“I confess that Fermat's Theorem as an isolated proposition has very little interest for me, because I could easily lay down a multitude of such propositions, which one could neither prove nor dispose of.”

— Carl Friedrich Gauss

A reply to Olbers' 1816 attempt to entice him to work on Fermat's Theorem. As quoted in The World of Mathematics (1956) Edited by J. R. Newman

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Carl Friedrich Gauss 50

German mathematician and physical scientist 1777–1855

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.
1950s

“I realized that anything to do with Fermat's Last Theorem generates too much interest.”

Andrew Wiles (1953) British mathematician

Nova Interview

“First then I will set out the very first theorem which became known to me by means of mechanics, namely that
Any segment of a section of a right angled cone (i. e., a parabola) is four-thirds of the triangle which has the same base and equal height,
and after this I will give each of the other theorems investigated by the same method. Then at the end of the book I will give the geometrical [proofs of the propositions]…”

Archimedes book The Method of Mechanical Theorems

The Method of Mechanical Theorems

“In every country it always is and must be the interest of the great body of the people to buy whatever they want of those who sell it cheapest. The proposition is so very manifest that it seems ridiculous to take any pains to prove it; nor could it ever have been called in question had not the interested sophistry of merchants and manufacturers confounded the common sense of mankind. Their interest is, in this respect, directly opposite to that of the great body of the people.”

Adam Smith (1723–1790) Scottish moral philosopher and political economist

Source: (1776), Book IV, Chapter III, Part II, p. 531.

“There are numerous theorems in economics that rely upon mathematically fallacious propositions.”

Steve Keen (1953) Australian economist

Source: Debunking Economics - The Naked Emperor Of The Social Sciences (2001), Chapter 12, Don't Shoot Me, I'm Only The Piano, p. 259

“Pure Mathematics is the class of all propositions of the form “p implies q,” where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member, the notion of such that, the notion of relation, and such further notions as may be involved in the general notion of propositions of the above form. In addition to these, mathematics uses a notion which is not a constituent of the propositions which it considers, namely the notion of truth.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

Principles of Mathematics (1903), Ch. I: Definition of Pure Mathematics, p. 3
1900s

“225. What I hold fast to is not one proposition but a nest of propositions.”

Ludwig Wittgenstein book On Certainty

On Certainty (1969)

“28 Proposition. The image of the Beast, is these degenerate Princes, that in name onely were called Roman Emporours, and were neither Romans of blood, nor Emperours of Magnanimitie.”

John Napier (1550–1617) Scottish mathematician

A Plaine Discovery of the Whole Revelation of St. John (1593), The First and Introductory Treatise

“I have studied it, and I can prove its truth as clearly as any proposition ever submitted to the mind of man.”

Alexander Hamilton (1757–1804) Founding Father of the United States

John Church Hamilton, History of the republic of the United States of America: as traced in the writings of Alexander Hamilton and of his cotemporaries, v. 7 p. 790. John Church Hamilton was Alexander Hamilton's son. He gives his source for the first quotation as the Reminiscences of General Morton, but gives no source for the second.
Attributed
Context: It was the tendency to infidelity he saw so rife that led him often to declare in the social circle his estimate of Christian truth. “I have examined carefully,” he said to a friend from his boyhood, “the evidence of the Christian religion; and, if I was sitting as a juror upon its authenticity, I should unhesitatingly give my verdict in its favor.” To another person, he observed, “I have studied it, and I can prove its truth as clearly as any proposition ever submitted to the mind of man.”

“Rules for Demonstrations. I. Not to undertake to demonstrate any thing that is so evident of itself that nothing can be given that is clearer to prove it. II. To prove all propositions at all obscure, and to employ in their proof only very evident maxims or propositions already admitted or demonstrated. III. To always mentally substitute definitions in the place of things defined, in order not to be misled by the ambiguity of terms which have been restricted by definitions.”

Blaise Pascal (1623–1662) French mathematician, physicist, inventor, writer, and Christian philosopher

The Art of Persuasion

“I confess that Fermat's Theorem as an isolated proposition has very little interest for me, because I could easily lay down a multitude of such propositions, which one could neither prove nor dispose of.”

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Carl Friedrich Gauss 50

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