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

Today in Science History - Quickie Quiz
Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
more quiz questions >>
Home > Dictionary of Science Quotations > Scientist Names Index C > George Chrystal Quotes

George Chrystal
(8 Mar 1851 - 3 Nov 1911)

Scottish physicist and mathematician who wrote books on algebra. He is particularly notable for his studies of seiches (standing wave patterns in large inland bodies of water, caused when strong winds and rapid changes in atmospheric pressure push water to one end of the lake, and the water wave there reflects back on itself.)

Science Quotes by George Chrystal (7 quotes)

Any conception which is definitely and completely determined by means of a finite number of specifications, say by assigning a finite number of elements, is a mathematical conception. Mathematics has for its function to develop the consequences involved in the definition of a group of mathematical conceptions. Interdependence and mutual logical consistency among the members of the group are postulated, otherwise the group would either have to be treated as several distinct groups, or would lie beyond the sphere of mathematics.
— George Chrystal
In 'Mathematics', Encyclopedia Britannica (9th ed.).
Science quotes on:  |  Assign (13)  |  Beyond (308)  |  Complete (204)  |  Completely (135)  |  Conception (154)  |  Consequence (203)  |  Consistency (31)  |  Consistent (48)  |  Definite (110)  |  Definition (221)  |  Definitions and Objects of Mathematics (33)  |  Determine (144)  |  Develop (268)  |  Distinct (97)  |  Element (310)  |  Finite (59)  |  Function (228)  |  Group (78)  |  Interdependence (4)  |  Involve (90)  |  Involved (90)  |  Lie (364)  |  Logical (55)  |  Mathematics (1328)  |  Mean (809)  |  Means (579)  |  Member (41)  |  Mutual (52)  |  Number (699)  |  Otherwise (24)  |  Postulate (38)  |  Say (984)  |  Several (32)  |  Specification (7)  |  Sphere (116)  |  Treat (35)

Every mathematical book that is worth reading must be read “backwards and forwards”, if I may use the expression. I would modify Lagrange’s advice a little and say, “Go on, but often return to strengthen your faith.” When you come on a hard or dreary passage, pass it over; and come back to it after you have seen its importance or found the need for it further on.
— George Chrystal
In Algebra, Part 2 (1889), Preface, viii.
Science quotes on:  |  Advice (55)  |  Back (390)  |  Backwards (17)  |  Book (392)  |  Dreary (5)  |  Expression (175)  |  Faith (203)  |  Far (154)  |  Find (998)  |  Forward (102)  |  Hard (243)  |  Importance (286)  |  Count Joseph-Louis de Lagrange (26)  |  Little (707)  |  Mathematics (1328)  |  Modify (15)  |  Must (1526)  |  Need (290)  |  Often (106)  |  Pass (238)  |  Passage (50)  |  Read (287)  |  Reading (133)  |  Return (124)  |  Say (984)  |  See (1081)  |  Strengthen (23)  |  Study And Research In Mathematics (61)  |  Use (766)  |  Worth (169)

Quantity is that which is operated with according to fixed mutually consistent laws. Both operator and operand must derive their meaning from the laws of operation. In the case of ordinary algebra these are the three laws already indicated [the commutative, associative, and distributive laws], in the algebra of quaternions the same save the law of commutation for multiplication and division, and so on. It may be questioned whether this definition is sufficient, and it may be objected that it is vague; but the reader will do well to reflect that any definition must include the linear algebras of Peirce, the algebra of logic, and others that may be easily imagined, although they have not yet been developed. This general definition of quantity enables us to see how operators may be treated as quantities, and thus to understand the rationale of the so called symbolical methods.
— George Chrystal
In 'Mathematics', Encyclopedia Britannica (9th ed.).
Science quotes on:  |  Accord (36)  |  According (237)  |  Algebra (113)  |  Already (222)  |  Both (493)  |  Call (769)  |  Consistent (48)  |  Definition (221)  |  Definitions and Objects of Mathematics (33)  |  Derive (65)  |  Develop (268)  |  Distributive (2)  |  Division (65)  |  Do (1908)  |  Enable (119)  |  Fix (25)  |  General (511)  |  Include (90)  |  Law (894)  |  Linear (13)  |  Logic (287)  |  Meaning (233)  |  Method (505)  |  Methods (204)  |  Multiplication (43)  |  Must (1526)  |  Mutually (7)  |  Object (422)  |  Operate (17)  |  Operation (213)  |  Operator (3)  |  Ordinary (160)  |  Other (2236)  |  Charles Sanders Peirce (22)  |  Quantity (132)  |  Quaternion (9)  |  Question (621)  |  Rationale (7)  |  Reader (40)  |  Reflect (32)  |  Save (118)  |  See (1081)  |  Sufficient (128)  |  Understand (606)  |  Vague (47)  |  Will (2355)

