The divine inspiration of madness – its ambiguity, its creativity, its higher sanity, and the cover and legitimacy it gives to protest against oppression and bullies of all stripes – these were the ideas which energised Miloš Forman in his remarkable work. He was the Czech new wave émigré who brought the spirit of anti-Soviet rebellion to Hollywood and made its sly comic strategies and humanist passion flower in dozens of different ways. He also became one of the many directors whose work was shaped by working with the great screenwriter Jean-Claude Carrière.

Forman was a sensational Oscar winner with One Flew Over the Cuckoo’s Nest (1975) starring Jack Nicholson as the hyperactive crook who fakes madness to get what he thinks is the soft option of a psychiatric facility; and Amadeus (1984), the gripping myth about F Murray Abraham’s thin-lipped Antonio Salieri planning to kill Tom Hulce’s impish Mozart – the mediocre rational careerist enviously destroying the disorderly genius. Forman became feted for conjuring drama and star performances from the bristling ensemble of smaller roles. And the madhouse scene, in all its poignant farce and Foucauldian political surveillance became a keynote of his movies, even resurfacing in his final, flawed work Goya’s Ghosts in 2006 with Natalie Portman, Javier Bardem and Stellan Skårsgard.

Forman studied screenwriting at the Academy of the Performing Arts in Prague and his first big success was A Blonde in Love (1965) which, like so much in pop culture from the west, tapped into the romantic and erotic dissatisfaction, as well as the social restlessness, of the young. A young woman who works in a shoe factory has a one-night stand with a guy, but on moving to the big city to be with him, and on crucially meeting his parents (that unsatisfactory older generation) sees that there is something very wrong.

His next big hit was the sensational – but interestingly subtle and indirect – satire The Firemen’s Ball in 1967, a virtual real-time account of an evening fundraiser for the local fire service in which bureaucracy and pompous uniform-wearing officialdom are sent up. Importantly, a building actually burns to the ground in the course of a night dedicated to firefighting. It is a brilliant and persuasive comedy. But it was banned by the Czech authorities, a paradoxical act of important criticism which revealed the film’s and Forman’s importance, and their own hamfisted clumsiness. After the tanks were sent into Prague, Forman established himself in New York.

His 1971 comedy Taking Off touched again on the theme of the stuffy and now preposterous older generation failing to understand their children, but it was his 1975 movie One Flew Over the Cuckoo’s Nest which propelled Forman into the big league. This was based on the Ken Kesey novel which had already been adapted for the stage with Kirk Douglas in the lead role. With the help of his producer son Michael Douglas, Kirk was persuaded to step down in favour of the hot newcomer Jack Nicholson and under Forman’s guidance, his boisterous performance amidst the gallery of holy fools and other unholy people was electric. It was a brilliant film, though still perhaps not entirely understood: Forman directed a great scene in which the hated Nurse Ratched reveals herself to be not driven by sadism but a kind of blinkered, misguided professionalism. Forman’s protégé James Mangold drew on the master’s work for his own film Girl, Interrupted, with Angelina Jolie in the comparable sacrificial-wild-child role.

Hair was Forman’s next movie, a screen adaptation of the counter-culture anti-war musical which made protest acceptable to the theatregoing classes. It was another example of how Forman had a flair for the zeitgeist and for artistic dissent, but it perhaps didn’t quite approximate the impact Hair had had on stage: a theatre work which itself looks a little genteel compared to the rock legends of the time. But his movie was a very intelligent, fluent piece of work.

Amadeus was Forman’s next theatrical adaptation — and again the actor who had made the lead role a hit on stage had to be persuaded to step aside. This was the brilliant Simon Callow, who perhaps deserved a chance to be directed by Forman and it is a shame that his performance was not immortalised on screen. But Tom Hulce, with his sudden, shriekingly nervous and trumphant laugh, was still a very successful Mozart and F Murray Abraham was horribly malcontented as Salieri, and chillingly convincing as someone who foresees his own destiny in hell.

Amadeus is less renowned than Cuckoo’s Nest among Forman’s work, but in some ways it hangs together better. And it really is, to use a critical platitude often given to more solemn work, “mesmerising”. It was ideal for Forman’s own sophistication and his real, lived experience of art and the authorities: how the agencies of the state, in all their stultifying pomposity, will claim to be patrons or sponsors of the arts, but only to spread the word of conformism, to assist in the business of controlling people’s hearts and minds, and in doing so create malign mediocrity. Perhaps Forman saw a battalion of Salieris in Czechoslovakia and all over Eastern Europe, blandly consenting to a soulless regime in return for petty distinctions.

In his later career, Forman directed Valmont, an adaptation of Les Liaisons Dangereuses, a movie which was perhaps more obviously passionate and erotic than Stephen Frears’s Dangerous Liaisons which had come out the year before — but which upstaged Forman’s version, with its colossal performances from Glenn Close and John Malkovich.

Forman was to address two more classic American bad boys: the porn publisher Larry Flynt and the cult comic Andy Kaufman. In The People Vs Larry Flynt (1996), Woody Harrelson’s impulsive and extravagant Flynt becomes a highly unlikely and satirically ambiguous poster boy for freedom of speech. In Man on the Moon (1999), Jim Carrey plays Kaufman as the rock-n-roll wild man of standup. Forman never quite solved the problem of whether and how the film was allowed to be funny on its own account, but it was great casting and Forman clearly empathised with the comedian and his lonely, courageous artform.

Forman was a fascinating and triumphant 20th century artist — his career was a carnival subversion of tyrannies.