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Home > Category Index for Science Quotations > Category Index R > Category: Rigorous

Rigorous Quotes (10 quotes)

Descriptive geometry has two objects: the first is to establish methods to represent on drawing paper which has only two dimensions,—namely, length and width,—all solids of nature which have three dimensions,—length, width, and depth,—provided, however, that these solids are capable of rigorous definition.
The second object is to furnish means to recognize accordingly an exact description of the forms of solids and to derive thereby all truths which result from their forms and their respective positions.
From On the Purpose of Descriptive Geometry as translated by Arnold Emch in David Eugene Smith, A Source Book in Mathematics (1929), 426.
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Facts are the materials of science, but all Facts involve Ideas. … we must, for the purposes of science, take care that the Ideas are clear and rigorously applied.
Aphorism 4, 'Aphorisms Concerning Science', The Philosophy of the Inductive Sciences (1840), Vol. 1, xxxvii.
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If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.
Address (28 Mar 1912), Michigan School Masters' Club, Ann Arbor, 'The Humanization of the Teaching of Mathematics. Printed in Science (26 Apr 1912). Collected in The Human Worth of Rigorous Thinking: Essays and Addresses (1916), 65-66.
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Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems—general and specific statements—can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences.
Essay,'Private Games', in Lewis Wolpert, Alison Richards (eds.), A Passion for Science (1988), 53.
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Phony psychics like Uri Geller have had particular success in bamboozling scientists with ordinary stage magic, because only scientists are arrogant enough to think that they always observe with rigorous and objective scrutiny, and therefore could never be so fooled–while ordinary mortals know perfectly well that good performers can always find a way to trick people.
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Sign language is the equal of speech, lending itself equally to the rigorous and the poetic, to philosophical analysis or to making love.
In The Times (16 Jun 1994).
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Suppose we loosely define a religion as any discipline whose foundations rest on an element of faith, irrespective of any element of reason which may be present. Quantum mechanics for example would be a religion under this definition. But mathematics would hold the unique position of being the only branch of theology possessing a rigorous demonstration of the fact that it should be so classified.
Concluding remark in 'Consistency and Completeness—A Résumé', The American Mathematical Monthly (May 1956), 63, No.5, 305.
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The following story is true. There was a little boy, and his father said, “Do try to be like other people. Don’t frown.” And he tried and tried, but could not. So his father beat him with a strap; and then he was eaten up by lions. Reader, if young, take warning by his sad life and death. For though it may be an honour to be different from other people, if Carlyle’s dictum about the 30 million be still true, yet other people do not like it. So, if you are different, you had better hide it, and pretend to be solemn and wooden-headed. Until you make your fortune. For most wooden-headed people worship money; and, really, I do not see what else they can do. In particular, if you are going to write a book, remember the wooden-headed. So be rigorous; that will cover a multitude of sins. And do not frown.
From 'Electromagnetic Theory, CXII', The Electrician (23 Feb 1900), Vol. 44, 615.
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There is an occasional glimmer of fertility [as compounds], the chemical equivalent of a blade of grass [in a desert]. So, gone … is the justification for “inert.” [Group 0 elements] are now known collectively as the noble gases, a name intended to imply a kind of chemical aloofness rather than a rigorous chastity.
In The Periodic Kingdom: A Journey Into the Land of the Chemical Elements (1995), 9.
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While it is never safe to affirm that the future of Physical Science has no marvels in store even more astonishing than those of the past, it seems probable that most of the grand underlying principles have been firmly established, and that further advances are to be sought chiefly in the rigorous applications of these principles to all the phenomena which come under our notice. It is here that the science of measurement shows its importance—where the quantitative results are more to be desired than qualitative work. An eminent physicist has remarked that the future truths of Physical Science are to be looked for in the sixth place of decimals.
University of Chicago, Annual Register 1894-1895 (1894), 150. Michelson also incorporated these lines in his address, 'Some of the Objects and Methods of Physical Science', at the opening of the Physics and Electrical Engineering Laboratory at the University of Kansas, reprinted in The Electrical Engineer (1 Jan 1896), 21, No. 400, 9.
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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
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- 90 -
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- 80 -
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- 70 -
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- 60 -
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- 50 -
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- 40 -
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- 30 -
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- 20 -
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