The Collaborative International Dictionary of English v.0.48:

Irreducible \Ir`re*du"ci*ble\, a.
   1. Incapable of being reduced, or brought into a different
      state; incapable of restoration to its proper or normal
      condition; as, an irreducible hernia.
      [1913 Webster]

   2. (Math.) Incapable of being reduced to a simpler form of
      expression; as, an irreducible formula.
      [1913 Webster]

   Irreducible case (Alg.), a particular case in the solution
      of a cubic equation, in which the formula commonly
      employed contains an imaginary quantity, and therefore
      fails in its application. -- Ir`re*du"ci*ble*ness, n. --
      -- Ir`re*du"ci*bly, adv.
      [1913 Webster]

WordNet (r) 3.0 (2006):

irreducible
    adj 1: incapable of being made smaller or simpler; "an
           irreducible minimum"; "an irreducible formula"; "an
           irreducible hernia" [ant: reducible]