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

Today in Science History - Quickie Quiz
Who said: “Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index A > Category: Applicable

Applicable Quotes (11 quotes)

...it is not to be taken in the sense of our day, which we reckon by the course of the sun; but it must have another meaning, applicable to the
three days mentioned before the creation of the heavenly bodies.
iv.26
Science quotes on:  |  Body (247)  |  Course (84)  |  Creation (242)  |  Heavenly (8)  |  Mean (101)  |  Mention (23)  |  Reckon (16)  |  Sense (321)  |  Sun (276)

Generality of points of view and of methods, precision and elegance in presentation, have become, since Lagrange, the common property of all who would lay claim to the rank of scientific mathematicians. And, even if this generality leads at times to abstruseness at the expense of intuition and applicability, so that general theorems are formulated which fail to apply to a single special case, if furthermore precision at times degenerates into a studied brevity which makes it more difficult to read an article than it was to write it; if, finally, elegance of form has well-nigh become in our day the criterion of the worth or worthlessness of a proposition,—yet are these conditions of the highest importance to a wholesome development, in that they keep the scientific material within the limits which are necessary both intrinsically and extrinsically if mathematics is not to spend itself in trivialities or smother in profusion.
In Die Entwickdung der Mathematik in den letzten Jahrhunderten (1884), 14-15.
Science quotes on:  |  Abstruse (5)  |  Apply (77)  |  Article (22)  |  Brevity (7)  |  Claim (71)  |  Common (122)  |  Condition (163)  |  Criterion (18)  |  Degenerate (14)  |  Development (289)  |  Difficult (121)  |  Elegance (30)  |  Expense (15)  |  Fail (58)  |  Form (314)  |  Formulate (15)  |  General (160)  |  Generality (34)  |  Importance (218)  |  Intrinsic (12)  |  Intuition (57)  |  Count Joseph-Louis de Lagrange (26)  |  Limit (126)  |  Mathematician (384)  |  Mathematics (1205)  |  Method (239)  |  Modern Mathematics (38)  |  Necessary (154)  |  Point Of View (41)  |  Precision (52)  |  Presentation (18)  |  Profusion (3)  |  Property (126)  |  Proposition (83)  |  Rank (32)  |  Read (145)  |  Scientific (236)  |  Single (120)  |  Smother (3)  |  Special Case (6)  |  Spend (43)  |  Study (476)  |  Theorem (90)  |  Triviality (2)  |  Wholesome (7)  |  Worth (99)  |  Worthless (21)  |  Write (154)

I love mathematics not only because it is applicable to technology but also because it is beautiful.
In Eberhard Zeidler, Quantum Field Theory (2006), 955.
Science quotes on:  |  Beautiful (144)  |  Love (224)  |  Mathematics (1205)  |  Technology (222)

Indeed, the aim of teaching [mathematics] should be rather to strengthen his [the pupil’s] faculties, and to supply a method of reasoning applicable to other subjects, than to furnish him with an instrument for solving practical problems.
In John Perry (ed.), Discussion on the Teaching of Mathematics (1901), 84. The discussion took place on 14 Sep 1901 at the British Association at Glasgow, during a joint meeting of the mathematics and physics sections with the education section. The proceedings began with an address by John Perry. Magnus spoke in the Discussion that followed.
Science quotes on:  |  Aim (89)  |  Faculty (70)  |  Furnish (42)  |  Instrument (95)  |  Mathematics (1205)  |  Method (239)  |  Practical (133)  |  Problem (497)  |  Pupil (36)  |  Reasoning (100)  |  Solve (78)  |  Strengthen (22)  |  Subject (240)  |  Supply (47)  |  Teach (188)  |  Teaching of Mathematics (39)

