Categories Quote by Saunders Mac Lane

. . . the membership relation for sets can often be replaced by the composition operation for functions. This leads to an alternative foundation…

— Saunders Mac Lane

Before one can generalize, formalize, and axiomatize, there must be a mathematical substance.

— Hermann Weyl

There's a branch of math called the foundations of math. It's kind of like quantum mechanics. It's about how this very complex theory of…

— Tristan Perich

Before you generalize, formalize, and axiomatize there must be mathematical substance.

— Hermann Weyl

Mathematics as a science, commenced when first someone, probably a Greek, proved propositions about "any" things or about "some" things, without specifications of definite…

— Alfred North Whitehead

“In other words, general set theory is pretty trivial stuff really, but, if you want to be a mathematician, you need some and here…

— Paul Halmos

Mathematics is an experimental science, and definitions do not come first, but later on.

— Oliver Heaviside

What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else. Roughly speaking, people know…

— Stanislaw Ulam

The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear…

— Willard Van Orman Quine

What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else.

— Stanislaw Ulam

Mathematics is often defined as the science of space and number . . . it was not until the recent resonance of computers and…

— Lynn Steen

“No prior knowledge of specification or modeling is assumed beyond a highschool-level familiarity with the basic notions of set theory.”

— Daniel Jackson