfaction due to any adaptation of the solution to the needs of our mind, and it is because of this very adaptation that this solution can be for us an instrument. Consequently this esthetic satisfaction is bound up with the economy of thought.
In 'The Future of Mathematics', Monist, 20, 80. Translated from the French by George Bruce Halsted.
Science quotes on:  |  Accustom (52)  |  Accustomed (46)  |  Adaptation (58)  |  Aesthetic (46)  |  Aggregate (23)  |  All (4108)  |  Analogy (71)  |  Attach (56)  |  Balance (77)  |  Better (486)  |  Both (493)  |  Bound (119)  |  Chance (239)  |  Complexity (111)  |  Comprehend (40)  |  Contrast (44)  |  Demonstration (113)  |  Detail (146)  |  Diverse (17)  |  Due (141)  |  Elegance (37)  |  Ensemble (7)  |  Fact (1210)  |  Feeling (250)  |  Generalization (57)  |  Glance (34)  |  Great (1574)  |  Happy (105)  |  Harmony (102)  |  Importance (286)  |  Indeed (324)  |  Instrument (144)  |  Introduce (63)  |  Law (894)  |  Mathematician (387)  |  Mathematics (1328)  |  Mean (809)  |  Means (579)  |  Meeting (20)  |  Method (505)  |  Methods (204)  |  Mind (1338)  |  More (2559)  |  Neighboring (5)  |  Object (422)  |  Order (632)  |  Other (2236)  |  Permit (58)  |  Possible (552)  |  Problem (676)  |  Pure (291)  |  Reason (744)  |  Result (677)  |  Satisfaction (74)  |  See (1081)  |  Set (394)  |  Simplicity (167)  |  Single (353)  |  Solution (267)  |  Study And Research In Mathematics (61)  |  Symmetry (43)  |  Think (1086)  |  Thought (953)  |  Together (387)  |  Unexpected (52)  |  Unforeseen (10)  |  Unity (78)  |  Word (619)  |  Yield (81)

Mathematics, indeed, is the very example of brevity, whether it be in the shorthand rule of the circle, c = πd, or in that fruitful formula of analysis, e = -1, —a formula which fuses together four of the most important concepts of the science,—the logarithmic base, the transcendental ratio π, and the imaginary and negative units.
In 'The Poetry of Mathematics', The Mathematics Teacher (May 1926), 19, No. 5, 293.
Science quotes on:  |  Analysis (233)  |  Base (117)  |  Brevity (8)  |  Circle (110)  |  Circumference (23)  |  Concept (221)  |  Example (94)  |  Formula (98)  |  Fuse (5)  |  Imaginary (16)  |  Important (209)  |  Indeed (324)  |  Logarithm (12)  |  Mathematics (1328)  |  Most (1731)  |  Negative (63)  |  Ratio (39)  |  Rule (294)  |  Science (3879)  |  Shorthand (5)  |  Together (387)  |  Transcendental (10)  |  Unit (33)

My definition of science is … somewhat as follows: Science is an interconnected series of concepts and conceptual schemes that have developed as a result of experimentation and observation and are fruitful of further experimentation and observations. In this definition the emphasis is on the word “fruitful.”
In Science and Common Sense (1951), 25.
Science quotes on:  |  Concept (221)  |  Definition (221)  |  Develop (268)  |  Emphasis (17)  |  Experimentation (7)  |  Follow (378)  |  Observation (555)  |  Result (677)  |  Scheme (57)  |  Science (3879)  |  Series (149)  |  Word (619)

New frontiers of the mind are before us, and if they are pioneered with the same vision, boldness, and drive with which we have waged this war we can create a fuller and more fruitful employment and a fuller and more fruitful life.
Letter to Vannevar Bush (17 Nov 1944). As printed in Vannevar Bush, Science, the Endless Frontier: A report to the President (1945), viii.
Science quotes on:  |  Boldness (10)  |  Create (235)  |  Drive (55)  |  Employment (32)  |  Frontier (38)  |  Life (1795)  |  Mind (1338)  |  More (2559)  |  New (1216)  |  Pioneer (33)  |  Vision (123)  |  Wage (5)  |  War (225)