It was his [Leibnitz’s] love of method and order, and the conviction that such order and harmony existed in the real world, and that our success in understanding it depended upon the degree and order which we could attain in our own thoughts, that originally was probably nothing more than a habit which by degrees grew into a formal rule. This habit was acquired by early occupation with legal and mathematical questions. We have seen how the theory of combinations and arrangements of elements had a special interest for him. We also saw how mathematical calculations served him as a type and model of clear and orderly reasoning, and how he tried to introduce method and system into logical discussions, by reducing to a small number of terms the multitude of compound notions he had to deal with. This tendency increased in strength, and even in those early years he elaborated the idea of a general arithmetic, with a universal language of symbols, or a characteristic which would be applicable to all reasoning processes, and reduce philosophical investigations to that simplicity and certainty which the use of algebraic symbols had introduced into mathematics.
A mental attitude such as this is always highly favorable for mathematical as well as for philosophical investigations. Wherever progress depends upon precision and clearness of thought, and wherever such can be gained by reducing a variety of investigations to a general method, by bringing a multitude of notions under a common term or symbol, it proves inestimable. It necessarily imports the special qualities of number—viz., their continuity, infinity and infinite divisibility—like mathematical quantities—and destroys the notion that irreconcilable contrasts exist in nature, or gaps which cannot be bridged over. Thus, in his letter to Arnaud, Leibnitz expresses it as his opinion that geometry, or the philosophy of space, forms a step to the philosophy of motion—i.e., of corporeal things—and the philosophy of motion a step to the philosophy of mind.
In Leibnitz (1884), 44-45. [The first sentence is reworded to better introduce the quotation. —Webmaster]
Science quotes on:  |  Acquire (39)  |  Algebraic (5)  |  Arithmetic (121)  |  Arrangement (60)  |  Attain (45)  |  Attitude (59)  |  Bridge (30)  |  Bring (90)  |  Calculation (100)  |  Certainty (131)  |  Characteristic (96)  |  Clear (98)  |  Clearness (11)  |  Combination (91)  |  Common (122)  |  Compound (58)  |  Continuity (30)  |  Contrast (29)  |  Conviction (71)  |  Corporeal (5)  |  Deal (49)  |  Degree (82)  |  Depend (90)  |  Destroy (80)  |  Discussion (48)  |  Early (62)  |  Elaborate (21)  |  Element (162)  |  Exist (148)  |  Express (65)  |  Favorable (12)  |  Form (314)  |  Formal (33)  |  Gain (70)  |  Gap (23)  |  General (160)  |  Geometry (232)  |  Grow (99)  |  Habit (112)  |  Harmony (72)  |  Highly (16)  |  Idea (580)  |  Import (5)  |  Increase (146)  |  Inestimable (4)  |  Infinite (130)  |  Infinity (72)  |  Introduce (42)  |  Investigation (176)  |  Language (228)  |  Lecture (68)  |  Legal (8)  |  Gottfried Wilhelm Leibniz (49)  |  Letter (51)  |  Logical (55)  |  Love (224)  |  Mathematicians and Anecdotes (141)  |  Mathematics (1205)  |  Mental (78)  |  Method (239)  |  Mind (760)  |  Model (81)  |  Motion (160)  |  Multitude (20)  |  Nature (1223)  |  Necessarily (30)  |  Nothing (395)  |  Notion (59)  |  Number (282)  |  Occupation (41)  |  Opinion (176)  |  Order (242)  |  Orderly (14)  |  Original (57)  |  Philosophical (23)  |  Philosophy (259)  |  Precision (52)  |  Probable (20)  |  Process (267)  |  Progress (368)  |  Prove (109)  |  Purpose (194)  |  Quality (95)  |  Quantity (65)  |  Question (404)  |  Quotation (8)  |  Real World (14)  |  Reason (471)  |  Reduce (53)  |  Rule (177)  |  See (369)  |  Sentence (28)  |  Serve (58)  |  Simplicity (147)  |  Small (163)  |  Space (257)  |  Special (77)  |  Special Interest (2)  |  Step (110)  |  Strength (81)  |  Success (250)  |  Symbol (73)  |  System (191)  |  Tendency (56)  |  Term (122)  |  Theory (696)  |  Thought (546)  |  Try (141)  |  Type (52)  |  Understand (340)  |  Universal (105)  |  Variety (71)  |  Year (299)

