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Mathematical analysis is as extensive as nature itself; it defines all perceptible relations, measures times, spaces, forces, temperatures ; this difficult science is formed slowly, but it preserves every principle which it has once acquired; it grows and strengthens itself incessantly in the midst of the many variations and errors of the human mind.
It's chief attribute is clearness; it has no marks to express confused notations. It brings together phenomena the most diverse, and discovers the hidden analogies which unite them.
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Often quoted as Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them.

 

Joseph Fourier

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Sex cannot be understood because nature cannot be understood. Science is a method of logical analysis of nature’s operations. It has lessened human anxiety about the cosmos by demonstrating the materiality of nature’s forces, and their frequent predictability. But science is always playing catch-up ball. Nature breaks its own rules whenever it wants. Science cannot avert a single thunderbolt. Western science is a product of the Apollonian mind: its hope is that by naming and classification, by the cold light of intellect, archaic night can be pushed back and defeated.

 

Camille Paglia

 

Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments. We also notice that, the farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separate branches of the science. So it happens that, with the extension of mathematics, its organic character is not lost but only manifests itself the more clearly.

 

David Hilbert

 

Our design, not respecting arts, but philosophy, and our subject, not manual, but natural powers, we consider chiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces, whether attractive or impulsive; and therefore we offer this work as mathematical principles of philosophy; for all the difficulty of philosophy seems to consist in this — from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena...

 

Isaac Newton

 

The whole analogy of natural operations furnishes so complete and crushing an argument against the intervention of any but what are termed secondary causes, in the production of all the phenomena of the universe; that, in view of the intimate relations between Man and the rest of the living world; and between the forces exerted by the latter and all other forces, I can see no excuse for doubting that all are co-ordinated terms of Nature's great progression, from the formless to the formed—from the inorganic to the organic—from blind force to conscious intellect and will.

 

Thomas Henry Huxley

 

Every one who has seriously investigated a novel question, who has really interrogated Nature with a view to a distinct answer, will bear me out in saying that it requires intense and sustained effort of imagination. The relations of sequence among the phenomena must be seen; they are hidden; they can only be seen mentally; a thousand suggestions rise before the mind, but they are recognised as old suggestions, or as inadequate to reveal what is sought; the experiments by which the problem may be solved have to be imagined; and to imagine a good experiment is as difficult as to invent a good fable, for we must have distinctly present — clear mental vision — the known qualities and relations of all the objects, and must see what will be the effect of introducing some new qualifying agent. If any one thinks this is easy, let him try it: the trial will teach him a lesson respecting the methods of intellectual activity not without its use.

 

George Henry Lewes