The work of Alain Badiou, while praising mathematics and attributing to it an important role in a philosophical system of Hegelian immensity, confronts mathematics as a practice located in a world with profound and difficult questions regarding its role in the world.
Can mathematics consider itself at a remove from politics, ethics, or the truth procedures of art?
I will argue that mathematics should take up this challenge, and responsibility assigned to it, in a way that goes beyond strictly technical points. There is something like an ethos of mathematics, a sort of manifesto of affirmationism, unwritten or implicit, too often concealed by the philosophical hesitations of the proverbial working mathematician.