Mathematics is the language of languages, the best school for sharpening thought and expression, is applicable to all processes in nature; and Germany needs mathematical gymnasia. Mathematics is God’s form of speech, and simplifies all things organic and inorganic. As knowledge becomes real, complete and great it approximates mathematical forms. It mediates between the worlds of mind and of matter.
Summarizing the ideas presented by Christian Heinrich Dillmann in Die Mathematik die Fackelträgerin einer neuen Zeit (1889). From book review, 'Recent Literature on Arithmetic and Arithmetical Teaching', in Granville Stanley Hall (ed.), The Pedagogical Seminary (1892), 2, 168. Dillmann’s book title translates as “Mathematics the Torchbearer of a New Era”. (However, Conant concluded that it was a “loosely-written, vague and incoherent book, which belies every anticipation awakened by its attractive title.”)
Science quotes on:  |  Approximate (10)  |  Become (172)  |  Best (173)  |  Complete (87)  |  Expression (110)  |  Form (314)  |  Germany (13)  |  God (535)  |  Great (534)  |  Inorganic (13)  |  Knowledge (1306)  |  Language (228)  |  Mathematics (1205)  |  Matter (343)  |  Mediate (4)  |  Mind (760)  |  Nature (1223)  |  Need (287)  |  Organic (55)  |  Process (267)  |  Real (149)  |  School (119)  |  Sharpen (16)  |  Simplify (11)  |  Speech (47)  |  Thought (546)  |  World (898)

Nothing is less applicable to life than mathematical reasoning. A proposition in mathematics is decidedly false or true. Everywhere else the true is mingled with the false.
Quoted, without citation, in David Eugene Smith, The Teaching of Elementary Mathematics (1904), 170.
Science quotes on:  |  Everywhere (24)  |  False (99)  |  Less (102)  |  Life (1131)  |  Mathematics (1205)  |  Mingle (7)  |  Nothing (395)  |  Proposition (83)  |  Reasoning (100)  |  True (208)

The origin of a science is usually to be sought for not in any systematic treatise, but in the investigation and solution of some particular problem. This is especially the case in the ordinary history of the great improvements in any department of mathematical science. Some problem, mathematical or physical, is proposed, which is found to be insoluble by known methods. This condition of insolubility may arise from one of two causes: Either there exists no machinery powerful enough to effect the required reduction, or the workmen are not sufficiently expert to employ their tools in the performance of an entirely new piece of work. The problem proposed is, however, finally solved, and in its solution some new principle, or new application of old principles, is necessarily introduced. If a principle is brought to light it is soon found that in its application it is not necessarily limited to the particular question which occasioned its discovery, and it is then stated in an abstract form and applied to problems of gradually increasing generality.
Other principles, similar in their nature, are added, and the original principle itself receives such modifications and extensions as are from time to time deemed necessary. The same is true of new applications of old principles; the application is first thought to be merely confined to a particular problem, but it is soon recognized that this problem is but one, and generally a very simple one, out of a large class, to which the same process of investigation and solution are applicable. The result in both of these cases is the same. A time comes when these several problems, solutions, and principles are grouped together and found to produce an entirely new and consistent method; a nomenclature and uniform system of notation is adopted, and the principles of the new method become entitled to rank as a distinct science.
In A Treatise on Projections (1880), Introduction, xi. Published as United States Coast and Geodetic Survey, Treasury Department Document, No. 61.
Science quotes on:  |  Abstract (86)  |  Add (40)  |  Adopt (19)  |  Application (170)  |  Apply (77)  |  Arise (49)  |  Become (172)  |  Both (81)  |  Bring (90)  |  Case (99)  |  Cause (285)  |  Class (84)  |  Condition (163)  |  Confine (26)  |  Consistent (18)  |  Deem (6)  |  Department (47)  |  Discovery (680)  |  Distinct (46)  |  Effect (166)  |  Employ (35)  |  Entirely (33)  |  Entitle (3)  |  Especially (31)  |  Exist (148)  |  Expert (50)  |  Extension (31)  |  Finally (26)  |  Find (408)  |  First (314)  |  Form (314)  |  Generality (34)  |  Generally (15)  |  Gradually (21)  |  Great (534)  |  Group (72)  |  History (369)  |  Improvement (74)  |  Increase (146)  |  Insoluble (15)  |  Introduce (42)  |  Investigation (176)  |  Know (556)  |  Large (130)  |  Light (347)  |  Limit (126)  |  Machinery (33)  |  Mathematics (1205)  |  Merely (82)  |  Method (239)  |  Modification (35)  |  Nature (1223)  |  Necessarily (30)  |  Necessary (154)  |  New (496)  |  Nomenclature (138)  |  Notation (23)  |  Occasion (23)  |  Old (147)  |  Ordinary (73)  |  Origin (88)  |  Original (57)  |  Particular (76)  |  Performance (33)  |  Physical (134)  |  Piece (38)  |  Powerful (68)  |  Principle (292)  |  Problem (497)  |  Process (267)  |  Produce (102)  |  Propose (23)  |  Question (404)  |  Rank (32)  |  Receive (60)  |  Recognize (69)  |  Reduction (41)  |  Require (85)  |  Result (389)  |  Same (156)  |  Science (2067)  |  Seek (107)  |  Several (31)  |  Similar (35)  |  Simple (178)  |  Solution (216)  |  Solve (78)  |  Soon (34)  |  State (137)  |  Study And Research In Mathematics (61)  |  Sufficiently (9)  |  System (191)  |  Systematic (33)  |  Thought (546)  |  Time (595)  |  Together (79)  |  Tool (87)  |  Treatise (34)  |  True (208)  |  Uniform (18)  |  Usually (31)  |  Work (635)  |  Workman (13)

