Broadly speaking, pure mathematics is mathematics which studies entirely abstract concepts. From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics, and at variance with the trend towards meeting the needs of navigation, astronomy, physics, engineering, and so on. Another insightful view put forth is that pure mathematics is not necessarily applied mathematics.
Read more about Pure Mathematics: Generality and Abstraction, Purism, Subfields
Famous quotes containing the words pure mathematics, pure and/or mathematics:
“The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience.”
—Willard Van Orman Quine (b. 1908)
“But all its chief delight was still
On Roses thus its self to fill:
And its pure virgin Limbs to fold
In whitest sheets of Lillies cold.
Had it liv’d long it would have been
Lillies without, Roses within.”
—Andrew Marvell (1621–1678)
“The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism.”
—Willard Van Orman Quine (b. 1908)