Orthodoxy can be as stubborn in science as in religion. I do not know how to shake it except by vigorous imagination that inspires unconventional work and contains within itself an elevated potential for inspired error. As the great Italian economist Vilfredo Pareto wrote: ‘Give me a fruitful error any time, full of seeds, bursting with its own corrections. You can keep your sterile truth for yourself.’ Not to mention a man named Thomas Henry Huxley who, when not in the throes of grief or the wars of parson hunting, argued that ‘irrationally held truths may be more harmful than reasoned errors.’
…...
Science quotes on:  |  Argue (23)  |  Burst (39)  |  Contain (68)  |  Correction (40)  |  Do (1908)  |  Economist (17)  |  Elevate (12)  |  Error (321)  |  Full (66)  |  Give (202)  |  Great (1574)  |  Grief (18)  |  Harmful (12)  |  Hold (95)  |  Hunt (30)  |  Hunting (23)  |  Imagination (328)  |  Inspire (52)  |  Italian (12)  |  Keep (101)  |  Know (1518)  |  Man (2251)  |  Mention (82)  |  More (2559)  |  Name (333)  |  Orthodoxy (9)  |  Vilfredo Pareto (5)  |  Parson (3)  |  Potential (69)  |  Reason (744)  |  Religion (361)  |  Science (3879)  |  Seed (93)  |  Shake (41)  |  Sterile (21)  |  Stubborn (13)  |  Time (1877)  |  Truth (1057)  |  Unconventional (4)  |  Vigorous (20)  |  War (225)  |  Work (1351)  |  Write (230)

Scientific method is not just a method which it has been found profitable to pursue in this or that abstruse subject for purely technical reasons. It represents the only method of thinking that has proved fruitful in any subject—that is what we mean when we call it scientific. It is not a peculiar development of thinking for highly specialized ends; it is thinking, so far as thought has become conscious of its proper ends and of the equipment indispensable for success in their pursuit ... When our schools truly become laboratories of knowledge-making, not mills fitted out with information-hoppers, there will no longer be need to discuss the place of science in education.
Address to Section L, Education, of the American Association for the Advancement of Science, at Boston (1909), 'Science as Subject-Matter and as Method'. Published in Science (28 Jan 1910), N.S. Vol. 31, No. 787, 127.
Science quotes on:  |  Abstruse (10)  |  Become (815)  |  Call (769)  |  Development (422)  |  Education (378)  |  End (590)  |  Equipment (43)  |  Information (166)  |  Knowledge (1529)  |  Making (300)  |  Mean (809)  |  Method (505)  |  Mill (16)  |  Peculiar (113)  |  Profitable (28)  |  Proper (144)  |  Purely (109)  |  Pursue (58)  |  Pursuit (121)  |  Reason (744)  |  Represent (155)  |  School (219)  |  Science (3879)  |  Science Education (15)  |  Scientific (941)  |  Scientific Method (175)  |  Subject (521)  |  Success (302)  |  Thinking (414)  |  Thought (953)  |  Truly (116)  |  Will (2355)

Since the Creator had made the facts of the after-life inaccessible to man, He must not have required that man understand death in order to live fruitfully.
In The Lost World of Thomas Jefferson (1948, 1993), 262.
Science quotes on:  |  Creator (91)  |  Death (388)  |  Fact (1210)  |  Facts (553)  |  Inaccessible (18)  |  Life (1795)  |  Live (628)  |  Man (2251)  |  Must (1526)  |  Order (632)  |  Required (108)  |  Understand (606)

Superstrings are totally lacking in empirical support, yet they offer an elegant theory with great explanatory power. I wish I could be around fifty years from now to know whether superstrings turn out to be a fruitful theory or whether they are just another blind alley in the search for a “theory of everything.”
As quoted in Kendrick Frazier, 'A Mind at Play: An Interview with Martin Gardner', Skeptical Inquirer (Mar/Apr 1998), 22, No. 2, 37.
Science quotes on:  |  Blind (95)  |  Blind Alley (4)  |  Elegant (36)  |  Empirical (54)  |  Everything (476)  |  Explanation (234)  |  Great (1574)  |  Know (1518)  |  Lack (119)  |  Offer (141)  |  Power (746)  |  Search (162)  |  Superstring (4)  |  Support (147)  |  Theory (970)  |  Theory Of Everything (2)  |  Turn (447)  |  Turn Out (9)  |  Wish (212)  |  Year (933)

That man can interrogate as well as observe nature was a lesson slowly learned in his evolution. Of the two methods by which he can do this, the mathematical and the experimental, both have been equally fruitful—by the one he has gauged the starry heights and harnessed the cosmic forces to his will; by the other he has solved many of the problems of life and lightened many of the burdens of humanity.
In 'The Evolution of the Idea of Experiment in Medicine', in C.G. Roland, Sir William Osler, 1849-1919: A Selection for Medical Students (1982), 103. As cited in William Osler and Mark E. Silverman (ed.), The Quotable Osler (2002), 249
Science quotes on:  |  Both (493)  |  Burden (27)  |  Cosmic (72)  |  Do (1908)  |  Equally (130)  |  Evolution (590)  |  Experiment (695)  |  Experimental (192)  |  Force (487)  |  Harness (23)  |  Humanity (169)  |  Interrogation (4)  |  Learn (629)  |  Learned (235)  |  Lesson (57)  |  Life (1795)  |  Man (2251)  |  Mathematics (1328)  |  Method (505)  |  Methods (204)  |  Nature (1926)  |  Observation (555)  |  Observe (168)  |  Other (2236)  |  Problem (676)  |  Two (937)  |  Will (2355)