The scientific method of examining facts is not peculiar to one class of phenomena and to one class of workers; it is applicable to social as well as to physical problems, and we must carefully guard ourselves against supposing that the scientific frame of mind is a peculiarity of the professional scientist.
From The Grammar of Science (1892), 8.
Science quotes on:  |  Care (95)  |  Class (84)  |  Examination (65)  |  Fact (733)  |  Guard (18)  |  Peculiar (45)  |  Peculiarity (19)  |  Physical (134)  |  Problem (497)  |  Professional (37)  |  Scientific Method (166)  |  Scientist (522)  |  Social (108)  |  Supposition (37)  |  Worker (30)

To ask what qualities distinguish good from routine scientific research is to address a question that should be of central concern to every scientist. We can make the question more tractable by rephrasing it, “What attributes are shared by the scientific works which have contributed importantly to our understanding of the physical world—in this case the world of living things?” Two of the most widely accepted characteristics of good scientific work are generality of application and originality of conception. . These qualities are easy to point out in the works of others and, of course extremely difficult to achieve in one’s own research. At first hearing novelty and generality appear to be mutually exclusive, but they really are not. They just have different frames of reference. Novelty has a human frame of reference; generality has a biological frame of reference. Consider, for example, Darwinian Natural Selection. It offers a mechanism so widely applicable as to be almost coexistent with reproduction, so universal as to be almost axiomatic, and so innovative that it shook, and continues to shake, man’s perception of causality.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 230.
Science quotes on:  |  Accept (65)  |  Achieve (64)  |  Address (12)  |  Appear (118)  |  Application (170)  |  Ask (160)  |  Attribute (38)  |  Axiomatic (2)  |  Biological (35)  |  Case (99)  |  Causality (10)  |  Central (34)  |  Characteristic (96)  |  Conception (92)  |  Concern (110)  |  Consider (81)  |  Continue (65)  |  Contribute (27)  |  Darwinian (9)  |  Different (186)  |  Difficult (121)  |  Distinguish (64)  |  Easy (102)  |  Example (94)  |  Exclusive (16)  |  Extremely (15)  |  First (314)  |  Frame (26)  |  Frame of Reference (4)  |  Generality (34)  |  Good (345)  |  Hear (63)  |  Human (550)  |  Importantly (3)  |  Innovative (2)  |  Living Things (5)  |  Mechanism (52)  |  Mutually (7)  |  Natural Selection (90)  |  Novelty (23)  |  Of Course (20)  |  Offer (43)  |  Originality (18)  |  Perception (64)  |  Physical World (12)  |  Point Out (8)  |  Quality (95)  |  Question (404)  |  Really (78)  |  Reference (33)  |  Rephrase (2)  |  Reproduction (61)  |  Research (590)  |  Routine (19)  |  Scientific (236)  |  Scientist (522)  |  Shake (29)  |  Share (49)  |  Understand (340)  |  Universal (105)  |  Widely (8)  |  Work (635)  |  World (898)

[Mathematics is] the study of ideal constructions (often applicable to real problems), and the discovery thereby of relations between the parts of these constructions, before unknown.
In 'Mathematics', Century Dictionary.
Science quotes on:  |  Construction (83)  |  Definitions and Objects of Mathematics (33)  |  Discovery (680)  |  Ideal (72)  |  Mathematics (1205)  |  Often (106)  |  Part (222)  |  Problem (497)  |  Real (149)  |  Relation (154)  |  Study (476)  |  Unknown (107)


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.