The research reported here focuses on an examination of the conceptual underpinnings of two areas of mathematical thought, fractions and proof. The analysis makes use of the theoretical framework of conceptual integration, and draws on spontaneous gesture as an important data source. The question of how gestures evoke meaning is addressed within the context of two studies, one involving prospective elementary school teachers discussing fractions, and the other involving doctoral students in mathematics talking about and carrying out proofs. In both situations, gestures and their accompanying language are analyzed in terms of conceptual mappings from more basic conceptual spaces.