“But what has made this problem special for amateurs is that there's a tiny possibility that there does exist an elegant 17th-century proof.”

— Andrew Wiles

Nova Interview

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British mathematician 1953

Ludwig von Bertalanffy (1901–1972) austrian biologist and philosopher

Source: General System Theory (1968), 5. The Organism Considered as Physical System, p. 132

“The positive energy theorem was for half a century or more an open challenge to relativists. Many attempts were made to prove flat spacetime was stable, but none completely succeeded completely until a majestic tour de force of geometric reasoning of Shoen and Yau. This was followed two years later by a proof of Witten, which was as elegant as it was short. It is this proof of Witten’s that we take as a template here for the quantum theory.”

Lee Smolin (1955) American cosmologist

"Positive energy in quantum gravity" arXiv (Jun 10, 2014)

“I have often thought that Strafford was an ideal type, both for governor of Ireland in the 17th century, and governor of India in the 20th century.”

John Morley, 1st Viscount Morley of Blackburn (1838–1923) British Liberal statesman, writer and newspaper editor

Letter to Lord Minto (19 September 1907), quoted in D. A. Hamer, Lord Morley: Liberal Intellectual in Politics (1968), p. 56
1900s

“The quest to rationally prove the possibility of sentience in a computer (or perhaps in the Internet) is the modern version of proving God's existence. …eventually a cybernetically minded twenty-first century version of Kant will appear in order to present a tedious "proof" that such adventures are futile.”

Jaron Lanier (1960) American computer scientist, musician, and author

"One Half of a Manifesto," The New Humanists: Science at the Edge (2003)

“Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?”

Paul R. Halmos (1916–2006) American mathematician

I Want to be a Mathematician: An Automathography (1985)

“The release of atomic energy has not created a new problem. It has merely made more urgent the necessity of solving an existing one.”

Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity

Statement on the Atomic Bomb to Raymond Swing, before 1 October 1945, as reported in Atlantic Monthly, vol. 176, no. 5 (November 1945), in Einstein on Politics, p. 373
1940s

“They [laboratory groups] bypass such questions as how one comes to know that a problem exists, what it does to solution adequacy to be working on several different things concurrently with problem solving, what it's like to go about solving a felt, intuited problem rather than an explicitly stated consensually validated problem which was made visible to all members at a specific point in time.”

Karl E. Weick (1936) Organisational psychologist

Karl E. Weick (1971, p. 9), as cited in: Harry L. Davis. " Decision Making within the Household http://www.unternehmenssteuertag.de/fileadmin/user_upload/Redaktion/Seco@home/nachhaltiger_Energiekonsum/Literatur/entscheidungen_haushalte/Decision_Making_within_the_Household.pdf," The Journal of Consumer Research, Vol. 2, No. 4. (Mar., 1976), pp. 241-260.
1970s

“Euclid … manages to obtain a rigorous proof without ever dealing with infinity, by reducing the problem [of the infinitude of primes] to the study of finite numbers. This is exactly what contemporary mathematical analysis does.”

Lucio Russo (1944) Italian historian and scientist

2.4, "Discrete Mathematics and the Notion of Infinity", p. 45
The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had to Be Reborn (2004)

“The real question of life after death isn't whether or not it exists, but even if it does what problem this really solves.”

Ludwig Wittgenstein (1889–1951) Austrian-British philosopher

“The way forward does not lie in amateur and comically timeless linguistic sociology which takes ‘forms of life’ for granted (and this is what philosophy has been recently), but in the systematic study of forms of life which does not take them for granted at all.”

Ernest Gellner (1925–1995) Czech anthropologist, philosopher and sociologist

The crisis in the humanities and in the mainstream of philosophy (1964), reprinted in The Devil in Modern Philosophy (1974)
Context: The way forward does not lie in amateur and comically timeless linguistic sociology which takes ‘forms of life’ for granted (and this is what philosophy has been recently), but in the systematic study of forms of life which does not take them for granted at all. It hardly matters whether such an inquiry is called philosophy or sociology.

“But what has made this problem special for amateurs is that there's a tiny possibility that there does exist an elegant 17th-century proof.”

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