In mathematics education, researchers have proposed a wide range of improvements of teaching practice in school, but only a few of these proposals have sustainably changed mathematics education in the desired form. This article takes off with the assumption that this gap between ideals and practice can be understood and challenged through a better understanding of the social functions of mathematics education. Functionalism is a sociological paradigm, which is based on the assumption that sub-systems of society support each other. The application of this theory to mathematics education seeks to illuminate the social connectedness of classroom practice and incorporates various studies from the field of mathematics education and beyond. Its originality lies in its ability to integrate and order results from many different socio-political studies in mathematics education and to identify research desiderata in the field. On this basis, I show that in spite of official discourses on the use-value of mathematics, we lack evidence that mathematics education is functional in providing socially necessary qualifications in mathematics. Instead, possible other functions of mathematics education such as the training of economically beneficial character traits, the legitimisation of mathematics as a social tool of power, the transfer of social advantages from parents to children, the training of a bureaucratic mentality and the projection of societal wishes and fears are discussed. The results do not only provoke further debate on educational goals of mathematics education but may form a basis on which to plan educational innovation with particular attention towards social constraints underlying mathematics education.