The better educated we are and the more acquired information we have, the better prepared shall we find our minds for making great and fruitful discoveries.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 38.
Science quotes on:  |  Acquired (78)  |  Acquisition (45)  |  Better (486)  |  Discovery (780)  |  Education (378)  |  Find (998)  |  Great (1574)  |  Information (166)  |  Making (300)  |  Mind (1338)  |  More (2559)  |  Preparation (58)

The deep study of nature is the most fruitful source of mathematical discoveries. By offering to research a definite end, this study has the advantage of excluding vague questions and useless calculations; besides it is a sure means of forming analysis itself and of discovering the elements which it most concerns us to know, and which natural science ought always to conserve.
Théorie Analytique de la Chaleur, Discours Préliminaire. Translation as in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914), 89.
Science quotes on:  |  Advantage (134)  |  Analysis (233)  |  Calculation (127)  |  Concern (228)  |  Deep (233)  |  Definite (110)  |  Discovery (780)  |  Element (310)  |  End (590)  |  Forming (42)  |  Know (1518)  |  Mathematics (1328)  |  Mean (809)  |  Means (579)  |  Most (1731)  |  Natural (796)  |  Natural Science (128)  |  Nature (1926)  |  Question (621)  |  Research (664)  |  Science (3879)  |  Study (653)  |  Vague (47)

The discovery which has been pointed to by theory is always one of profound interest and importance, but it is usually the close and crown of a long and fruitful period, whereas the discovery which comes as a puzzle and surprise usually marks a fresh epoch and opens a new chapter in science.
Becquerel Memorial Lecture, Journal of the Chemical Society, Transactions (1912), 101(2), 2005. Quoted by Simon Flexnor in 'The Scientific Career for Women', a commencement address at Bryn Mawr College (2 Jun 1921), The Scientific Monthly (Aug 1921), 13, 98.
Science quotes on:  |  Crown (38)  |  Discovery (780)  |  Epoch (45)  |  Fresh (67)  |  Importance (286)  |  Interest (386)  |  Long (790)  |  New (1216)  |  Open (274)  |  Period (198)  |  Point (580)  |  Profound (104)  |  Puzzle (44)  |  Science (3879)  |  Surprise (86)  |  Theory (970)  |  Usually (176)

