"The mathematician speculates the causes of a certain sensible effect, without considering its actual existence; for the contemplation of universals excludes the knowledge of particulars; and he whose intellectual eye is fixed on that which is general and comprehensive, will think but little of that which is sensible and singular. (Proclus Lycaeus, cca 5th century)
"Indeed, many geometric things can be discovered or elucidated by algebraic principles, and yet it does not follow that algebra is geometrical, or even that it is based on geometric principles (as some would seem to think). This close affinity of arithmetic and geometry comes about, rather, because geometry is, as it were, subordinate to arithmetic, and applies universal principles of arithmetic to its special objects." (John Wallis, "Mathesis Universalis", 1657)
"Algebra is a general Method of Computation by certain Signs and Symbols which have been contrived for this Purpose, and found convenient. It is called an Universal Arithmetic, and proceeds by Operations and Rules similar to those in Common Arithmetic, founded upon the same Principles." (Colin Maclaurin, "A Treatise on Algebra", 1748)
"Mathematical analysis […] in the study of all phenomena, interprets them by the same language, as if to attest the unity and simplicity of the plan of the universe, and take still more evident that unchangeable order which presides over all natural causes. […] There cannot be a language more universal and more simple, more free from errors and obscurities, more worthy to express the invariable relations of all natural things." (Baron Jean-Baptiste-Joseph Fourier,"Théorie Analytique de la Chaleur", 1822)
"Every theorem in geometry is a law of external nature, and might have been ascertained by generalizing from observation and experiment, which in this case resolve themselves into comparisons and measurements. But it was found practicable, and being practicable was desirable, to deduce these truths by ratiocination from a small number of general laws of nature, the certainty and universality of which was obvious to the most careless observer, and which compose the first principles and ultimate premises of the science." (John S Mill, "A System of Logic, Ratiocinative and Inductive", 1843)
"Partitions constitute the sphere in which analysis lives, moves, and has its being; and no power of language can exaggerate or paint too forcibly the importance of this till recently almost neglected, but vast, subtle, and universally permeating, element of algebraical thought and expression." (James J Sylvester, "On the Partition of Numbers", 1857)
"Every process of what has been called Universal Geometry - the great creation of Descartes and his successors, in which a single train of reasoning solves whole classes of problems at once, and others common to large groups of them - is a practical lesson in the management of wide generalizations, and abstraction of the points of agreement from those of difference among objects of great and confusing diversity, to which the purely inductive sciences cannot furnish many superior. Even so elementary an operation as that of abstracting from the particular configuration of the triangles or other figures, and the relative situation of the particular lines or points, in the diagram which aids the apprehension of a common geometrical demonstration, is a very useful, and far from being always an easy, exercise of the faculty of generalization so strangely imagined to have no place or part in the processes of mathematics." (John S Mill, "An Examination of Sir William Hamilton’s Philosophy", 1865)
"Music is like geometric figures and numbers, which are the universal forms of all possible objects of experience." (Friedrich Nietzsche,"Birth of Tragedy", 1872)
"Mathematics connect themselves on the one side with common life and physical science; on the other side with philosophy in regard to our notions of space and time, and in the questions which have arisen as to the universality and necessity of the truths of mathematics and the foundation of our knowledge of them." (Arthur Cayley, 1888)
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