The logic of the subject [algebra], which, both educationally and scientifically speaking, is the most important part of it, is wholly neglected. The whole training consists in example grinding. What should have been merely the help to attain the end has become the end itself. The result is that algebra, as we teach it, is neither an art nor a science, but an ill-digested farrago of rules, whose object is the solution of examination problems. … The result, so far as problems worked in examinations go, is, after all, very miserable, as the reiterated complaints of examiners show; the effect on the examinee is a well-known enervation of mind, an almost incurable superficiality, which might be called Problematic Paralysis—a disease which unfits a man to follow an argument extending beyond the length of a printed octavo page.
— George Chrystal
In Presidential Address British Association for the Advancement of Science (1885), Nature, 32, 447-448.
Science quotes on:  |  Algebra (113)  |  All (4108)  |  Argument (138)  |  Art (657)  |  Attain (125)  |  Become (815)  |  Beyond (308)  |  Both (493)  |  Call (769)  |  Complaint (11)  |  Consist (223)  |  Digest (9)  |  Disease (328)  |  Education (378)  |  Effect (393)  |  End (590)  |  Enervation (2)  |  Examination (98)  |  Examiner (5)  |  Example (94)  |  Far (154)  |  Follow (378)  |  Grind (11)  |  Help (105)  |  Important (209)  |  Incurable (10)  |  Known (454)  |  Logic (287)  |  Man (2251)  |  Merely (316)  |  Mind (1338)  |  Miserable (7)  |  Most (1731)  |  Neglect (63)  |  Neglected (23)  |  Object (422)  |  Page (30)  |  Paralysis (9)  |  Part (222)  |  Problem (676)  |  Reiterate (2)  |  Result (677)  |  Rule (294)  |  Science (3879)  |  Science And Art (184)  |  Scientific (941)  |  Show (346)  |  Solution (267)  |  Speaking (119)  |  Subject (521)  |  Superficial (12)  |  Teach (277)  |  Teaching of Mathematics (39)  |  Training (80)  |  Unfit (12)  |  Whole (738)  |  Wholly (88)  |  Work (1351)

The mathematical conception is, from its very nature, abstract; indeed its abstractness is usually of a higher order than the abstractness of the logician.
— George Chrystal
In 'Mathematics', Encyclopedia Britannica (1883), Vol. 15, 636.
Science quotes on:  |  Abstract (124)  |  Conception (154)  |  Indeed (324)  |  Logician (17)  |  Mathematics (1328)  |  Mathematics And Logic (12)  |  Nature (1926)  |  Order (632)  |  Usually (176)

The problem for a writer of a text-book has come now, in fact, to be this—to write a book so neatly trimmed and compacted that no coach, on looking through it, can mark a single passage which the candidate for a minimum pass can safely omit. Some of these text-books I have seen, where the scientific matter has been, like the lady’s waist in the nursery song, compressed “so gent and sma’,” that the thickness barely, if at all, surpasses what is devoted to the publisher’s advertisements. We shall return, I verily believe, to the Compendium of Martianus Capella. The result of all this is that science, in the hands of specialists, soars higher and higher into the light of day, while educators and the educated are left more and more to wander in primeval darkness.
— George Chrystal
In Presidential Address British Association for the Advancement of Science (1885), Nature, 32, 448. [Martianus Capella, who flourished c.410-320, wrote a compendium of the seven liberal arts. —Webmaster]
Science quotes on:  |  Advertisement (13)  |  All (4108)  |  Barely (5)  |  Book (392)  |  Candidate (8)  |  Coach (5)  |  Compact (13)  |  Compress (2)  |  Darkness (68)  |  Devote (35)  |  Devoted (59)  |  Educator (5)  |  Fact (1210)  |  Higher (37)  |  Lady (11)  |  Light (607)  |  Looking (189)  |  Mark (43)  |  Matter (798)  |  Minimum (12)  |  More (2559)  |  Neat (5)  |  Nursery (4)  |  Omit (11)  |  Pass (238)  |  Passage (50)  |  Primeval (15)  |  Problem (676)  |  Publisher (3)  |  Result (677)  |  Return (124)  |  Safely (8)  |  Science (3879)  |  Scientific (941)  |  Single (353)  |  Soar (23)  |  Song (37)  |  Specialist (28)  |  Student (300)  |  Surpass (32)  |  Teaching of Mathematics (39)  |  Text-Book (5)  |  Thickness (5)  |  Through (849)  |  Trim (3)  |  Waist (2)  |  Wander (35)  |  Write (230)  |  Writer (86)

This formula [for computing Bernoulli’s numbers] was first given by James Bernoulli…. He gave no general demonstration; but was quite aware of the importance of his theorem, for he boasts that by means of it he calculated intra semi-quadrantem horæ! the sum of the 10th powers of the first thousand integers, and found it to be
91,409,924,241,424,243,424,241,924,242,500.

