Source : Webster's Revised Unabridged Dictionary (1913)

Pure \Pure\, a. [Compar. {Purer}; superl. {Purest}.] [OE. pur,
   F. pur, fr. L. purus; akin to putus pure, clear, putare to
   clean, trim, prune, set in order, settle, reckon, consider,
   think, Skr. p? to clean, and perh. E. fire. Cf. {Putative}.]
   1. Separate from all heterogeneous or extraneous matter; free
      from mixture or combination; clean; mere; simple; unmixed;
      as, pure water; pure clay; pure air; pure compassion.

            The pure fetters on his shins great.  --Chaucer.

            A guinea is pure gold if it has in it no alloy. --I.
                                                  Watts.

   2. Free from moral defilement or quilt; hence, innocent;
      guileless; chaste; -- applied to persons. ``Keep thyself
      pure.'' --1 Tim. v. 22.

            Now the end of the commandment is charity out of a
            pure heart, and of a good conscience. --1 Tim. i. 5.

   3. Free from that which harms, vitiates, weakens, or
      pollutes; genuine; real; perfect; -- applied to things and
      actions. ``Pure religion and impartial laws.'' --Tickell.
      ``The pure, fine talk of Rome.'' --Ascham.

            Such was the origin of a friendship as warm and pure
            as any that ancient or modern history records.
                                                  --Macaulay.

   4. (Script.) Ritually clean; fitted for holy services.

            Thou shalt set them in two rows, six on a row, upon
            the pure table before the Lord.       --Lev. xxiv.
                                                  6.

   5. (Phonetics) Of a single, simple sound or tone; -- said of
      some vowels and the unaspirated consonants.

   {Pure-impure}, completely or totally impure. ``The
      inhabitants were pure-impure pagans.'' --Fuller.

   {Pure blue}. (Chem.) See {Methylene blue}, under {Methylene}.
      

   {Pure chemistry}. See under {Chemistry}.

   {Pure mathematics}, that portion of mathematics which treats
      of the principles of the science, or contradistinction to
      applied mathematics, which treats of the application of
      the principles to the investigation of other branches of
      knowledge, or to the practical wants of life. See
      {Mathematics}. --Davies & Peck (Math. Dict. )

   {Pure villenage} (Feudal Law), a tenure of lands by uncertain
      services at the will of the lord. --Blackstone.

   Syn: Unmixed; clear; simple; real; true; genuine;
        unadulterated; uncorrupted; unsullied; untarnished;
        unstained; stainless; clean; fair; unspotted; spotless;
        incorrupt; chaste; unpolluted; undefiled; immaculate;
        innocent; guiltless; guileless; holy.

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)
      (a) 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.
      (b) 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} or {Pure mathematics}. See {Mathematics}.

Source : WordNet®

pure mathematics
     n : the branches of mathematics that study and develop the
         principles of mathematics for their own sake rather than
         for their immediate usefulness