Metaphors are recognized as bridging scientists' challenges in communication with the public. In mathematics, however, which often involves abstract concepts and relations, less attention has been paid to the role of metaphors in public communication. In this article we examine the metaphors appearing in the discourse of 10 mathematicians in five radio broadcasts to communicate advanced mathematical concepts and activities to the public. Using Cameron's metaphor categorization procedure, we recognized seven systematic metaphors, MATH AS: SLOG, A SYSTEM, DISCOVERY, BUILDING AND CONSTRUCTING, A KEY, VISUOSPATIAL, and SLIPPERY/MYSTERIOUS, in the contexts of negative numbers, symmetry, pi, the Poincaré conjecture, and prime numbers. Mathematicians' talk displayed these metaphoric resources in an emergent and situated way to communicate approximations of advanced ideas. The context and participants' reactions created a transforming cycle for the interchangeable use of metaphors for both theory-constructive and pedagogical functions.