In 1967 he joined a study group organized by Louis Althusser, became increasingly influenced by Jacques Lacan and became a member of the editorial board of Cahiers pour l'Analyse.

[9] By then he "already had a solid grounding in mathematics and logic (along with Lacanian theory)",[9] and his own two contributions to the pages of Cahiers "anticipate many of the distinctive concerns of his later philosophy".

[9] The student uprisings of May 1968 reinforced Badiou's commitment to the far Left, and he participated in increasingly militant groups, such as the Union des communistes de France marxiste-léniniste [fr] (UCFml).

To quote Badiou himself, the UCFml is "the Maoist organization established in late 1969 by Natacha Michel, Sylvain Lazarus, myself and a fair number of young people".

[10] During this time, Badiou joined the faculty of the newly founded University of Paris VIII (Vincennes-Saint Denis) which was a bastion of counter-cultural thought.

There he engaged in fierce intellectual debates with fellow professors Gilles Deleuze and Jean-François Lyotard, whose philosophical works he considered unhealthy deviations from the Althusserian program of a scientific Marxism.

In the 1980s, as both Althusserian structural Marxism and Lacanian psychoanalysis went into decline (after Lacan died and Althusser was committed to a psychiatric hospital), Badiou published more technical and abstract philosophical works, such as Théorie du sujet (1982), and his magnum opus, Being and Event (1988).

Nonetheless, Badiou has never renounced Althusser or Lacan, and sympathetic references to Marxism and psychoanalysis are not uncommon in his more recent works (most notably Petit panthéon portatif / Pocket Pantheon).

In 2002, he was a co-founder of the Centre International d'Etude de la Philosophie Française Contemporaine, alongside Yves Duroux and his former student Quentin Meillassoux.

In the last decade, an increasing number of Badiou's works have been translated into English, such as Ethics, Deleuze, Manifesto for Philosophy, Metapolitics, and Being and Event.

Short pieces by Badiou have likewise appeared in American and English periodicals, such as Lacanian Ink, New Left Review, Radical Philosophy, Cosmos and History and Parrhesia.

Unusually for a contemporary European philosopher his work is increasingly being taken up by militants in countries like India, the Democratic Republic of Congo and South Africa.

Badiou's work engages a detailed decrypting of texts, in line with philosophers such as Foucault, Deleuze, Balibar, Bourdieu, Derrida, Bouveresse and Engel, all of whom he studied with at the Ecole Normale Superieure.

[15] According to Badiou, philosophy is suspended from four conditions (art, love, politics, and science), each of them fully independent "truth procedures."

The dominating ideology of the day, which Badiou terms "democratic materialism," denies the existence of truth and only recognizes "bodies" and "languages."

In Handbook of Inaesthetics Badiou both draws on the original Greek meaning and the later Kantian concept of "aesthesis" as "material perception" and coins the phrase "inaesthetic" to refer to a concept of artistic creation that denies "the reflection/object relation" yet, at the same time, in reaction against the idea of mimesis, or poetic reflection of "nature", he affirms that art is "immanent" and "singular".

His view of the link between philosophy and art is tied into the motif of pedagogy, which he claims functions so as to "arrange the forms of knowledge in a way that some truth may come to pierce a hole in them".

This effort leads him, in Being and Event, to combine rigorous mathematical formulae with his readings of poets such as Mallarmé and Hölderlin and religious thinkers such as Pascal.

[18] Being and Event offers an example of this slow uptake, in fact: it was translated into English only in 2005, a full seventeen years after its French publication.

Mathematician Alan Sokal and physicist Jean Bricmont write that Badiou proposes, with seemingly "utter seriousness," a blending of psychoanalysis, politics and set theory that they contend is preposterous.

[19] Similarly, philosopher and aesthetics writer Roger Scruton has questioned Badiou's grasp of the foundation of mathematics, writing in 2012: An example of a critique from a mathematician's point of view is the essay 'Badiou's Number: A Critique of Mathematics as Ontology' by Ricardo L. Nirenberg and David Nirenberg,[21] which takes issue in particular with Badiou's matheme of the Event in Being and Event, which has already been alluded to in respect of the 'axiom of foundation' above.

By enacting fidelity to the event within these four domains one performs a 'generic procedure', which in its undecidability is necessarily experimental, and one potentially recasts the situation in which being takes place.

Alain Badiou is a founding member (along with Natacha Michel and Sylvain Lazarus) of the militant French political organisation L'Organisation Politique, which was active from 1985 until it disbanded in 2007.

[22] It called itself a post-party organization concerned with direct popular intervention in a wide range of issues (including immigration, labor, and housing).

In addition to numerous writings and interventions, L'Organisation Politique highlighted the importance of developing political prescriptions concerning undocumented migrants (les sans papiers), stressing that they must be conceived primarily as workers and not immigrants.

[24] This book generated a strong response, and the wrangling became a cause célèbre with articles going back and forth in the French newspaper Le Monde and in the cultural journal Les Temps modernes.

Linguist and Lacanian philosopher Jean-Claude Milner, a past president of Collège international de philosophie, accused Badiou of anti-Semitism.

[25] Badiou forcefully rebutted this charge, declaring that his accusers often conflate a nation-state with religious preference and will label as anti-Semitic anyone who objects to this tendency: "It is wholly intolerable to be accused of anti-Semitism by anyone for the sole reason that, from the fact of the extermination, one does not conclude as to the predicate "Jew" and its religious and communitarian dimension that it receive some singular valorization – a transcendent annunciation!

The solution is the creation of a secular and democratic Palestine...which would show that it is perfectly possible to create a place in these lands where, from a political point of view and regardless of the apolitical continuity of customs, there is 'neither Arab nor Jew.'

Badiou claims that Sarkozy’s rise is the return of a kind of ‘Pétainist’ mass subjectivity first instigated by the Vichy regime’s collaboration with the Nazis in World War II; the enemy that is being acquiesced to now, though, is of course capital.”[30]