Celebrating 18 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 R > Category: Rigor

Rigor Quotes (12 quotes)


Almost every major systematic error which has deluded men for thousands of years relied on practical experience. Horoscopes, incantations, oracles, magic, witchcraft, the cures of witch doctors and of medical practitioners before the advent of modern medicine, were all firmly established through the centuries in the eyes of the public by their supposed practical successes. The scientific method was devised precisely for the purpose of elucidating the nature of things under more carefully controlled conditions and by more rigorous criteria than are present in the situations created by practical problems.
Personal Knowledge (1958), 183.
Science quotes on:  |  Advent (4)  |  Care (73)  |  Century (94)  |  Circumstance (48)  |  Control (93)  |  Criteria (6)  |  Cure (88)  |  Delusion (13)  |  Devising (7)  |  Elucidation (6)  |  Error (230)  |  Establishment (29)  |  Experience (268)  |  Eye (159)  |  Horoscope (2)  |  Incantation (4)  |  Magic (67)  |  Major (24)  |  Medicine (322)  |  Modern (104)  |  Nature (1029)  |  Oracle (4)  |  Practicality (6)  |  Practitioner (12)  |  Precisely (11)  |  Problem (362)  |  Public (82)  |  Purpose (138)  |  Reliance (9)  |  Scientific Method (155)  |  Situation (41)  |  Success (202)  |  Supposition (33)  |  System (141)  |  Thousand (106)  |  Witch Doctor (2)  |  Witchcraft (4)  |  Year (214)

I do not hope for any relief, and that is because I have committed no crime. I might hope for and obtain pardon, if I had erred, for it is to faults that the prince can bring indulgence, whereas against one wrongfully sentenced while he was innocent, it is expedient, in order to put up a show of strict lawfulness, to uphold rigor… . But my most holy intention, how clearly would it appear if some power would bring to light the slanders, frauds, and stratagems, and trickeries that were used eighteen years ago in Rome in order to deceive the authorities!
In Letter to Nicolas-Claude Fabri de Peiresc (22 Feb 1635). As quoted in translation in Giorgio de Santillana, The Crime of Galileo (1976), 324.
Science quotes on:  |  Authority (50)  |  Commit (17)  |  Crime (20)  |  Deceive (8)  |  Fault (27)  |  Fraud (12)  |  Holy (14)  |  Hope (129)  |  Indulgence (3)  |  Innocent (8)  |  Intention (25)  |  Lawfulness (3)  |  Light (246)  |  Pardon (4)  |  Relief (13)  |  Rome (11)  |  Science And Religion (267)  |  Sentence (20)  |  Stratagem (2)  |  Trickery (2)

If physics leads us today to a world view which is essentially mystical, it returns, in a way, to its beginning, 2,500 years ago. ... This time, however, it is not only based on intuition, but also on experiments of great precision and sophistication, and on a rigorous and consistent mathematical formalism.
In The Tao of Physics (1975), 19.
Science quotes on:  |  Beginning (114)  |  Experiment (543)  |  Formalism (5)  |  Intuition (39)  |  Mathematics (587)  |  Mysticism (5)  |  Physics (301)  |  Precision (38)  |  Sophistication (8)  |  View (115)  |  World (667)

If there is something very slightly wrong in our definition of the theories, then the full mathematical rigor may convert these errors into ridiculous conclusions.
Feynman Lectures on Gravitation, edited by Brian Hatfield (2002), 21.
Science quotes on:  |  Conclusion (120)  |  Convert (15)  |  Definition (152)  |  Mathematics (587)  |  Ridiculous (9)  |  Theory (582)

If you disregard the very simplest cases, there is in all of mathematics not a single infinite series whose sum has been rigorously determined. In other words, the most important parts of mathematics stand without a foundation.
In Letter to a friend, as quoted in George Finlay Simmons, Calculus Gems (1992), 188.
Science quotes on:  |  Case (64)  |  Disregard (8)  |  Foundation (75)  |  Importance (183)  |  Infinite Series (2)  |  Mathematics (587)  |  Simplicity (126)  |  Sum (30)

Mathematics is of two kinds, Rigorous and Physical. The former is Narrow: the latter Bold and Broad. To have to stop to formulate rigorous demonstrations would put a stop to most physico-mathematical inquiries. Am I to refuse to eat because I do not fully understand the mechanism of digestion?
As quoted by Charles Melbourne Focken in Dimensional Methods and Their Applications (1953), 17.
Science quotes on:  |  Bold (3)  |  Broad (18)  |  Demonstration (51)  |  Digestion (23)  |  Eating (21)  |  Formulation (20)  |  Kind (99)  |  Mathematics (587)  |  Mechanism (41)  |  Narrow (33)  |  Physical (94)  |  Refusal (20)  |  Stop (56)

