Mathematics education needs a better appreciation of the dominant power structures in the educational field: Bourdieu's theory of capital provides a good starting point. We argue from Bourdieu's perspective that school mathematics provides capital that is finely tuned to generationally reproduce the social structures that serve to keep the powerful in power, while ensuring that less powerful groups are led to accept their own failure in mathematics. Bourdieu's perspective thereby highlights theoretical inadequacies in much mathematics education research, insofar as it presumes a consensus about a ‘what works agenda’ for improving achievement for all. Drawing on one case where we manufactured awkward facts, we illustrate a Bourdieusian interpretation of mathematics capital as reproductive, and the crucial role of its cultural arbitrary. We then criticise the Bourdieusian concept of ‘mathematical capital’ as the value of mathematical competence in practice and propose to extend his tools to include the contradictory ‘use’ and ‘exchange’ values of mathematics instead: we will show how this conceptualisation goes ‘beyond Bourdieu’ and helps explain how teaching-learning might (ideally) produce ‘cultural use value’ in mathematical competence, while still recognising the contradictions teachers and learners face. Finally, we suggest how critical education research generally can benefit from this theoretical framework: (1) in exposing the interest of the dominant classes; but also (2) in researching critical pedagogic alternatives that challenge orthodoxy in educational policy and practice both in mathematics education and more generally.