The enthusiasm of Sylvester for his own work, which manifests itself here as always, indicates one of his characteristic qualities: a high degree of subjectivity in his productions and publications. Sylvester was so fully possessed by the matter which for the time being engaged his attention, that it appeared to him and was designated by him as the summit of all that is important, remarkable and full of future promise. It would excite his phantasy and power of imagination in even a greater measure than his power of reflection, so much so that he could never marshal the ability to master his subject-matter, much less to present it in an orderly manner.
Considering that he was also somewhat of a poet, it will be easier to overlook the poetic flights which pervade his writing, often bombastic, sometimes furnishing apt illustrations; more damaging is the complete lack of form and orderliness of his publications and their sketchlike character, … which must be accredited at least as much to lack of objectivity as to a superfluity of ideas. Again, the text is permeated with associated emotional expressions, bizarre utterances and paradoxes and is everywhere accompanied by notes, which constitute an essential part of Sylvester’s method of presentation, embodying relations, whether proximate or remote, which momentarily suggested themselves. These notes, full of inspiration and occasional flashes of genius, are the more stimulating owing to their incompleteness. But none of his works manifest a desire to penetrate the subject from all sides and to allow it to mature; each mere surmise, conceptions which arose during publication, immature thoughts and even errors were ushered into publicity at the moment of their inception, with utmost carelessness, and always with complete unfamiliarity of the literature of the subject. Nowhere is there the least trace of self-criticism. No one can be expected to read the treatises entire, for in the form in which they are available they fail to give a clear view of the matter under contemplation.
Sylvester’s was not a harmoniously gifted or well-balanced mind, but rather an instinctively active and creative mind, free from egotism. His reasoning moved in generalizations, was frequently influenced by analysis and at times was guided even by mystical numerical relations. His reasoning consists less frequently of pure intelligible conclusions than of inductions, or rather conjectures incited by individual observations and verifications. In this he was guided by an algebraic sense, developed through long occupation with processes of forms, and this led him luckily to general fundamental truths which in some instances remain veiled. His lack of system is here offset by the advantage of freedom from purely mechanical logical activity.
The exponents of his essential characteristics are an intuitive talent and a faculty of invention to which we owe a series of ideas of lasting value and bearing the germs of fruitful methods. To no one more fittingly than to Sylvester can be applied one of the mottos of the Philosophic Magazine:
“Admiratio generat quaestionem, quaestio investigationem investigatio inventionem.”
In Mathematische Annalen (1898), 50, 155-160. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 176-178.
Science quotes on:  |   (2863)  |  Ability (152)  |  Active (76)  |  Activity (210)  |  Advantage (134)  |  All (4108)  |  Analysis (233)  |  Applied (177)  |  Attention (190)  |  Available (78)  |  Being (1278)  |  Carelessness (6)  |  Character (243)  |  Characteristic (148)  |  Complete (204)  |  Conception (154)  |  Conclusion (254)  |  Conjecture (49)  |  Consist (223)  |  Constitute (97)  |  Contemplation (73)  |  Creative (137)  |  Criticism (78)  |  Degree (276)  |  Desire (204)  |  Develop (268)  |  Easier (53)  |  Enthusiasm (52)  |  Error (321)  |  Essential (199)  |  Everywhere (94)  |  Expect (200)  |  Exponent (6)  |  Expression (175)  |  Fail (185)  |  Flight (98)  |  Form (959)  |  Free (232)  |  Freedom (129)  |  Fundamental (250)  |  Future (429)  |  General (511)  |  Generalization (57)  |  Genius (284)  |  Germ (53)  |  Gift (104)  |  Gifted (23)  |  Greater (288)  |  High (362)  |  Idea (843)  |  Illustration (48)  |  Imagination (328)  |  Inception (3)  |  Indicate (61)  |  Individual (404)  |  Induction (77)  |  Inspiration (75)  |  Intelligible (34)  |  Invention (369)  |  Lack (119)  |  Literature (103)  |  Long (790)  |  Master (178)  |  Mathematicians and Anecdotes (141)  |  Matter (798)  |  Mature (16)  |  Measure (232)  |  Mechanical (140)  |  Method (505)  |  Methods (204)  |  Mind (1338)  |  Moment (253)  |  More (2559)  |  Must (1526)  |  Never (1087)  |  Numerical (39)  |  Objectivity (16)  |  Observation (555)  |  Occasional (22)  |  Occupation (48)  |  Orderliness (9)  |  Orderly (38)  |  Overlook (31)  |  Owe (71)  |  Owing (39)  |  Penetrate (67)  |  Possess (156)  |  Power (746)  |  Present (619)  |  Presentation (23)  |  Production (183)  |  Promise (67)  |  Proximate (4)  |  Publication (101)  |  Pure (291)  |  Purely (109)  |  Read (287)  |  Reasoning (207)  |  Reflection (90)  |  Remain (349)  |  Remote (83)  |  Self (267)  |  Sense (770)  |  Series (149)  |  Side (233)  |  Subject (521)  |  Subject-Matter (8)  |  Summit (25)  |  Surmise (7)  |  James Joseph Sylvester (58)  |  System (537)  |  Talent (94)  |  Themselves (433)  |  Thought (953)  |  Through (849)  |  Time (1877)  |  Trace (103)  |  Treatise (44)  |  Truth (1057)  |  Unfamiliarity (5)  |  Utterance (10)  |  Value (365)  |  Veil (26)  |  Verification (31)  |  View (488)  |  Will (2355)  |  Work (1351)  |  Writing (189)

The errors of great men are venerable because they are more fruitful than the truths of little men.
Friedrich Wilhelm Nietzsche and Walter Kaufmann (ed. & trans.), The Portable Nietzsche (1954), 30.
Science quotes on:  |  Error (321)  |  Great (1574)  |  Little (707)  |  Men (20)  |  More (2559)  |  Truth (1057)  |  Venerable (7)

The events of the past few years have led to a critical examination of the function of science in society. It used to be believed that the results of scientific investigation would lead to continuous progressive improvements in conditions of life; but first the War and then the economic crisis have shown that science can be used as easily for destructive and wasteful purposes, and voices have been raised demanding the cessation of scientific research as the only means of preserving a tolerable civilization. Scientists themselves, faced with these criticisms, have been forced to consider, effectively for the first time, how the work they are doing is connected around them. This book is an attempt to analyse this connection; to investigate how far scientists, individually and collectively, are responsible for this state of affairs, and to suggest what possible steps could be taken which would lead to a fruitful and not to a destructive utilization of science.
The Social Function of Science (1939), xlii.
Science quotes on:  |  Attempt (251)  |  Book (392)  |  Civilization (204)  |  Condition (356)  |  Connect (125)  |  Connection (162)  |  Consider (416)  |  Continuous (82)  |  Crisis (24)  |  Critical (66)  |  Criticism (78)  |  Doing (280)  |  Economic (81)  |  Event (216)  |  Examination (98)  |  First (1283)  |  Function (228)  |  Improvement (108)  |  Investigate (103)  |  Investigation (230)  |  Lead (384)  |  Life (1795)  |  Mean (809)  |  Means (579)  |  Past (337)  |  Possible (552)  |  Preserving (18)  |  Purpose (317)  |  Research (664)  |  Result (677)  |  Science (3879)  |  Scientific (941)  |  Scientist (820)  |  Society (326)  |  State (491)  |  Step (231)  |  Themselves (433)  |  Time (1877)  |  Utilization (15)  |  War (225)  |  Work (1351)  |  Year (933)