Measurement has too often been the leitmotif of many investigations rather than the experimental examination of hypotheses. Mounds of data are collected, which are statistically decorous and methodologically unimpeachable, but conclusions are often trivial and rarely useful in decision making. This results from an overly rigorous control of an insignificant variable and a widespread deficiency in the framing of pertinent questions. Investigators seem to have settled for what is measurable instead of measuring what they would really like to know.
'Patient Care—Mystical Research or Researchable Mystique/', Clinical Research (1964), 12, no. 4, 422.
Science quotes on:  |  Collection (38)  |  Conclusion (120)  |  Control (93)  |  Data (100)  |  Decision (58)  |  Deficiency (8)  |  Examination (60)  |  Experiment (543)  |  Framing (2)  |  Hypothesis (227)  |  Insignificance (9)  |  Investigation (123)  |  Investigator (28)  |  Knowledge (1128)  |  Like (18)  |  Measurement (148)  |  Methodology (8)  |  Pertinent (3)  |  Question (315)  |  Rare (31)  |  Result (250)  |  Settle (10)  |  Statistics (125)  |  Trivial (30)  |  Usefulness (70)  |  Variable (9)  |  Widespread (9)

Real science exists, then, only from the moment when a phenomenon is accurately defined as to its nature and rigorously determined in relation to its material conditions, that is, when its law is known. Before that, we have only groping and empiricism.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (reprint 1999), 74.
Science quotes on:  |  Accuracy (52)  |  Condition (119)  |  Definition (152)  |  Determination (53)  |  Empiricism (16)  |  Existence (254)  |  Groping (3)  |  Knowledge (1128)  |  Law (418)  |  Material (124)  |  Moment (61)  |  Nature (1029)  |  Phenomenon (218)  |  Real (95)  |  Relation (96)  |  Science (1699)

The great masters of modern analysis are Lagrange, Laplace, and Gauss, who were contemporaries. It is interesting to note the marked contrast in their styles. Lagrange is perfect both in form and matter, he is careful to explain his procedure, and though his arguments are general they are easy to follow. Laplace on the other hand explains nothing, is indifferent to style, and, if satisfied that his results are correct, is content to leave them either with no proof or with a faulty one. Gauss is as exact and elegant as Lagrange, but even more difficult to follow than Laplace, for he removes every trace of the analysis by which he reached his results, and studies to give a proof which while rigorous shall be as concise and synthetical as possible.
History of Mathematics (3rd Ed., 1901), 468.
Science quotes on:  |  Analysis (123)  |  Anecdote (17)  |  Concise (4)  |  Contemporary (22)  |  Content (39)  |  Contrast (16)  |  Correct (53)  |  Difficult (62)  |  Easy (56)  |  Elegant (8)  |  Exact (38)  |  Explanation (161)  |  Faulty (2)  |  Carl Friedrich Gauss (55)  |  Count Joseph-Louis de Lagrange (11)  |  Pierre-Simon Laplace (50)  |  Leave (63)  |  Perfection (71)  |  Procedure (16)  |  Proof (192)  |  Reasoning (79)  |  Remove (18)  |  Result (250)  |  Satisfy (14)  |  Style (15)  |  Synthetic (12)

The only way in which to treat the elements of an exact and rigorous science is to apply to them all the rigor and exactness possible.
Quoted in De Morgan, Trigonometry and Double Algebra (1849), Title page.
Science quotes on:  |  Apply (38)  |  Exact (38)  |  Science (1699)  |  Teaching (99)  |  Treat (17)

True rigor is productive, being distinguished in this from another rigor which is purely formal and tiresome, casting a shadow over the problems it touches.
From address to the section of Algebra and Analysis, International Congress of Arts and Sciences, St. Louis (22 Sep 1904), 'On the Development of Mathematical Analysis and its Relation to Certain Other Sciences,' as translated by M.W. Haskell in Bulletin of the American Mathematical Society (May 1905), 11, 417.
Science quotes on:  |  Casting (3)  |  Distinguish (32)  |  Formal (11)  |  Problem (362)  |  Productive (10)  |  Purely (15)  |  Shadow (35)  |  Touch (48)  |  True (120)

[about Fourier] It was, no doubt, partially because of his very disregard for rigor that he was able to take conceptual steps which were inherently impossible to men of more critical genius
…...
Science quotes on:  |  Conceptual (8)  |  Critical (34)  |  Disregard (8)  |  Doubt (121)  |  Fourier (2)  |  Genius (186)  |  Impossible (68)  |  Inherently (5)  |  Partially (2)  |  Step (67)


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.