"Mathematical science […] has these divisions: arithmetic, music, geometry, astronomy. Arithmetic is the discipline of absolute numerable quantity. Music is the discipline which treats of numbers in their relation to those things which are found in sound." (Cassiodorus, cca. 6th century)
"Astronomy itself is a venerable science, and might become a stepping stone to something more august, a science which I think is a convenient passage to mystical theology, for the happy body of heaven has matter underneath it, and its motion has seemed to the leaders in philosophy to be an imitation of mind. It proceeds to its demonstrations in no uncertain way, for it uses as its servants geometry and arithmetic, which it would not be improper to call a fixed standard of truth." (Synesius, "On an Astrolabe", cca. 5th century)
"As far as hypotheses go, let no one expect anything in the way of certainty from astronomy, since astronomy can offer us nothing certain, lest, if anyone take as true that which has been constructed for another use, he go away from this discipline a bigger fool than when he came to it." (Nicholas Copernicus, "De Revolutionibus Orbium Coelestium" ["On the Revolutions of the Heavenly Spheres"], 1543)
"For many parts of Nature can neither be invented with sufficient subtlety, nor demonstrated with sufficient perspicuity, nor accommodated to use with sufficient dexterity, without the aid and intervention of Mathematic: of which sort are Perspective, Music, Astronomy, cosmography, Architecture, Machinery, and some others." (Sir Francis Bacon, "De Augmentis", Bk. 3 [The Advancement of Learning], 1605)
"There is nothing in Nature that does more show the piercing Force of Human Understanding, the sublimity of its Speculations and deep researchers, than true Astronomy. It raises our Minds above our Senses, and even in contradiction to them, shows us the true System of the World: the faculty of Reason by which we have made these great discoveries in the Heavens must needs be derived from Heaven, since no Earthly Principle can attain so great a Perfection." (John Keill, "An Introduction to the True Astronomy", 1721)
"Astronomy is perhaps the science whose discoveries owe least to chance, in which human understanding appears in its whole magnitude, and through which man can best learn how small he is." (Georg C Lichtenberg, Notebook C, 1772-1773)
"Of all the natural sciences, astronomy is that which presents the longest series of discoveries. The first appearance of the heavens is indeed far removed from that enlarged view, by which we comprehend at the present day, the past and future states of the system of the world." (Pierre-Simon Laplace," The Systems of the World" Vol. 1, 1830)
"We may therefore define Astronomy as the science by which we discover the laws of the geometrical and mechanical phenomena presented by the heavenly bodies." (Auguste Comte, “The Positive Philosophy”, 1830)
"The term ‘science’ should be kept for disciplines such as mathematics or astronomy, whose object is pure knowledge. That every theory of art may contain discrete sciences goes without saying, and need not worry us. But it is also to be noted that no science can exist without some element of art: in mathematics, for instance, the use of arithmetic and algebra is an art. But art may go still further. The reason is that, no matter how obvious and palpable the difference between knowledge and ability may be in the totality of human achievement, it is still extremely difficult to separate them entirely in the individual." (Carl von Clausewitz, "On War", 1832)
"The ideas which these sciences, Geometry, Theoretical Arithmetic and Algebra involve extend to all objects and changes which we observe in the external world; and hence the consideration of mathematical relations forms a large portion of many of the sciences which treat of the phenomena and laws of external nature, as Astronomy, Optics, and Mechanics. Such sciences are hence often termed Mixed Mathematics, the relations of space and number being, in these branches of knowledge, combined with principles collected from special observation; while Geometry, Algebra, and the like subjects, which involve no result of experience, are called Pure Mathematics." (Whewell, William, "The Philosophy of the Inductive Sciences" , 1858)
"Astronomy is the science of which the human mind may most justly boast. It owes this indisputable pre-eminence to the elevated nature of its object, to the grandeur of its means of investigation, to the certainty, the utility, and the unparalleled magnificence of its results." (François Arago, "Biographies of Distinguished Scientific Men", [Eulogy on Laplace] 1859)
