| Sumario: | Alain Badiou's work provides an important opportunity for critical human geographers to enhance our grasp of a range of abstract mathematical concepts while clarifying that toward which we must remain critical. Yet the geographical encounter with Badiou thus far has been needlessly hampered by, and has itself reinforced, a certain pessimism about the ability of qualitatively-trained geographers to deal in any meaningful way with his mathematical arguments. Challenging this pessimism, the present paper argues that if we trust ourselves a bit more to think through, with, and against mathematical concepts, we can in fact learn a great deal from Badiou. To illustrate this claim, the paper draws upon mathematical dimensions of Badiou's arguments – as well as some ideas from Gestalt theory – to highlight failures both of his ontological and of his phenomenological projects. In light of the latter failure, however, Badiou's mathematical concepts suggest the possibility of an analysis of qualitative geographical phenomena that both retains a place for subjectivity and leaves space for the recognition of 'proto-quantitative relations'. The paper closes by suggesting how Badiou's abstract mathematical concept of the 'transcendental' can help to understand the manipulative production of space in twenty-first century capitalism.
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