"Mathematics is not a book confined within a cover and bound between brazen clasps, whose contents it needs only patience to ransack; it is not a mine, whose treasures may take long to reduce into possession, but which fill only a limited number of veins and lodes; it is not a soil, whose fertility can be exhausted by the yield of successive harvests; it is not a continent or an ocean, whose area can be mapped out and its contour defined; it is as limitless as the space which it finds too narrow for its aspirations; its possibilities are as infinite as the worlds which are forever crowding in and multiplying upon the astronomer's gaze; it is incapable of being restricted within assigned boundaries or being reduced to definitions of permanent validity as the consciousness, the life, which seems to slumber in each monad, in every atom of matter, in each leaf and bud and cell and is forever ready to burst forth into new forms of vegetable and animal existence." (James J Sylvester, The Educational Times", 1877)
"It [astronomy] is, above all others, a science that cultivates the imagination. Yet its theories and distances are based upon rigorous mathematical demonstrations. Thus the study has at once the beauty of poetry and the exactness of Geometry." (Joel D Steele," The Story of the Stars: New Descriptive Astronomy", 1884)
"[Astronomy] is a science of hairbreadths and fractions of a second. It exists only by the rigid enforcement of arduous accuracy and unwearying diligence. Whatever secrets the universe still has in store for man will only be communicated on these terms." (Agnes M Clerke, "A Popular History of Astronomy during the Nineteenth Century", 1885)
"[Astronomy] seems to have the strongest hold on minds which are not intimately acquainted with its work. The view taken by such minds is not distracted by the technical details which trouble the investigator, and its great outlines are seen through an atmosphere of sentiment, which softens out the algebraic formulae with which the astronomer is concerned into those magnificent conceptions of creation which are the delight of all minds, trained or untrained." (Simon Newcomb, Harper’s Magazine, 1885)
"Although the astronomer has achieved many successes in studying comets, yet these objects still remain outside the surveyed fields of astronomy - now, as in the old days when men spoke of sun and moon, planet and stars, as including all the members of the heavenly host." (Richard A Proctor, "The Twentieth Century, Whence Came the Comets?", Vol. 29 (111), 1886)
"Between mathematicians and astronomers some misunderstanding exists with respect to the meaning of the term 'convergence'. Mathematicians [...] stipulate that a series is convergent if the sum of the terms tends to a predetermined limit even if the first terms decrease very slowly. Conversely, astronomers are in the habit of saying that a series converges whenever the first twenty terms, for example, decrease rapidly even if the following terms might increase indefinitely. [...] Both rules are legitimate; the first for theoretical research and the second for numerical applications. Both must prevail, but in two entirely separate domains of which the boundaries must be accurately defined. Astronomers do not always know these boundaries accurately but rarely exceed them; the approximation with which they are satisfied usually keeps them far on this side of the boundary. In addition, their instinct guides them and, if they are wrong, a check on the actual observation promptly reveals their error [...]" (Henri Poincaré, "New Methods in Celestial Mechanics" ["Les méthodes nouvelles de la mécanique céleste"], 1892)
"Astronomy is the most accurate of the sciences. All the truths which it teaches are absolutely demonstrated, and cannot be disputed by any mind which gives itself the trouble, or rather the pleasure, to gain information in the study of this admirable science."Camille Flammarion," Popular Astronomy: A General Description of the Heavens" Book I, 1894)
"Astronomy, the oldest and most juvenile of the sciences, may still have some surprises in store. May anti-matter be commended to its care!" (Arthur Schuster, "Letter to the Editor, Potential Matter - A Holiday Dream", Nature Vol. 58 (1503), 1898)
"Certainly, if a system moves under the action of given forces and its initial conditions have given values in the mathematical sense, its future motion and behavior are exactly known. But, in astronomical problems, the situation is quite different: the constants defining the motion are only physically known, that is with some errors; their sizes get reduced along the progresses of our observing devices, but these errors can never completely vanish." (Jacques Hadamard, "Les surfaces à courbures opposées et leurs lignes géodésiques", Journal de mathématiques pures et appliquées 5e (4), 1898)
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