The facts of nature are what they are, but we can only view them through the spectacles of our mind. Our mind works largely by metaphor and comparison, not always (or often) by relentless logic. When we are caught in conceptual traps, the best exit is often a change in metaphor–not because the new guideline will be truer to nature (for neither the old nor the new metaphor lies ‘out there’ in the woods), but because we need a shift to more fruitful perspectives, and metaphor is often the best agent of conceptual transition.
…...
Science quotes on:  |  Agent (70)  |  Best (459)  |  Catch (31)  |  Change (593)  |  Comparison (102)  |  Conceptual (10)  |  Exit (4)  |  Fact (1210)  |  Facts (553)  |  Guideline (4)  |  Largely (13)  |  Lie (364)  |  Logic (287)  |  Metaphor (33)  |  Mind (1338)  |  More (2559)  |  Nature (1926)  |  Need (290)  |  New (1216)  |  Often (106)  |  Old (481)  |  Perspective (28)  |  Relentless (8)  |  Shift (44)  |  Spectacle (33)  |  Spectacles (10)  |  Through (849)  |  Transition (26)  |  Trap (6)  |  True (212)  |  View (488)  |  Will (2355)  |  Wood (92)  |  Work (1351)

The fundamental hypothesis of genetic epistemology is that there is a parallelism between the progress made in the logical and rational organization of knowledge and the corresponding formative psychological processes. With that hypothesis, the most fruitful, most obvious field of study would be the reconstituting of human history—the history of human thinking in prehistoric man. Unfortunately, we are not very well informed in the psychology of primitive man, but there are children all around us, and it is in studying children that we have the best chance of studying the development of logical knowledge, physical knowledge, and so forth.
'Genetic Epistemology', Columbia Forum (1969), 12, 4.
Science quotes on:  |  All (4108)  |  Best (459)  |  Chance (239)  |  Child (307)  |  Children (200)  |  Correspondence (23)  |  Development (422)  |  Epistemology (8)  |  Field (364)  |  Formation (96)  |  Fundamental (250)  |  Genetic (108)  |  Genetics (101)  |  History (673)  |  Human (1468)  |  Hypothesis (296)  |  Inform (47)  |  Information (166)  |  Knowledge (1529)  |  Logic (287)  |  Man (2251)  |  Most (1731)  |  Obvious (126)  |  Organization (114)  |  Parallelism (2)  |  Physical (508)  |  Prehistoric (10)  |  Primitive (75)  |  Primitive Man (5)  |  Process (423)  |  Progress (465)  |  Psychological (42)  |  Psychology (154)  |  Rational (90)  |  Study (653)  |  Studying (70)  |  Thinking (414)  |  Unfortunately (38)

The history of acceptance of new theories frequently shows the following steps: At first the new idea is treated as pure nonsense, not worth looking at. Then comes a time when a multitude of contradictory objections are raised, such as: the new theory is too fancy, or merely a new terminology; it is not fruitful, or simply wrong. Finally a state is reached when everyone seems to claim that he had always followed this theory. This usually marks the last state before general acceptance.
In 'Field Theory and the Phase Space', collected in Melvin Herman Marx, Psychological Theory: Contemporary Readings (1951), 299.
Science quotes on:  |  Acceptance (52)  |  Claim (146)  |  Contradictory (7)  |  Fancy (50)  |  Finally (26)  |  First (1283)  |  Follow (378)  |  Following (16)  |  General (511)  |  History (673)  |  Idea (843)  |  Last (426)  |  Looking (189)  |  Merely (316)  |  Multitude (47)  |  New (1216)  |  Nonsense (48)  |  Objection (32)  |  Pure (291)  |  Raised (3)  |  Reach (281)  |  Show (346)  |  State (491)  |  Step (231)  |  Terminology (12)  |  Theory (970)  |  Time (1877)  |  Treatment (130)  |  Usually (176)  |  Worth (169)  |  Wrong (234)

