In this paper we describe and discuss how mathematical values influence researchers’ choices when practicing mathematics. Our paper is based on a qualitative investigation of mathematicians’ practices, and its goal is to gain an empirically grounded understanding of mathematical values. More specifically, we will analyze the values connected to mathematicians’ choice of problems and their choice of argumentative style when communicating their results. We suggest that these two situations can be understood as relating to the three mathematical values: recognizability, formalizability and believability. Furthermore, we discuss three meta-issues concerning the general nature of mathematical values, namely 1) the origin of mathematical values, 2) the extent to which different values change over time and 3) the situatedness of mathematical values; that is the extent to which mathematical values depend on the specific context in which you are located. We conclude the chapter by recommending a methodological pluralism in future investigations of mathematical values