Elipse

Man is not a circle with a single centre; he is an ellipse with two foci. Facts are one, ideas are the other.

Victor Hugo, Les Miserables

On progress

The progress of mathematics may be viewed as a movement from the infinite to the finite. At the start, the possibilities of a theory, for example the theory of enumeration, appear boundless. Rules for the enumeration of sets subject to various conditions appear to obey an indefinite variety of recursions and seem to lead to a bounty of generating functions. We are naively led to conjecture that the class of enumerable objects is infinite and unclassifiable.
As cases pile upon cases, however, patterns begin to emerge. Freakish instances are quietly disregarded; impossible problems are recognized as such, and what is left gets organized along a few general criteria. We will do all we can to boil these criteria down to one, but we will probably have to be satisfied with a small finite number.

Gian-Carlo Rota

Definition of math

Mathematics is the study of analogies between analogies. All science is. Scientists want to show that thins that don´t look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding.