I'm a huge fan of Terry Gilliam. That being said, being a huge fan of Terry Gilliam can be a lot of work. Hence, the Gilliam Theorem.
Gilliam started his popular career as the lone American in Monty Python, and his first (co-)directing credit was Monty Python and the Holy Grail (1975). I'm going to go out on a limb and suggest he's the member of the troupe who most eagerly embraced the challenge of advancing his ambitions past Monty Python itself.
Which is not to say the others (Graham Chapman has certainly looked better, though) have slacked off, but their projects have had a much looser continuity. That's also to say, Gilliam is the one who has had the highest profile in terms of what he's done, which is to continue directing films, so that when you say John Cleese, you think of Fawlty Towers or A Fish Called Wanda and scores of comedic supporting roles, or say Eric Idle and think of Spamalot! or Not the Messiah or even The Rutles, and whatever it is you think of in association with Terry Jones (who was the other co-director of Holy Grail, by the way, and for me personally known for writing Douglas Adams's Starship Titanic) or Michael Palin (not related to that other Palin).
Anyway, the point is, the parrot has ceased to be, and I won't go on insulting Monty Python, but rather discuss Terry Gilliam...
After Holy Grail, Gilliam went about crafting the rest of his directorial career, which began with a Python-esque effort called Jabberwocky (1977). He went on to begin forming his own legacy with the more distinctive Time Bandits (1981), which is usually considered his first notable effort. It's certainly a very interesting film.
His most universally acclaimed film, Brazil (1985), followed, also the one that began Gilliam's career of trying to catch up with whatever he was supposed to be doing. Which is to say, in a different way entirely, Gilliam inadvertently became the modern Orson Welles, the director who constantly has to prove himself all over again, if he's to do his own projects at all, with studio meddling constantly getting in the way. Time Bandits, like Citizen Kane, proved perhaps too much to live up to, and so the more he wanted to explore his personal creative vision, the more interference Gilliam experienced.
He followed with The Adventures of Baron Munchausen (1988), which is something I saw for the first time in college, and maybe that was the best possible time to discover Gilliam post-Python, because Munchausen is pretty weird but also wildly imaginative in exactly the way a college student can appreciate. (Really, there is hardly any period better than college than to discover a passion for film.)
Gilliam's biggest mainstream hit was The Fisher King (1991) featuring Jeff Bridges and Robin Williams, which perhaps worked because of the straight man routine, in that Bridges grounds the film in reality while observing Williams, who seems to be utterly insane. But the truth turns out to be the first instance of Gilliam finding a more transcendent tone. If you find yourself unfamiliar with Gilliam's work, this would be the ideal introduction.
His biggest box office hit, though, was Twelve Monkeys (1995), featuring a time traveling Bruce Willis and an insane Brad Pitt, which borrows some of what Gilliam learned making Fisher King, allowing the real world to be present but in a very unreal way, which may be the best way to describe his instincts as a filmmaker.
Following that was Fear and Loathing in Las Vegas (1998), a movie about Hunter S. Thompson. It's Gilliam's only attempt to date at depicting the real world as an inherently surreal experience.
There's a long break until The Brothers Grimm (2005), which begins Gilliam's recent instinct to revisit his earlier work and see what else he can say about it. In a lot of ways, Grimm is an updated Jabberwocky. It's also his first collaboration with the late Heath Ledger.
I didn't even know Tideland (2006) existed until recently, which is a clear indication of the direction Gilliam's mainstream career has gone.
My favorite Gilliam is The Imaginarium of Doctor Parnassus (2009), which received any attention at all because it was the project Ledger was filming at the time of his death. The Ledger everyone cared about, however, had already been immortalized in The Dark Knight, a singular performance in an otherwise still-underrated career that still has yet to be fully appreciated. Much as Gilliam's, really. Gilliam chose, within the existing framework of his story, to fill out Ledger's remaining work by casting three replacements, Johnny Depp, Jude Law, and Colin Farrell. Yet the best thing about it is Christopher Plummer, who plays a kind of Gandalf or Dumbledore if they had never met Bilbo or Harry Potter, someone forced to make a Faustian deal (with a Devil played by Tom Waits, whom many observers have remarked Ledger based his Joker on) against his daughter's future. Also worth noting that it features the mainstream debut of Andrew Garfield.
The Zero Theorem (2014) is a kind of Brazil revisited, in some ways, an office worker-of-a-kind making an existential breakthrough, but in a thoroughly Imaginarium way. The star is Christoph Waltz, who has been so sensational in two successive Quentin Tarantino films (Inglourious Basterds and Django Unchained, both winning him Best Supporting Actor honors at the Oscars), and I thought his presence alone might have been enough to make Gilliam creatively visible again. Clearly I was wrong.
The problem, as introduced in Brazil, is that Gilliam has become something of a Sisyphus, pushing a boulder up a hill endlessly. Nowhere is that more evident than in Lost in La Mancha, a documentary about his previous attempt to make what is once again his current project, The Man Who Killed Don Quixote. In Lost, all the forces imaginable worked against him, and film production was ultimately cancelled.
All of which has resulted in making a very visible creator an obscure personality during the height of his career. Gilliam has never lacked for ambition, and he has seized every opportunity presented him, but he has tended to be out of sync with just about everyone. The '80s were a perfect decade for his instincts, and he proved eminently adaptable in the '90s, but he's played catch-up ever since. People are always asking where all the creativity is in film, and arguably no director has ever demonstrated as much of it as Gilliam, yet seldom has anyone acknowledged that. It's always about timing, of course, and whether or not his instincts have been agreeable to wide audiences.
The Gilliam Theorem suggests that creativity alone isn't always what audiences want, no matter what they say. They want familiarity. When Gilliam has done work that looks like what others are doing, with his own elements peaking at the edges, he's been successful. When he's pushed his own elements to the forefront, he ends up marginalized. The only comparable filmmaker I can think of is Tarsem, responsible for the genius of The Fall but still best known for his first film, The Cell. Tarsem tends to tell his stories from established vantage points (The Cell is a story about a serial killer, The Fall about a little girl hearing stories from a suicidal stunt man...which I guess is less of a good example than it seems; Immortals, meanwhile, is another Greek myth movie, while Mirror Mirror is Snow White).
Like Christopher Nolan's Interstellar, Gilliam attempts to answer the big questions in Zero Theorem (such as, you know, the meaning of life, this time with far less Python!). By necessity, and because he tends to swing for the fences with every project, Gilliam has had to go back over territory familiar from his own work, but that will leave future fans with a much richer tapestry to examine. He will be a director still worth talking about years from now precisely for the challenges he has continually embraced, his interest in pushing boundaries. Commercially, it can be a recipe for disaster. But in terms of results, a feast. Every creator does that, by the way, but few of them do it as fruitfully. They're learning at slower speeds. Working in Monty Python pushed Gilliam further and faster than most, presenting a whole set of challenges he was eager to embrace. How quickly he reached new milestones became almost insurmountable for others to continue following. And yet he kept going.