“What seems certain is that Pythagoras developed the idea of mathematical logic… He realized that numbers exist independently of the tangible world and therefore their study was untainted by inaccuracies of perception. This meant he could discover truths which were independent of opinion of prejudice and which were more absolute then any previous knowledge.”

— Simon Singh

Fermat's Last Theorem (1997)

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Simon Singh 4

British author 1964

Celia Green (1935) British philosopher

Advice to Clever Children (1981)

“A modern theory of knowledge which takes account of the relational as distinct from the merely relative character of all historical knowledge must start with the assumption that there are spheres of thought in which it is impossible to conceive of absolute truth existing independently of the values and position of the subject and unrelated to the social context.”

Karl Mannheim (1893–1947) Hungarian sociologist

Ideology and Utopia (1929)

“Perhaps she was not really so perfect, but he had made her so in his mind. People did this; he had seen it. As though the world of humans was created from their desires as much as their perception—an issue the empiricists tried to deal with in their natural philosophy.
Although he realized this was a trivial truth, still, trying to comprehend the reality of a situation was his constant activity. He could not necessarily trust the word of ministers, who all had their own purposes; nor what his mother might think, for her own perception was colored by her desire to see people in certain ways. One did not trust the periodicals, certainly, and pamphleteers were never disinterested. Everyone seemed to see the world and events a little differently, depending on their own personal mixture of desire and pragmatism. In history there were any number of rulers whose perception of events was so far removed from reality that it led to calamity. Prince Wilam did not want to be one of those—at any cost. Even if it meant giving up the world as he desired it to be.”

Sean Russell (1952) author

Source: Sea Without a Shore (1996), Chapter 26 (p. 352)

“Laplace created a number of new mathematical methods that were subsequently expanded into branches of mathematics, but he never cared for mathematics except as it helped him to study nature.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 495

“In other words, the fundamental principles and indispensable postulates of every genuinely productive science are not based on pure logic but rather on the metaphysical hypothesis — which no rules of logic can refute — that there exists an outer world which is entirely independent of ourselves. It is only through the immediate dictate of our consciousness that we know that this world exists. And that consciousness may to a certain degree be called a special sense.”

Max Planck (1858–1947) German theoretical physicist

Where is science going? The Universe in the light of modern physics. (1932)

“So many people today — and even professional scientists — seem to me like someone who has seen thousands of trees but has never seen a forest. A knowledge of the historic and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering. This independence created by philosophical insight is — in my opinion — the mark of distinction between a mere artisan or specialist and a real seeker after truth.”

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

Letter to Robert A. Thorton, Physics Professor at University of Puerto Rico (7 December 1944) [EA-674, Einstein Archive, Hebrew University, Jerusalem]. Thorton had written to Einstein on persuading colleagues of the importance of philosophy of science to scientists (empiricists) and science.
1940s
Context: I fully agree with you about the significance and educational value of methodology as well as history and philosophy of science. So many people today — and even professional scientists — seem to me like someone who has seen thousands of trees but has never seen a forest. A knowledge of the historic and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering. This independence created by philosophical insight is — in my opinion — the mark of distinction between a mere artisan or specialist and a real seeker after truth.

“Most mathematicians are by nature Platonists who cheerfully, unreflectingly and habitually employ such loaded phrases as 'We assume there exists…' or 'Therefore there exists…' an entity with such and such characteristics. Challenged by the realist they would probably reply that since the truths of mathematics are absolute, universal and eternal it is hard indeed to deny them an existence independent of human intelligence.”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

“A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so.”

John Von Neumann (1903–1957) Hungarian-American mathematician and polymath

"The Role of Mathematics in the Sciences and in Society" (1954) an address to Princeton alumni, published in John von Neumann : Collected Works (1963) edited by A. H. Taub ; also quoted in Out of the Mouths of Mathematicians : A Quotation Book for Philomaths (1993) by R. Schmalz
Context: A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so. By and large it is uniformly true in mathematics that there is a time lapse between a mathematical discovery and the moment when it is useful; and that this lapse of time can be anything from 30 to 100 years, in some cases even more; and that the whole system seems to function without any direction, without any reference to usefulness, and without any desire to do things which are useful.

“Is there any knowledge in the world which is so certain that no reasonable man could doubt it?”

Bertrand Russell The Problems of Philosophy

Source: 1910s, The Problems of Philosophy (1912)

“The essence of being an independent expert is not only the expertise, which must be a given and is conscientiously assessed by this Council before appointing rapporteurs, but the capacity to carry out the mandate free of intimidation or interference, free of thinking barriers, or of political correctness. An independent expert would fail the mandate and the Council if he or she were to rehash existing wisdoms and engage in rhetoric that only confirms the status quo. The essence of the independent expert is his independence to think outside systems, beyond prejudices, to give impulses, offer new perspectives -- and to make bold proposals to the Human Rights Council.”

Alfred de Zayas (1947) American United Nations official

Alfred de Zayas' comments to the remarks made by NGOs and States during the United Nations (UN) Human Rights Council Session http://www.ohchr.org/EN/NewsEvents/Pages/DisplayNews.aspx?NewsID=13713&LangID=E Comments by Alfred de Zayas, Independent Expert on the promotion of a democratic and equitable international order, following the Interactive Dialogue on the presentation of his thematic report.
2013

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