Susan: What is algebra exactly; is it those three-cornered things? Phoebe: It is x minus y equals z plus y and things like that. And all the time you… - William Rowan Hamilton

The analytical equations, unknown to the ancient geometers, which Descartes was the first to introduce into the study of curves and surfaces, are not restricted to the properties of figures, and to those properties which are the object of rational mechanics; they extend to all general phenomena. There cannot be a language more universal and more simple, more free from errors and from obscurities, that is to say more worthy to express the invariable relations of natural things.
Considered from this point of view, 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.
Its chief attribute is clearness; it has no marks to express confused notions. It brings together phenomena the most diverse, and discovers the hidden analogies which unite them.

Our epoch is the epoch of increasing consciousness; in this field Mathematics has done its bit. It has made us conscious of the limits of its own capabilities.

Researchers of the brain believe that mathematical truths make little sense to our mind, particularly..the examination of random outcomes.