"The term ‘science’ should be kept for disciplines such as mathematics or astronomy, whose object is pure knowledge. That every theory of art may contain discrete sciences goes without saying, and need not worry us. But it is also to be noted that no science can exist without some element of art: in mathematics, for instance, the use of arithmetic and algebra is an art. But art may go still further. The reason is that, no matter how obvious and palpable the difference between knowledge and ability may be in the totality of human achievement, it is still extremely difficult to separate them entirely in the individual." (Carl von Clausewitz, "On War", 1832)
"The ideas which these sciences, Geometry, Theoretical Arithmetic and Algebra involve extend to all objects and changes which we observe in the external world; and hence the consideration of mathematical relations forms a large portion of many of the sciences which treat of the phenomena and laws of external nature, as Astronomy, Optics, and Mechanics. Such sciences are hence often termed Mixed Mathematics, the relations of space and number being, in these branches of knowledge, combined with principles collected from special observation; while Geometry, Algebra, and the like subjects, which involve no result of experience, are called Pure Mathematics." (Whewell, William, "The Philosophy of the Inductive Sciences" , 1858)
"Astronomy is the science of which the human mind may most justly boast. It owes this indisputable pre-eminence to the elevated nature of its object, to the grandeur of its means of investigation, to the certainty, the utility, and the unparalleled magnificence of its results." (François Arago, "Biographies of Distinguished Scientific Men", [Eulogy on Laplace] 1859)
"Astronomy is one of the sublimest fields of human investigation. The mind that grasps its facts and principles receives something of the enlargement and grandeur belonging to the science itself. It is a quickener of devotion." (Horace Mann, "Thoughts Selected From the Writings of Horace Mann", 1872)
"So completely is nature mathematical that some of the more exact natural sciences, in particular astronomy and physics, are in their theoretic phases largely mathematical in character, while other sciences which have hitherto been compelled by the complexity of their phenomena and the inexactitude of their data to remain descriptive and empirical, are developing towards the mathematical ideal, proceeding upon the fundamental assumption that mathematical relations exist between the forces and the phenomena, and that nothing short, of the discovery and formulations of these relations would constitute definitive knowledge of the subject. Progress is measured by the closeness of the approximation to this ideal formulation." (Jacob W A Young, "The Teaching of Mathematics", 1907)
"Physics can teach us only what the laws of nature are today. It is only Astronomy that can teach us what the initial conditions for these laws are." (Eugene P Wigner, "The Case for Astronomy", Proceedings of the American Philosophical Society Vol. 8 (1), 1964)
"Yet nature does not always prefer conventional explanations, least of all in astronomy." (Roger Penrose, "Black Holes", Scientific American Vol. 226 (5), 1972)
"The pre-eminence of astronomy rests on the peculiarity that it can be treated mathematically; and the progress of physics, and most recently biology, has hinged equally on finding formulations of their laws that can be displayed as mathematical models." (Jacob Bronowski, "The Ascent of Man", 1973)
"So completely is nature mathematical that some of the more exact natural sciences, in particular astronomy and physics, are in their theoretic phases largely mathematical in character, while other sciences which have hitherto been compelled by the complexity of their phenomena and the inexactitude of their data to remain descriptive and empirical, are developing towards the mathematical ideal, proceeding upon the fundamental assumption that mathematical relations exist between the forces and the phenomena, and that nothing short, of the discovery and formulations of these relations would constitute definitive knowledge of the subject. Progress is measured by the closeness of the approximation to this ideal formulation." (Jacob W A Young, "The Teaching of Mathematics", 1907)
"Physics can teach us only what the laws of nature are today. It is only Astronomy that can teach us what the initial conditions for these laws are." (Eugene P Wigner, "The Case for Astronomy", Proceedings of the American Philosophical Society Vol. 8 (1), 1964)
"Yet nature does not always prefer conventional explanations, least of all in astronomy." (Roger Penrose, "Black Holes", Scientific American Vol. 226 (5), 1972)
"The pre-eminence of astronomy rests on the peculiarity that it can be treated mathematically; and the progress of physics, and most recently biology, has hinged equally on finding formulations of their laws that can be displayed as mathematical models." (Jacob Bronowski, "The Ascent of Man", 1973)
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