The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.
Address in memory of Karl Weierstrass. As quoted in Journal of the University of Bombay (1933), 2, 201. Also in Tobias Dantzig, Number: The Language of Science (1937), 237. Also partially quoted as epigraph in in James Roy Newman, The World of Mathematics (1956), Vol. 3, 1593. which dates the address as 1921. Another translation for perhaps the same address ('On the Infinite'), in honor of Weierstrass, dates it as 4 Jun 1925, in Paul Benacerraf (ed.) Philosophy of Mathematics (1983), 183. See this alternate version elsewhere on this page, beginning, “From time immemorial…”.
Science quotes on:  |  Clarification (7)  |  Concept (221)  |  Greater (288)  |  Idea (843)  |  Infinite (231)  |  Intellect (233)  |  Man (2251)  |  Move (216)  |  Need (290)  |  Other (2236)  |  Profound (104)  |  Question (621)  |  Spirit (265)  |  Stand (274)  |  Stimulate (18)

The Mathematics, I say, which effectually exercises, not vainly deludes or vexatiously torments studious Minds with obscure Subtilties, perplexed Difficulties, or contentious Disquisitions; which overcomes without Opposition, triumphs without Pomp, compels without Force, and rules absolutely without Loss of Liberty; which does not privately over-reach a weak Faith, but openly assaults an armed Reason, obtains a total Victory, and puts on inevitable Chains; whose Words are so many Oracles, and Works as many Miracles; which blabs out nothing rashly, nor designs anything from the Purpose, but plainly demonstrates and readily performs all Things within its Verge; which obtrudes no false Shadow of Science, but the very Science itself, the Mind firmly adhering to it, as soon as possessed of it, and can never after desert it of its own Accord, or be deprived of it by any Force of others: Lastly the Mathematics, which depends upon Principles clear to the Mind, and agreeable to Experience; which draws certain Conclusions, instructs by profitable Rules, unfolds pleasant Questions; and produces wonderful Effects; which is the fruitful Parent of, I had almost said all, Arts, the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human Affairs.
Address to the University of Cambridge upon being elected Lucasian Professor of Mathematics (14 Mar 1664). In Mathematical Lectures (1734), xxviii.
Science quotes on:  |  Advantage (134)  |  Agreeable (18)  |  All (4108)  |  Arm (81)  |  Art (657)  |  Certain (550)  |  Chain (50)  |  Compel (30)  |  Conclusion (254)  |  Delude (3)  |  Demonstrate (76)  |  Depend (228)  |  Desert (56)  |  Design (195)  |  Difficulty (196)  |  Draw (137)  |  Effect (393)  |  Estimates of Mathematics (30)  |  Exercise (110)  |  Experience (467)  |  Faith (203)  |  False (100)  |  Force (487)  |  Foundation (171)  |  Fountain (16)  |  Human (1468)  |  Inevitable (49)  |  Instruction (91)  |  Liberty (25)  |  Loss (110)  |  Mathematics (1328)  |  Mind (1338)  |  Miracle (83)  |  Never (1087)  |  Nothing (966)  |  Obscure (62)  |  Obtain (163)  |  Opposition (48)  |  Oracle (4)  |  Other (2236)  |  Overcome (39)  |  Parent (76)  |  Perform (121)  |  Pomp (2)  |  Possess (156)  |  Principle (507)  |  Profitable (28)  |  Purpose (317)  |  Question (621)  |  Rashly (2)  |  Reach (281)  |  Reason (744)  |  Rule (294)  |  Say (984)  |  Science (3879)  |  Science And Art (184)  |  Shadow (72)  |  Soon (186)  |  Studious (5)  |  Thing (1915)  |  Torment (18)  |  Total (94)  |  Triumph (73)  |  Verge (10)  |  Victory (39)  |  Weak (71)  |  Wonderful (149)  |  Word (619)  |  Work (1351)

The origin of an adaptive structure and the purposes it comes to fulfill are only chance combinations. Purposefulness is a very human conception for usefulness. It is usefulness looked at backwards. Hard as it is to imagine, inconceivably hard it may appear to many, that there is no direct relation between the origin of useful variations and the ends they come to serve, yet the modern zoologist takes his stand as a man of science on this ground. He may admit in secret to his father confessor, the metaphysician, that his poor intellect staggers under such a supposition, but he bravely carries forward his work of investigation along the only lines that he has found fruitful.
'For Darwin', The Popular Science Monthly (1909), 74, 380.
Science quotes on:  |  Adaptation (58)  |  Backwards (17)  |  Chance (239)  |  Combination (144)  |  Conception (154)  |  Direct (225)  |  End (590)  |  Father (110)  |  Forward (102)  |  Ground (217)  |  Hard (243)  |  Human (1468)  |  Imagine (164)  |  Intellect (233)  |  Investigation (230)  |  Look (582)  |  Man (2251)  |  Metaphysician (7)  |  Modern (385)  |  Origin (239)  |  Poor (136)  |  Purpose (317)  |  Relation (157)  |  Science (3879)  |  Secret (194)  |  Stand (274)  |  Structure (344)  |  Supposition (50)  |  Useful (250)  |  Usefulness (86)  |  Variation (90)  |  Work (1351)  |  Zoologist (12)

