“Spherical trigonometry and certain other theorems, to which the author has added a new one of frequent application, then serve for the solution of the problems which the comparison of the various directions involved can present.”

— Carl Friedrich Gauss

"Gauss's Abstract of the Disquisitiones Generales circa Superficies Curvas presented to the Royal Society of Gottingen" (1827) Tr. James Caddall Morehead & Adam Miller Hiltebeitel in General Investigations of Curved Surfaces of 1827 and 1825 http://books.google.com/books?id=SYJsAAAAMAAJ& (1902) <br class="br">Context: In researches in which an infinity of directions of straight lines in space is concerned, it is advantageous to represent these directions by means of those points upon a fixed sphere, which are the end points of the radii drawn parallel to the lines. The centre and the radius of this auxiliary sphere are here quite arbitrary. The radius may be taken equal to unity. This procedure agrees fundamentally with that which is constantly employed in astronomy, where all directions are referred to a fictitious celestial sphere of infinite radius. Spherical trigonometry and certain other theorems, to which the author has added a new one of frequent application, then serve for the solution of the problems which the comparison of the various directions involved can present.

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Carl Friedrich Gauss50

German mathematician and physical scientist 1777–1855

Sukavich Rangsitpol (1935) Thai politician

citizenship in the changing world of tomorrow.

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C. West Churchman (1913–2004) American philosopher and systems scientist

Source: 1940s - 1950s, Introduction to Operations Research (1957), p. 8, cited in: R.L. McCown (2001) "Learning to bridge the gap between science-based decision support and the practice of farming". In: Aust. J. Agric. Res., Vol 52, p. 560-561

“A theorem is a proposition which is a strict logical consequence of certain definitions and other propositions”

Anatol Rapoport (1911–2007) Russian-born American mathematical psychologist

Anatol Rapoport. " Various meanings of “theory”." http://www.acsu.buffalo.edu/~fczagare/PSC%20504/Rapoport%20(1958).pdf American Political Science Review 52.04 (1958): 972-988. <br class="br">1950s

“Blood-brotherhood is one recurring cultural solution to the problem of recognizing powerful emotional bonds between men that avoids effeminizing comparisons to romantic courtship and affirms the masculinity of the men involved.”

Jack Donovan (1974) American activist, editor and writer

Blood-Brotherhood and Other Rites of Male Alliance (2009).
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Jerry Fodor (1935–2017) American philosopher

Source: Modularity of Mind (1983), p. 126, partly cited in: Meredith Williams (2002) Wittgenstein, Mind, and Meaning: Toward a Social Conception of Mind. p. 104. Quote about the direction of information flow in perceptual and observer analysis.

“Niven made a name for himself as a hard SF author, which is to say, someone whose SF provides enough technical detail that the reader can be certain that various mechanisms and events couldn't work the way the author has them working.”

James Nicoll (1961) Canadian fiction reviewer

review of All the Myriad Ways by Larry Niven http://jamesdavisnicoll.com/review/remember-when-niven-was-fun, 2015 <br class="br">2010s

“Donald Judd spoke of a 'neutral' surface, but what is meant? Neutrality must involve some relationship (to other ways of painting, thinking?) He would have to include these in his work to establish the neutrality of that surface. He also used 'non' or 'not' – expressive – this is an early problem – a negative solution or – expression of new sense – which can help one into – what one has not known. 'Neutral' expresses an intention.”

Jasper Johns (1930) American artist

Book A (sketchbook), p 31, c 1963: as quoted in Jasper Johns, Writings, sketchbook Notes, Interviews, ed. Kirk Varnedoe, Moma New York, 1996, p. 50
1960s

“The Object of this Treatise is—(1) To point out to the student of Mathematics, who has not the advantage of a tutor, the course of study which it is most advisable that he should follow, the extent to which he should pursue one part of the science before he commences another, and to direct him as to the sort of applications which he should make. (2) To treat fully of the various points which involve difficulties and which are apt to be misunderstood by beginners, and to describe at length the nature without going into the routine of the operations.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

Source: On the Study and Difficulties of Mathematics (1831), Chapter I. Introductory Remarks on the Nature and Objects of Mathematics.

“Though the defects in Diophantus' proofs are in general due to the limitation of his symbolism, it is not so always. Very frequently indeed Diophantus introduces into a solution arbitrary conditions and determinations which are not in the problem. Of such "fudged" solutions, as a schoolboy would call them, two particular kinds are very frequent. Sometimes an unknown is assumed at a determinate value… Sometimes a new condition is introduced.”

James Gow (scholar) (1854–1923) scholar

A Short History of Greek Mathematics (1884)

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Max Wertheimer (1880–1943) Co-founder of Gestalt psychology

p 212
Productive thinking, 1945

“Spherical trigonometry and certain other theorems, to which the author has added a new one of frequent application, then serve for the solution of the problems which the comparison of the various directions involved can present.”

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Carl Friedrich Gauss50

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