Alain Badiou's philosophy is a consequential attempt to make the idea of generic existence intelligible with purely formal means. The aim of this thesis is to show how Badiou develops a mathematical ontology to think the idea of generic politics after the failure of Maoism and to demonstrate the limits of this approach. My thesis follows the chronology of Badiou's work, and I distinguish four periods : early work that includes the 'novels' 'Almagestes' (1964) and 'Portulans' (1967), and the yper-Althusserian theoretical texts of the mid- to late-1960s; Maoist theory that includes the pamphlets of the 1970s; 'Theory of the Subject' (1981); and finally, the Platonism of 'Being and Event' (1988) and 'Logics of Worlds' (2006). In chap...