The seeds of discoveries presented to us by chance will remain barren, if attention do not render them fruitful.
From the original French, “Les semences des découvertes présentées à tous par le hazard, sont stériles, si l’attention ne les séconde,” in De l'Homme, de ses Facultés Intellectuelles, et de son Éducation (1773), Tome 1, Discours 3, Chap. 3, 269. English version from Claude Adrien Helvétius and W. Hooper (trans.), 'On Man and his Education', A Treatise on Man, His Intellectual Faculties and His Education: A Posthumous Work of M. Helvetius (1777), Vol. 1, Essay 3, Chap. 3, 261.
Science quotes on:  |  Attention (190)  |  Barren (30)  |  Chance (239)  |  Discovery (780)  |  Do (1908)  |  Present (619)  |  Remain (349)  |  Render (93)  |  Seed (93)  |  Will (2355)

The solution, as all thoughtful people recognize, must lie in properly melding the themes of inborn predisposition and shaping through life’s experiences. This fruitful joining cannot take the false form of percentages adding to 100–as in ‘intelligence is 80 percent nature and 20 percent nurture,’ or ‘homosexuality is 50 percent inborn and 50 percent learned,’ and a hundred other harmful statements in this foolish format. When two ends of such a spectrum are commingled, the result is not a separable amalgam (like shuffling two decks of cards with different backs), but an entirely new and higher entity that cannot be decomposed (just as adults cannot be separated into maternal and paternal contributions to their totality).
…...
Science quotes on:  |   (2863)  |  Add (40)  |  Adult (19)  |  All (4108)  |  Back (390)  |  Card (4)  |  Contribution (89)  |  Deck (3)  |  Decompose (9)  |  Different (577)  |  End (590)  |  Entirely (34)  |  Entity (35)  |  Experience (467)  |  False (100)  |  Foolish (40)  |  Form (959)  |  Harmful (12)  |  High (362)  |  Hundred (229)  |  Inborn (4)  |  Intelligence (211)  |  Join (26)  |  Joining (11)  |  Learn (629)  |  Learned (235)  |  Lie (364)  |  Life (1795)  |  Maternal (2)  |  Must (1526)  |  Nature (1926)  |  New (1216)  |  Nurture (16)  |  Other (2236)  |  Paternal (2)  |  People (1005)  |  Percent (5)  |  Percentage (6)  |  Predisposition (4)  |  Properly (20)  |  Recognize (125)  |  Result (677)  |  Separable (3)  |  Separate (143)  |  Shape (72)  |  Shuffle (5)  |  Solution (267)  |  Spectrum (31)  |  Statement (142)  |  Theme (17)  |  Thoughtful (15)  |  Through (849)  |  Totality (15)  |  Two (937)

The sublime discoveries of Newton, and, together with these, his not less fruitful than wonderful application, of the higher mathesis to the movement of the celestial bodies, and to the laws of light, gave almost religious sanction to the corpuscular system and mechanical theory. It became synonymous with philosophy itself. It was the sole portal at which truth was permitted to enter. The human body was treated an hydraulic machine... In short, from the time of Kepler to that of Newton, and from Newton to Hartley, not only all things in external nature, but the subtlest mysteries of life, organization, and even of the intellect and moral being, were conjured within the magic circle of mathematical formulae.
Hints Towards the Formation of a more Comprehensive Theory of Life (1848). In The Collected Works of Samuel Taylor Coleridge: Shorter Works and Fragments (1995), H. J. Jackson and J. R. de J. Jackson (eds.), Vol. 11, 1, 498.
Science quotes on:  |  All (4108)  |  Application (242)  |  Being (1278)  |  Body (537)  |  Celestial (53)  |  Circle (110)  |  Enter (141)  |  David Hartley (5)  |  Human (1468)  |  Hydraulic (5)  |  Intellect (233)  |  Johannes Kepler (91)  |  Law (894)  |  Life (1795)  |  Light (607)  |  Machine (257)  |  Magic (86)  |  Mechanical (140)  |  Moral (195)  |  Movement (155)  |  Nature (1926)  |  Sir Isaac Newton (333)  |  Organization (114)  |  Philosophy (380)  |  Portal (7)  |  Religious (126)  |  Sanction (7)  |  Short (197)  |  Sole (49)  |  Sublime (46)  |  System (537)  |  Theory (970)  |  Thing (1915)  |  Time (1877)  |  Together (387)  |  Truth (1057)  |  Wonderful (149)

