"[…] if number is merely the product of our mind, space has a reality outside our mind whose laws we cannot a priori completely prescribe" (Carl F Gauss, 1830)
"The business of concrete mathematics is to discover the equations which express the mathematical laws of the phenomenon under consideration; and these equations are the starting-point of the calculus, which must obtain from them certain quantities by means of others." (Auguste Comte, "Course of Positive Philosophy", 1830)
"Science and knowledge are subject, in their extension and increase, to laws quite opposite to those which regulate the material world. Unlike the forces of molecular attraction, which cease at sensible distances; or that of gravity, which decreases rapidly with the increasing distance from the point of its origin; the farther we advance from the origin of our knowledge, the larger it becomes, and the greater power it bestows upon its cultivators, to add new fields to its dominions." (Charles Babbage, "On the Economy of Machinery and Manufactures", 1832)
"The more one reflects, the more one acknowledges that necessity governs the world. At each new progress of science ,that which seemed contingent is recognized as being necessary. Multiple relations are established between the branches that we had thought to be separate; we observe laws where we had thought there were only accidental events. We approach more and more the unity of being […]" (Sophie Germain, "Considerations sur l’etat des sciences et lettres, aux differentes epoques de leur culture", 1833)
"Physical astronomy is the science which compares and identifies the laws of motion observed on earth with the motions that take place in the heavens; and which traces, by an uninterrupted chain of deduction from the great principle that governs the universe, the revolutions and rotations of the planets, and the oscillations of the fluids at their surfaces; and which estimates the changes the system has hitherto undergone, or may hereafter experience - changes which require millions of years for their accomplishment." (Mary Somerville, "The Connection of the Physical Sciences", 1834)
"Geometry is that of mathematical science which is devoted to consideration of form and size, and may be said to be the best and surest guide to study of all sciences in which ideas of dimension or space are involved. Almost all the knowledge required by navigators, architects, surveyors, engineers, and opticians, in their respective occupations, is deduced from geometry and branches of mathematics. All works of art are constructed according to the rules which geometry involves; and we find the same laws observed in the works of nature. The study of mathematics, generally, is also of great importance in cultivating habits of exact reasoning; and in this respect it forms a useful auxiliary to logic." (William Chambers & Robert Chambers, "Chambers's Information for the People" Vol. 2, 1835)
"Nothing is more futile than theorizing about music. No doubt there are laws, mathematically strict laws, but these laws are not music; they are only its conditions […] The essence of music is revelation." (Heinrich Heine, "Letters on the French Stage", 1837)
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