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

Today in Science History - Quickie Quiz
Who said: “The Superfund legislation... may prove to be as far-reaching and important as any accomplishment of my administration. The reduction of the threat to America's health and safety from thousands of toxic-waste sites will continue to be an urgent…issue …”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index F > Category: Formerly

Formerly Quotes (5 quotes)

First, as concerns the success of teaching mathematics. No instruction in the high schools is as difficult as that of mathematics, since the large majority of students are at first decidedly disinclined to be harnessed into the rigid framework of logical conclusions. The interest of young people is won much more easily, if sense-objects are made the starting point and the transition to abstract formulation is brought about gradually. For this reason it is psychologically quite correct to follow this course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.
In Ueber den Mathematischen Unterricht an den hoheren Schulen; Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 11, 131.
Science quotes on:  |  Abstract (124)  |  Accomplishment (93)  |  Accumulate (26)  |  Addition (66)  |  Application (242)  |  Attention (190)  |  Author (167)  |  Base (117)  |  Basis (173)  |  Begin (260)  |  Beginning (305)  |  Being (1278)  |  Bring (90)  |  Case (99)  |  Completely (135)  |  Concern (228)  |  Conclusion (254)  |  Conviction (97)  |  Correct (86)  |  Course (409)  |  Danger (115)  |  Decade (59)  |  Development (422)  |  Difficult (246)  |  Do (1908)  |  End (590)  |  Essential (199)  |  Exclusive (29)  |  Extent (139)  |  Extreme (75)  |  First (1283)  |  Follow (378)  |  Former (137)  |  Formulation (36)  |  Framework (31)  |  Gradual (27)  |  Gradually (102)  |  Grammar (14)  |  Harness (23)  |  High (362)  |  High School (11)  |  Hold (95)  |  Implant (4)  |  Important (209)  |  Inclined (41)  |  Indispensable (28)  |  Inquire (23)  |  Instruction (91)  |  Interest (386)  |  Interesting (153)  |  Introduction (35)  |  Kernel (4)  |  Language (293)  |  Large (394)  |  Leave (130)  |  Lie (364)  |  Logic (287)  |  Lose (159)  |  Majority (66)  |  Mastery (34)  |  Mathematics (1328)  |  Matter (798)  |  Middle (16)  |  Modern (385)  |  More (2559)  |  Must (1526)  |  Need (290)  |  Object (422)  |  Other (2236)  |  Outer (13)  |  Pendulum (17)  |  People (1005)  |  Permit (58)  |  Point (580)  |  Possible (552)  |  Premise (37)  |  Proper (144)  |  Psychological (42)  |  Purpose (317)  |  Pursue (58)  |  Quicken (7)  |  Quickening (4)  |  Reason (744)  |  Receive (114)  |  Recommend (24)  |  Rigid (24)  |  School (219)  |  Secure (22)  |  Sense (770)  |  Set (394)  |  Set Aside (4)  |  Share (75)  |  Sharpen (22)  |  Side (233)  |  Solid (116)  |  Starting Point (14)  |  Student (300)  |  Stunt (7)  |  Subject (521)  |  Success (302)  |  Surely (101)  |  Swing (11)  |  Teach (277)  |  Teaching (188)  |  Teaching of Mathematics (39)  |  Tendency (99)  |  Think (1086)  |  Thinking (414)  |  Throughout (98)  |  Transition (26)  |  True (212)  |  Understand (606)  |  Understanding (513)  |  Want (497)  |  Whole (738)  |  Wise (131)  |  World (1774)  |  Young (227)

Formerly, when religion was strong and science weak, men mistook magic for medicine; now, when science is strong and religion weak, men mistake medicine for magic.
The Second Sin (1973), 115.
Science quotes on:  |  Magic (86)  |  Medicine (378)  |  Mistake (169)  |  Religion (361)  |  Science (3879)  |  Science And Religion (307)  |  Strength (126)  |  Strong (174)  |  Weak (71)  |  Weakness (48)

The more a science advances, the more will it be possible to understand immediately results which formerly could be demonstrated only by means of lengthy intermediate considerations: a mathematical subject cannot be considered as finally completed until this end has been attained.
In Formensystem binδrer Formen (1875), 2.
Science quotes on:  |  Advance (280)  |  Attain (125)  |  Complete (204)  |  Completed (30)  |  Consider (416)  |  Consideration (139)  |  Demonstrate (76)  |  End (590)  |  Finally (26)  |  Immediately (114)  |  Intermediate (37)  |  Lengthy (3)  |  Mathematics (1328)  |  Mean (809)  |  Means (579)  |  More (2559)  |  Possible (552)  |  Result (677)  |  Science (3879)  |  Study And Research In Mathematics (61)  |  Subject (521)  |  Understand (606)  |  Will (2355)

The solution of the difficulties which formerly surrounded the mathematical infinite is probably the greatest achievement of which our age has to boast.
In 'The Study of Mathematics', Philosophical Essays (1910), 77.
Science quotes on:  |  Achievement (179)  |  Age (499)  |  Boast (22)  |  Difficulty (196)  |  Great (1574)  |  Greatest (328)  |  Infinite (231)  |  Mathematics (1328)  |  Modern Mathematics (50)  |  Probably (49)  |  Solution (267)  |  Surround (30)

What vexes me most is, that my female friends, who could bear me very well a dozen years ago, have now forsaken me, although I am not so old in proportion to them as I formerly was: which I can prove by arithmetic, for then I was double their age, which now I am not.
In Letter (7 Feb 1736) to Alexander Pope, The Works of Jonathan Swift (1841), Vol. 2, 764.
Science quotes on:  |  Age (499)  |  Arithmetic (136)  |  Bear (159)  |  Double (15)  |  Dozen (10)  |  Female (50)  |  Forsake (4)  |  Friend (168)  |  Most (1731)  |  Old (481)  |  Proportion (136)  |  Prove (250)  |  Vex (9)  |  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 Einstein • Isaac Newton • Lord Kelvin • Charles Darwin • Srinivasa Ramanujan • Carl Sagan • Florence Nightingale • Thomas Edison • Aristotle • Marie Curie • Benjamin Franklin • Winston Churchill • Galileo Galilei • Sigmund Freud • Robert Bunsen • Louis Pasteur • Theodore Roosevelt • Abraham Lincoln • Ronald Reagan • Leonardo DaVinci • Michio Kaku • Karl Popper • Johann Goethe • Robert Oppenheimer • Charles Kettering  ... (more people)

Quotations about: • Atomic  Bomb • Biology • Chemistry • Deforestation • Engineering • Anatomy • Astronomy • Bacteria • Biochemistry • Botany • Conservation • Dinosaur • Environment • Fractal • Genetics • Geology • History of Science • Invention • Jupiter • Knowledge • Love • Mathematics • Measurement • Medicine • Natural Resource • Organic Chemistry • Physics • Physician • Quantum Theory • Research • Science and Art • Teacher • Technology • Universe • Volcano • Virus • Wind Power • Women Scientists • X-Rays • Youth • Zoology  ... (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.