We focus on the role of signs in the process of constructing proofs by mathematical induction of high-achieving post-graduate students. Using a multimodal semiotic perspective, speech, written inscription (symbols, drawings, etc.), and gestures are analysed, and two particular categories of signs are identified and observed: linking signs and iteration signs. We analyse what these signs reveal and how the students use them to formulate a conjecture and to structure the proof by mathematical induction.