There is an influence which is getting strong and stronger day by day, which shows itself more and more in all departments of human activity, and influence most fruitful and beneficial—the influence of the artist. It was a happy day for the mass of humanity when the artist felt the desire of becoming a physician, an electrician, an engineer or mechanician or—whatnot—a mathematician or a financier; for it was he who wrought all these wonders and grandeur we are witnessing. It was he who abolished that small, pedantic, narrow-grooved school teaching which made of an aspiring student a galley-slave, and he who allowed freedom in the choice of subject of study according to one's pleasure and inclination, and so facilitated development.
'Roentgen Rays or Streams', Electrical Review (12 Aug 1896). Reprinted in The Nikola Tesla Treasury (2007), 307. By Nikola Tesla
Science quotes on:  |   (2863)  |  According (237)  |  Activity (210)  |  All (4108)  |  Artist (90)  |  Aspiration (32)  |  Becoming (96)  |  Beneficial (13)  |  Choice (110)  |  Department (92)  |  Desire (204)  |  Development (422)  |  Electrician (6)  |  Engineer (121)  |  Freedom (129)  |  Grandeur (31)  |  Happy (105)  |  Human (1468)  |  Humanity (169)  |  Inclination (34)  |  Influence (222)  |  Mass (157)  |  Mathematician (387)  |  Mechanician (2)  |  More (2559)  |  Most (1731)  |  Narrow (84)  |  Pedantic (4)  |  Pedantry (5)  |  Physician (273)  |  Pleasure (178)  |  School (219)  |  Show (346)  |  Slave (37)  |  Small (477)  |  Strong (174)  |  Stronger (36)  |  Student (300)  |  Study (653)  |  Subject (521)  |  Teaching (188)  |  Witness (54)  |  Wonder (236)

This change in the conception of reality is the most profound and the most fruitful that physics has experienced since the time of Newton.
Refering to James Clerk Maxwell's contributions to physics.
'Maxwell's Influence on the Development of the Conception of Physical Reality', James Clerk Maxwell: A Commemorative Volume 1831-1931 (1931), 71.
Science quotes on:  |   (2863)  |  Change (593)  |  Clerk (13)  |  Conception (154)  |  Contribution (89)  |  Electrodynamics (10)  |  Maxwell (42)  |  James Clerk Maxwell (87)  |  Most (1731)  |  Sir Isaac Newton (333)  |  Physic (517)  |  Physics (533)  |  Profound (104)  |  Reality (261)  |  Time (1877)

Those who are fruitful in useful inventions and discoveries, in the practical mechanical arts, are men, not only of the greatest utility, but possess an understanding, which should be most highly estimated.
From 'Artist and Mechanic', The artist & Tradesman’s Guide: embracing some leading facts & principles of science, and a variety of matter adapted to the wants of the artist, mechanic, manufacturer, and mercantile community (1827), 143.
Science quotes on:  |  Art (657)  |  Discovery (780)  |  Greatest (328)  |  High (362)  |  Invention (369)  |  Mechanical (140)  |  Most (1731)  |  Possess (156)  |  Practical (200)  |  Regard (305)  |  Understanding (513)  |  Useful (250)  |  Utility (49)

To the manufacturer, chemistry has lately become fruitful of instruction and assistance. In the arts of brewing, tanning, dying, and bleaching, its doctrines are important guides. In making soap, glass, pottery, and all metallic wares, its principles are daily applied, and are capable of a still more useful application, as they become better understood.
From 'Artist and Mechanic', The artist & Tradesman’s Guide: embracing some leading facts & principles of science, and a variety of matter adapted to the wants of the artist, mechanic, manufacturer, and mercantile community (1827), 9.
Science quotes on:  |  All (4108)  |  Application (242)  |  Applied (177)  |  Art (657)  |  Assistance (20)  |  Become (815)  |  Better (486)  |  Brewing (2)  |  Capable (168)  |  Chemistry (353)  |  Daily (87)  |  Doctrine (75)  |  Dyeing (2)  |  Glass (92)  |  Guide (97)  |  Important (209)  |  Instruction (91)  |  Making (300)  |  Manufacturer (10)  |  More (2559)  |  Pottery (4)  |  Principle (507)  |  Soap (11)  |  Still (613)  |  Tanning (3)  |  Understood (156)  |  Useful (250)  |  Ware (2)

What chemists took from Dalton was not new experimental laws but a new way of practicing chemistry (he himself called it the “new system of chemical philosophy”), and this proved so rapidly fruitful that only a few of the older chemists in France and Britain were able to resist it.
The Structure of Scientific Revolutions (1962), 133.
Science quotes on:  |  Britain (24)  |  Call (769)  |  Chemical (292)  |  Chemist (156)  |  Chemistry (353)  |  John Dalton (21)  |  Experiment (695)  |  Experimental (192)  |  Himself (461)  |  Law (894)  |  New (1216)  |  Philosophy (380)  |  Rapidly (66)  |  System (537)  |  Way (1217)


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.