The Slovenian thinker, who provokes both right and left with his discourses on society and humanity, is now an inspiration for four new operas. How will he fare at the hands of Covent Garden?

He has been called the Elvis of philosophy and the Marx Brother, had a book of his philosophical jokes published in an edition of one by a conceptual artist and been linked via a viral internet hoax to Lady Gaga.

It should perhaps come as no surprise, then, that the Royal Opera House, eager to produce contemporary and iconoclastic work, has just announced that it has commissioned four new operas inspired by the writings of the leftwing Slovenian thinker, Slavoj Žižek, the most high-profile and controversial public philosopher of our time.

Signalling his commitment to staging new productions alongside the "bohèmes and traviatas", Kasper Holten, the Royal Opera House's director of opera, said that Žižek's work "challenged opera writers to write about their fears and hopes for the world now".

It is hard to think of another living philosopher whose work could lend itself to such extravagant reinterpretation, but Žižek, despite his beard and drably utilitarian dress sense, is no ordinary philosopher. He is, rather, a thinker of choice for the internet generation, whose commitment to old-school communism is matched only by his talent to provoke and bemuse both the right and the liberal left.

To this end, he has compared Julian Assange favourably to Mahatma Gandhi, while describing them both with admiration as terrorists. More controversially, he recently wrote: "The problem with Hitler was that he was 'not violent enough', his violence was not 'essential' enough." To be fair, this characteristically provocative claim was framed by a wider, deeper reflection on violence, revolution and what Žižek calls "gigantic spectacles of pseudo-revolution" such as Nazism, which, he argued, are staged to disrupt but not threaten the established capitalist order. Nevertheless, it led to a recent typically selective article in the Telegraph headlined "Is Slavoj Žižek a Left-Fascist? The English political philosopher John Gray, writing in the New York Times, echoed that sentiment in more measured terms, noting: "There may be some who are tempted to condemn Žižek as a philosopher of irrationalism whose praise of violence is more reminiscent of the far right than the radical left."

Nothing, though, about Žižek is simple or straightforward and that is exactly how he likes it. "I don't give clear answers to even the simplest, most direct questions," he told me when I interviewed him in 2010. "I like to complicate issues. I hate simple narratives. I suspect them. This is my automatic reaction."

That stance has underpinned the ongoing series of books that has made his name. The first, The Sublime Object of Ideology, published in 1989, compared Marx's treatise on commodities with Freud's dream theories by way of Kant and the radical psychoanalyst Jaques Lacan, one of Žižek's key influences. In The Fragile Absolute: Or Why is the Christian Legacy Worth Fighting For?, Žižek, an atheist, argued that Christians and Marxists should unite against "the contemporary onslaught of vapid spirituality".

Žižek was born in what was then communist Yugoslavia on 21 March 1949 to an economist father and an accountant mother. A loner, he read voraciously, his love of theory blossoming at university in Ljubljana, where he first fell under the spell of Lacan. His postgraduate thesis was rejected for being too critical of Marx and he subsequently struggled to find a teaching post, working instead as a translator of philosophy books.

In 1978, he was "banished to a marginal research institute", he told me, where he had time to write his breakthrough book, The Sublime Object of Ideology.The following year, he had a brief but intense flirtation with party politics, astounding his leftist friends by standing for election as a Liberal Democrat candidate. (He came fifth.) Chastened, he devoted himself exclusively to writing and, since then, buoyed by teaching posts at Columbia, Princeton and London's Birkbeck College, he has established himself as the world's most well-known and divisive contemporary thinker (only Noam Chomsky comes close).

He has been married at least twice: to Renata Saleci, a fellow Slovenian philosopher, and to Analia Hounie, a model – and Lacanian scholar – from Argentina. He has two sons, one in his 30s, the other 12 years old. Despite the Lady Gaga internet rumour, which prompted the Daily Star to report: "Pals fear Lady Gaga's head is being filled with extremist ideas by Slovenian-born Slavoj Žižek", he is currently single. (This is perhaps unsurprising given that the documentary Žižek! revealed that he keeps his underwear and socks, mostly of the free airline variety, in his kitchen drawers.)

Like a Marxist Morrissey, Žižek has a way with tantalising titles and a seemingly effortless talent to provoke: Did Somebody Say Totalitarianism? critiques one of his recurring bugbears, the so-called "liberal-democratic consensus"; In Defence of Lost Causes argues for a return to ideological engagement over the emptiness of post-modernism.

Alongside his dense and often wildly discursive theoretical works, he has written widely on film, tackling the Lacanian subtexts in the films of two of his favourite directors, Alfred Hitchcock and David Lynch, while, less plausibly, setting out the "somewhat naive, but nonetheless basically accurate, illustration of an important aspect of Lacanian theory" that lurks unseen in Kung Fu Panda.

This tendency to merge highbrow and popular culture has not enamoured Žižek to the academy, but he seems blithely unconcerned by his outsider status, which, one suspects, is more instinctive than adopted. In 2011, he summed up what he believed to be the philosophy establishment's prevailing view of him: "I should not be this man who talks about The Dark Knight and Hegel, about the value of WikiLeaks and Lady Gaga. I should be a mediocre philosophy professor in Ljubljana."

In performance, which is what his lectures have become, he cuts an often alarming figure, his thoughts flowing freely in rapid-fire sentences punctuated by guttural grunts, a variety of facial tics and his constant dabbing at his spittle-flecked beard. He does not so much ignore the contradictions in his writings as revel in them, which, alongside his prankster tendencies, have led some to conclude that he is the clown prince of post-postmodern philosophy rather than its saviour. In an acidic New Yorker profile, Rebecca Mead described Žižek's approach: "His favoured form of argument is paradox and his favoured mode of delivery is a kind of vaudevillian overstatement, buttressed by the appearance of utter conviction."

For all that, though, Žižek has singlehandedly dragged Marxist dialectics into the mainstream, attracting a mainly younger audience to his lectures and energising theoretical discourse like no one since Jacques Derrida or Roland Barthes in the heady post-structuralist days of the 1960s and 1970s.

What, then, are we to make of the most well-known thinker of our time? Is he, as Rebecca Mead insisted, the Marx Brother or, as Terry Eagleton put it, "the most formidably brilliant exponent of psychoanalysis, indeed of cultural theory in general to have emerged from Europe in some decades"? Or, is he both?

When I spoke to him for the publication of his book, Living in the End Times, in 2010, he leafed though the pages, going: "Bullshit. Some more bullshit. Blah, blah blah...", singling out only a few chapters as worthy of praise. (He also admitted to writing the chapter on the film Avatar before he had seen the film: "I am a good Hegelian. If you have a good theory, forget about the reality.")

In many ways, then, he is his own worst enemy, but that, too, may be part of his philosophical approach, to make us question the ideology of Žižekism as well as the ideologies of global capitalism and high and low culture.

His recent big, dense, scholarly, though no less scattergun, book on Hegel, which he described as "my true life's work", has done little to dent his reputation as the reigning prankster of philosophy, but he remains unrepentant. And popular.

The documentary film-maker, Sophie Fiennes, who has made two films about Žižek, including the forthcoming The Pervert's Guide to Ideology, comes closest to explaining his peculiar status.

"He is very much a thinker for our turbulent, high-speed, information-led lives precisely because he insists on the freedom to stop and think hard about who you are as an individual in this fragmented society. We need a radical hip priest and Slavoj is that in many ways."