Source : Webster's Revised Unabridged Dictionary (1913)

Mathematical \Math`e*mat"ic*al\, a. [See {Mathematic}.]
   Of or pertaining to mathematics; according to mathematics;
   hence, theoretically precise; accurate; as, mathematical
   geography; mathematical instruments; mathematical exactness.
   -- {Math`e*mat"ic*al*ly}, adv.

Source : WordNet®

mathematically
     adv : with respect to mathematics; "mathematically impossible"