Bigs Quote by Paul Halmos

...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept…

— Paul Halmos

The heart of mathematics is its problems.

— Paul Halmos

Great mathematics is achieved by solving difficult problems not by fabricating elaborate theories in search of a problem.

— Harold Davenport

Experience has shown repeatedly that a mathematical theory with a rich internal structure generally turns out to have significant implications for the understanding of…

— William Thurston

In the future, as in the past, the great ideas [of mathematics] must be simplifying ideas, the creator must always be one who clarifies,…

— Andre Weil

General Systems Theory is a name which has come into use to describe a level of theoretical model-building which lies somewhere between the highly…

— Kenneth E. Boulding

Without troublesome work, no one can have any concrete, full idea of what pure mathematical research is like or of the profusion of insights…

— Edmund Husserl

“A good example of the archetypal ideas which the archetypes produce are natural numbers or integers. With the aid of the integers the shaping…

— K. V. Laurikainen

“This quest to take a problem and see what happens in different situations is called generalizing, and it is this force that drives mathematics…

— Matt Parker

A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first…

— David Hilbert

Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.

— Alfred North Whitehead

The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience

— Immanuel Kant