— George Chrystal
In 'Bernoulli’s Expression for ΣNr', Algebra, Vol. 2 (1879, 1889), 209. The ellipsis is for the reference (Ars Conjectandi (1713), 97). [The Latin phrase, “intra semi-quadrantem horæ!” refers to within a fraction of an hour. —Webmaster]
Science quotes on:  |  Aware (31)  |  Boast (22)  |  Calculate (54)  |  Compute (18)  |  Demonstration (113)  |  First (1283)  |  Formula (98)  |  General (511)  |  Importance (286)  |  Integer (10)  |  Mathematicians and Anecdotes (141)  |  Mean (809)  |  Means (579)  |  Number (699)  |  Power (746)  |  Sum (102)  |  Theorem (112)  |  Thousand (331)



Quotes by others about George Chrystal (1)

Quite distinct from the theoretical question of the manner in which mathematics will rescue itself from the perils to which it is exposed by its own prolific nature is the practical problem of finding means of rendering available for the student the results which have been already accumulated, and making it possible for the learner to obtain some idea of the present state of the various departments of mathematics. … The great mass of mathematical literature will be always contained in Journals and Transactions, but there is no reason why it should not be rendered far more useful and accessible than at present by means of treatises or higher text-books. The whole science suffers from want of avenues of approach, and many beautiful branches of mathematics are regarded as difficult and technical merely because they are not easily accessible. … I feel very strongly that any introduction to a new subject written by a competent person confers a real benefit on the whole science. The number of excellent text-books of an elementary kind that are published in this country makes it all the more to be regretted that we have so few that are intended for the advanced student. As an example of the higher kind of text-book, the want of which is so badly felt in many subjects, I may mention the second part of Prof. Chrystal’s Algebra published last year, which in a small compass gives a great mass of valuable and fundamental knowledge that has hitherto been beyond the reach of an ordinary student, though in reality lying so close at hand. I may add that in any treatise or higher text-book it is always desirable that references to the original memoirs should be given, and, if possible, short historic notices also. I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history.
In Presidential Address British Association for the Advancement of Science, Section A (1890), Nature, 42, 466.
Science quotes on:  |   (2863)  |  Accessible (25)  |  Accumulate (26)  |  Add (40)  |  Advance (280)  |  Algebra (113)  |  All (4108)  |  Already (222)  |  Approach (108)  |  At Hand (4)  |  Attempt (251)  |  Available (78)  |  Avenue (14)  |  Badly (32)  |  Beautiful (258)  |  Benefit (114)  |  Beyond (308)  |  Book (392)  |  Branch (150)  |  Close (69)  |  Compass (34)  |  Competent (20)  |  Confer (11)  |  Contain (68)  |  Country (251)  |  Department (92)  |  Desirable (33)  |  Difficult (246)  |  Distinct (97)  |  Easily (35)  |  Elementary (96)  |  Example (94)  |  Excellent (28)  |  Expose (23)  |  Exposed (33)  |  Far (154)  |  Feel (367)  |  Find (998)  |  Fundamental (250)  |  Give (202)  |  Great (1574)  |  High (362)  |  Historic (7)  |  History (673)  |  Hitherto (6)  |  Idea (843)  |  Intend (16)  |  Introduction (35)  |  Journal (30)  |  Kind (557)  |  Knowledge (1529)  |  Last (426)  |  Learner (10)  |  Lie (364)  |  Literature (103)  |  Lose (159)  |  Lying (55)  |  Making (300)  |  Manner (58)  |  Mass (157)  |  Mathematics (1328)  |  Mean (809)  |  Means (579)  |  Memoir (13)  |  Mention (82)  |  Merely (316)  |  More (2559)  |  Nature (1926)  |  New (1216)  |  Notice (77)  |  Number (699)  |  Obtain (163)  |  Ordinary (160)  |  Original (58)  |  Part (222)  |  Peril (9)  |  Person (363)  |  Possible (552)  |  Practical (200)  |  Present (619)  |  Problem (676)  |  Prof (2)  |  Prolific (5)  |  Publish (36)  |  Question (621)  |  Reach (281)  |  Real (149)  |  Reality (261)  |  Reason (744)  |  Reference (33)  |  Regard (305)  |  Regret (30)  |  Render (93)  |  Rescue (13)  |  Result (677)  |  Science (3879)  |  Second (62)  |  Short (197)  |  Small (477)  |  State (491)  |  Strongly (9)  |  Student (300)  |  Study And Research In Mathematics (61)  |  Subject (521)  |  Suffer (41)  |  Technical (43)  |  Textbook (36)  |  Theory (970)  |  Transaction (13)  |  Treatise (44)  |  Useful (250)  |  Value (365)  |  Various (200)  |  Want (497)  |  Whole (738)  |  Why (491)  |  Will (2355)  |  Write (230)  |  Year (933)


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.