National Numeracy Strategy (NNS) guidance appears to characterise mathematical language as a set of specialist words with unambiguous definitions, yet analysis of the classroom transcript suggests that at least some mathematical concepts cannot be captured by such definitions. This paper explores the notion of definition within mathematics, considering both school mathematics and the field of academic mathematics research. Extracts of texts from these domains are analysed using tools drawn from systemic functional linguistics. The more advanced texts show definitions to be constructed and used in creative and purposeful ways. This contrasts with the one-to-one word-concept relationship apparent in the NNS guidance and in a text for "Intermediate Level" secondary students. This finding raises the question of the extent to which the linguistic models implicit in the texts for less advanced school students and their teachers allow students to learn more powerful aspects of mathematics.