It is unusual in art for collaborators to be of equal star-wattage. The pairing of Benjamin Britten and WH Auden was one such. Another, much longer-lasting, was Stravinsky and Balanchine, a partnership of equals that endured for nearly half a century. More recently, Antony Gormley has worked with both Akram Khan and Sidi Larbi Cherkaoui, to great effect. Can Turnage, McGregor and Wallinger replicate these? This has been the question.

When the subject of funding for the arts arises, the phrase “allowed to fail” is frequently heard: artists must be enabled to try new things, press against the outer edges of what they know. Enter Anne Teresa De Keersmaeker and Jérôme Bel, two of contemporary dance’s thinkers. They have tried, and failed, to choreograph the final section of Mahler’s Das Lied von der Erde, and in that attempt, they have produced an extraordinary evening: the anatomy of a failure.

Rambert is making a thing of acquiring classic works from the 20th-century contemporary repertory – and a very good thing, too. First staged by them last year, RainForest, a minor Merce Cunningham piece from 1968, was recently performed by the Cunningham company itself, in London on its final tour. And yet, while that performance was straight from the horse’s mouth, I think Rambert (whisper it) in reality do it better.

Time is a rare privilege in a choreographer’s career - in Britain, anyway. We don’t have the equivalents of Merce Cunningham, Martha Graham or Paul Taylor, who build careers into their eighties and beyond, with mighty efforts from private patrons and friendly art giants of their generation (Andy Warhol, Robert Rauschenberg, Isamu Noguchi et al). UK choreographers are fortunate to get 10 years until the Arts Council deems it time to push them out of the subsidised nest, to vanish in their late thirties, most of them.

There are various disinterments of supposedly iconic dance-makers going on in this year's Dance Umbrella (some live ones more dead than the dead ones), but no one is going to beat for sheer éclat Lucinda Childs’ astonishingly beautiful minimalist 1979 creation Dance, on this week at the Barbican.

Minimalism is now a comfortable old sofa for today’s generations of dance-watchers, often handed very small platefuls of ideas, but this 60-minute piece has an understated poise and rich cleverness that shows American modern dance at the very top of its artistic game.

I wasn’t around to see when Karole Armitage won her spurs in her twenties as a punk ballet choreographer in America in the 1970s and early Eighties, so we must rely on her programme-sheet biography to explain to us that she is “seen by some critics as the true choreographic heir" to George Balanchine and Merce Cunningham. After last night’s dismal showing by her group, Armitage Gone! Dance, at the Southbank Centre, the only possible response is, “Pull the other one” and a firm slap across the hubris.

Has the great pop diva Beyoncé plagiarised the great modern dance diva Anne Teresa de Keersmaeker? This is the burning question that has today sent disco popsters and fans of austere contemporary dance in a feverish crush to YouTube, comparing Beyoncé’s new "Countdown" vid with De Keersmaeker’s art-house dance Rosas danst Rosas. They’re turning over micro-flashes of Beyoncé, running them back, comparing them with… well, you have plenty of choose from, as De Keersmaeker doesn’t believe in throwing away her ideas in 10 seconds.

“Jazz is my adventure,” said Thelonious Monk. “I’m after new chords, new ways of syncopating, new figures, new runs. How to use notes differently. That’s it. Just using notes differently.” Based on the title of the new hour-long piece by Israeli choreographer Emanuel Gat, Brilliant Corners, named for Monk’s 1957 album, the naïve viewer might expect, at the very least, to hear some Monk. Not so. Gat has produced an always interesting, sometimes absorbing sight-and-sound world, but of Monk, or jazz, there is neither sight nor sound.

It takes more than utmost craft and rich personality to hold the stage as a soloist - it takes a touch of divine self-belief, which Akram Khan has never displayed to more magnetic effect before than in his new solo DESH. Actually solo is too small a word for this epic, lavish display of the starpower that Khan now emits in the world of dance theatre.

Dance is eating itself. Or dancers are eating themselves, rather. It's on-trend to defy the idea of the mute dancer, and instead have them verbally explaining themselves, their motivation, their art. This year’s Dance Umbrella launched last night with the “self-contemplation” of Cédric Andrieux, a handsome blond Frenchman, who regales us in a charming murmur for 80 minutes with the story of his career, with danced illustrations.