My interest in Alain Badiou is extra-philosophical. The man now makes customary appearances in the French media. He is, according to his own self-description, "by far the most translated and commented living French philosopher". His vitriolic libel against President Sarkozy has transformed himself into a pop icon of the radical left. Reading his philosophical treatises has now become a new symbol of Parisian chic. He even finds sycophants on financial markets, with the magazine Wilmott ("Serving The Quantitative Finance Community") carrying articles establishing the link between financial speculation and speculative philosophy.



So what will the candid and uninformed reader find in Badiou's theoretical writings? First, very little in terms of politics. There are some remarks here and there that we shouldn't topple Lenin's statues too early, or positive references to the historical sequence of the French Revolution, the Paris Commune, October 1917, the struggles for national liberation, Maoist upheavals, and May 1968. A chapter on 'Politics as a Truth Procedure' opposes the collective subject of politics with the aristocratic nature of love, science and art, where establishing truth claims needs only the recognition of two, one, or no one. Politics, the author notes, invariably encounters repression, by which the State reveals the measure of its excess. Scaling the obscurity in which State power shrouds itself in turn allows the advent of a truly egalitarian politics, the example of which is provided by the mysterious Political Organization to which the author belongs.



So the book is a philosophical treatise, not a political manifesto. Here a second surprise awaits the uninformed reader: as in Plato's Republic, he is greeted with the stern warning that "may no one enter here who is not a geometer". According to Badiou, "Mathematics provides philosophy with a weapon, a fearsome machine of thought, a catapult aimed at the bastions of ignorance, superstition and mental servitude". He finds in mathematical abstractions the cold anti-humanism, the stellar brilliance, the warlike quality, and the radical departure from everyday intuitions that he assigns to philosophy. Mathematics is the breeding ground of thought: "It is impossible to be lazy in mathematics. It is possibly the only kind of thinking in which the slightest lapse in concentration entails the disappearance, pure and simple, of what is being thought about." Nothing that concerns his realm is a matter of indifference to the mathematician. He never takes 'I don't know' for an answer. "Only in mathematics can one unequivocally maintain that if thought can formulate a problem, it can and will solve it, regardless of how long it takes."



Like Badiou notes, philosophers are generally sloppy with their maths, and contend themselves with trivial examples like 7+5=12, whereas they wouldn't dare considering Humpty-Dumpty rhymes as the paradigm of poetry, or a song by Julio Iglesias as representative of musical creation. They are able to comment on "a fragment by Anaximander, an elegy by Rilke, a seminar on the real by Lacan, but not the 2,500-year-old proof that there are an infinity of prime numbers". But becoming mathematically literate is a duty for contemporary philosophers, even if acquiring competence in the field requires years of initiation: "The re-entanglement of mathematics and philosophy is the operation that must be carried out by whoever wants to terminate the power of myths, whatever they may be."



Badiou conceives philosophy's role as consisting in informing mathematics of its own speculative grandeur. According to his opening statement, ontology, the master-narrative of continental philosophy, is "nothing other than mathematics as such". Mathematics is in effect the thinking of pure being, of being qua being. Mathematics thinks being, but is not the thinking of the thought that it is. "It is therefore up to philosophy to enunciate and validate this equation: mathematics=ontology. In doing so, philosophy unburdens itself of what appears to be its highest responsibility: it asserts that it is not up to it to think being qua being." In particular, mathematics provides philosophy with the proper concept of the infinite. It therefore annihilates the need to confine thinking within the ambit of finitude. By secularizing the infinite, it offers mankind the wherewithal to be atheist. Likewise, Badiou notes that logic, once considered as a branch of philosophy, is now a mathematical discipline "which has attained a degree of complexity equal to that of any other living region of this science". Logic can no longer be conceived as the "science of thinking" whose content has not changed since antiquity, or as "the grammar of consistent discourse" that defines the linguistic turn in contemporary philosophy.



According to the editors' note, this detour through mathematics makes Alain Badiou "a thinker capable of recasting the existing parameters of philosophical discourse", and his Being and Event, published in 1988, "may turn out to have effected the most profound and far-reaching renewal of the possibilities of philosophy since Heidegger's Being and Time". Badiou agrees with this characterization and obviously holds himself in high esteem: "It is by donning the contemporary matheme like a coat of armor that I have undertaken, alone at first, to undo the disastrous consequences of philosophy's 'linguistic turn'; to demarcate philosophy from phenomenological religiosity; to re-found the metaphysical triad of being, event and subject; to take a stand against poetic prophesying; to identify generic multiplicities as the ontological form of the true; to assign a place to Lacanian formalism; and, more recently, to articulate the logic of appearing."



What are we to make of such claims? Here the reviewer must refrain out of modesty, and leave members of the philosophical profession make more informed judgments. One should however interpret as a positive sign the many commentaries that Badiou's work has inspired, the enthusiastic endorsements by well-known social critics, and the promising ventures of young philosophers trained by the professor and taking on from where he left. Badiou's theoretical writings should be considered in isolation to his politics, and may have a more long-lasting impact on contemporary thought.