“Those who claim to discover everything but produce no proofs of the same may be confuted as having actually pretended to discover the impossible.”

On Spirals (225 B.C.)

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Archimedes20

Greek mathematician, physicist, engineer, inventor, and ast… -287–-212 BC

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“In our contemporary social and intellectual plight, it is nothing less than shocking to discover that those persons who claim to have discovered an absolute are usually the same people who also pretend to be superior to the rest. To find people in our day attempting to pass off to the world and recommending to others some nostrum of the absolute which they claim to have discovered is merely a sign of the loss of and the need for intellectual and moral certainty, felt by broad sections of the population who are unable to look life in the face.”

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“Should a person lay claim to a cause and produce his proofs, then those who seek to repudiate him are required to produce proofs like unto his.”

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Context: Should a person lay claim to a cause and produce his proofs, then those who seek to repudiate him are required to produce proofs like unto his. If they succeed in doing so, his words will prove vain and they will prevail; otherwise neither his words will cease nor the proofs he hath set forth will become void. I admonish you, O ye who are invested with the Bayán, if ye would fain assert your ascendancy, confront not any soul unless ye give proofs similar to that which he hath adduced; for Truth shall be firmly established, while aught else besides it is sure to perish.

“Those who have racked their brains to discover new proofs have perhaps been induced to do so by a compulsion they could not quite explain to themselves. Instead of giving us their new proofs they should have explained to us the motivation that constrained them to search for them.”

Georg Christoph Lichtenberg (1742–1799) German scientist, satirist

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“… they discovered only a small asteroid inhabited by a solitary old man who claimed repeatedly that nothing was true, though he was later discovered to be lying.”

Douglas Adams The Hitchhiker's Guide to the Galaxy pentalogy

Source: The Hitchhiker's Guide to the Galaxy

“I have discovered a truly remarkable proof of this theorem which this margin is too small to contain.”
Cuius rei demonstrationem mirabilem sane detexi hanc marginis exiguitas non caperet.

Pierre de Fermat (1601–1665) French mathematician and lawyer

Note written on the margins of his copy of Claude-Gaspar Bachet's translation of the famous Arithmetica of Diophantus, this was taken as an indication of what became known as Fermat's last theorem, a correct proof for which would be found only 357 years later; as quoted in Number Theory in Science and Communication (1997) by Manfred Robert Schroeder