“It was mathematics, the non-empirical science par excellence, wherein the mind appears to play only with itself, that turned out to be the science of sciences, delivering the key to those laws of nature and the universe that are concealed by appearances.”

— Hannah Arendt , book The Life of the Mind

Source: The Life of the Mind (1971/1978), p. 7.

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Hannah Arendt 85

Jewish-American political theorist 1906–1975

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“Not only must philosophy be in agreement with our empirical knowledge of Nature, but the origin and formation of the Philosophy of Nature presupposes and is conditioned by empirical physics. However, the course of a science's origin and the preliminaries of its construction are one thing, while the science itself is another. In the latter, the former can no longer appear as the foundation of the science; here, the foundation must be the necessity of the Concept.”

Georg Wilhelm Friedrich Hegel book Encyclopedia of the Philosophical Sciences

Encyclopedia of the Philosophical Sciences (1816)

“Mathematics is the key and door to the sciences.”

Galileo Galilei (1564–1642) Italian mathematician, physicist, philosopher and astronomer

As quoted in Building Fluency Through Practice and Performance (2008) by Timothy Rasinski and Lorraine Griffith, p. 64, but in fact a quotation by Roger Bacon: Et harum scientiarum porta et clavis est Mathematica, "And of these sciences the door and key is mathematics", from Bacon's Opus Majus (1267) https://books.google.co.uk/books?id=UfqcGd8NOFsC&pg=PA97&lpg=PA97&dq=%22porta+et+clavis%22+opus+majus&source=bl&ots=nGgt2Lhxqe&sig=88kIPB5EAKAKtm0APk6J5OrS1D0&hl=en&sa=X&ved=0ahUKEwiU36D2gIbLAhVBWBQKHSW9CKgQ6AEINDAE#v=onepage&q=%22porta%20et%20clavis%22%20opus%20majus&f=false.
Attributed

“The key is not to confuse myth and empirical results, or religion and science.”

Hannes Alfvén (1908–1995) Swedish electrical engineer and plasma physicist

Source: Dean of the Plasma Dissidents (1988), p. 196.
Context: Since religion intrinsically rejects empirical methods, there should never be any attempt to reconcile scientific theories with religion. An infinitely old universe, always evolving, may not be compatible with the Book of Genesis. However, religions such as Buddhism get along without having any explicit creation mythology and are in no way contradicted by a universe without a beginning or end. Creatio ex nihilo, even as religious doctrine, only dates to around AD 200. The key is not to confuse myth and empirical results, or religion and science.

“I maintain that in every special natural doctrine only so much science proper is to be met with as mathematics; for… science proper, especially of nature, requires a pure portion, lying at the foundation of the empirical, and based upon à priori knowledge of natural things. …the conception should be constructed. But the cognition of the reason through construction of conceptions is mathematical. A pure philosophy of nature in general, namely, one that only investigates what constitutes a nature in general, may thus be possible without mathematics; but a pure doctrine of nature respecting determinate natural things (corporeal doctrine and mental doctrine), is only possible by means of mathematics; and as in every natural doctrine only so much science proper is to be met with therein as there is cognition à priori, a doctrine of nature can only contain so much science proper as there is in it of applied mathematics.”

Immanuel Kant book Metaphysical Foundations of Natural Science

Preface, Tr. https://books.google.com/books?id=OCJLAAAAMAAJ Ernest Belfort Bax (1883)
Metaphysical Foundations of Natural Science (1786)

“A further turn is to be found in some "unmasking" accounts of natural science, which aim to show that its pretensions to deliver the truth are unfounded, because of social forces that control its activities. Unlike the case of history, these do not use truths of the same kind; they do not apply science to the criticism of science. They apply the social sciences, and typically depend on the remarkable assumption that the sociology of knowledge is in a better position to deliver truth about science than science is to deliver truth about the world.”

Bernard Williams (1929–2003) English moral philosopher

Source: Truth and Truthfulness (2002), p. 2

“The beginnings of science have often the appearance of chance. A felicitous accident throws a certain natural fact under the notice of an inquiring and philosophic mind.”

Dionysius Lardner (1793–1859) Irish science writer

Context: The beginnings of science have often the appearance of chance. A felicitous accident throws a certain natural fact under the notice of an inquiring and philosophic mind. Attention is awakened and investigation provoked. Similar phenomena under varied circumstances are eagerly sought for; and if in the natural course of events they do not present themselves, circumstances are designedly arranged so as to bring about their production. The seeds of science are thus sown, and soon begin to germinate.

“It can have no analogy in fact with the descriptions of those who know nothing of the subject; furthermore, it is not to be represented as this or that by any person whomsoever: it is that which it is, drawing from itself only, even as mathematics do, for it is the exact and absolute science of Nature and her laws.”

Eliphas Levi (1810–1875) French writer

Introduction
The History Of Magic (1860)

“Both in the natural sciences and in sociology direct perception is deceptive, leading to the view that we are confronted with something which is in itself just what it appears to be. This is by no means the case and has long ago been rejected by the physical sciences, and it would be interesting to find out why it is still virtually unchallenged in sociology.”

John Lewis (philosopher)

Max Weber and Value-free Sociology: A Marxist Critique (1975), p. 39.

“In those parts of the world where learning and science has prevailed, miracles have ceased; but in such parts of it as are barbarous and ignorant, miracles are still in vogue; which is of itself a strong presumption that in the infancy of letters, learning and science, or in the world's non-age, those who confided in miracles, as a proof of the divine mission of the first promulgators of revelation, were imposed upon by fictitious appearances instead of miracles.”

Ethan Allen (1738–1789) American general

Source: Reason: The Only Oracle Of Man (1784), Ch. VI Section III - Rare and Wonderful Phenomena no evidence of Miracles, nor are Diabolical Spirits able to effect them, or Superstitious Traditions to confirm them, nor can Ancient Miracles prove Recent Revelations

“You often hear that the language of science is mathematics. I don't completely agree with the article. I don't think it is a definite article. Mathematics is "a" language of science. But, it is only "a" language of science. The language of science is English. The language of science is Spanish.”

Daniel Alan Vallero (1953) American scientist

Acceptance speech, Alumni Achievement Award, Collinsville, Illinois. 2017.

“It was mathematics, the non-empirical science par excellence, wherein the mind appears to play only with itself, that turned out to be the science of sciences, delivering the key to those laws of nature and the universe that are concealed by appearances.”

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