What is "abstract mathematics"

Abstract \Ab"stract`\ (#; 277), a. [L. abstractus, p. p. of abstrahere to draw from, separate; ab, abs + trahere to draw. See Trace.]

1. Withdraw; separate. [Obs.]

   The more abstract . . . we are from the body.
   --Norris.

2. Considered apart from any application to a particular object; separated from matter; existing in the mind only; as, abstract truth, abstract numbers. Hence: ideal; abstruse; difficult.

3. (Logic)

   1. Expressing a particular property of an object viewed apart from the other properties which constitute it; -- opposed to concrete; as, honesty is an abstract word.
      --J. S. Mill.

   2. Resulting from the mental faculty of abstraction; general as opposed to particular; as, ``reptile'' is an abstract or general name.
      --Locke.

      A concrete name is a name which stands for a thing; an abstract name which stands for an attribute of a thing. A practice has grown up in more modern times, which, if not introduced by Locke, has gained currency from his example, of applying the expression ``abstract name'' to all names which are the result of abstraction and generalization, and consequently to all general names, instead of confining it to the names of attributes.
      --J. S. Mill.

4. Abstracted; absent in mind. ``Abstract, as in a trance.''
   --Milton.

   An abstract idea (Metaph.), an idea separated from a complex object, or from other ideas which naturally accompany it; as the solidity of marble when contemplated apart from its color or figure.

   Abstract terms, those which express abstract ideas, as beauty, whiteness, roundness, without regarding any object in which they exist; or abstract terms are the names of orders, genera or species of things, in which there is a combination of similar qualities.

   Abstract numbers (Math.), numbers used without application to things, as 6, 8, 10; but when applied to any thing, as 6 feet, 10 men, they become concrete.

   Abstract mathematics or Pure mathematics. See Mathematics.