Daniel Barenboim and Martha Argerich first met as children growing up in Buenos Aires. And it was like children that they sweetly left the platform hand in hand after their joint performance at the Proms last week: two living-legend pianists side by side in one of the hot-ticket concerts of the season.

That Argerich was there at all was a relief: among her legendary attributes is cancellation. And her scheduled repertoire was Liszt’s Concerto No 1, with Barenboim conducting his own West-Eastern Divan Orchestra formed from young musicians on both sides of the Israeli/Arab conflict in the Middle East.

Predictably, it was sensational: a vacuous score (or so I’d argue) given substance by an advocate of genius. At 75, her hair now slate-grey, Argerich has turned into a Ninja granny. The dynamic energy she still delivers in performance is electrifying. And like Barenboim, she brings the mystery of unforced “presence” to the stage, her music-making truthful, powerful, authentic.

When the Liszt was over, there was bound to be an encore – and it was no great surprise when Barenboim joined her at the keyboard, to perform one of the longest encores ever witnessed in a Prom: a Schubert Rondo for four hands that seemed to go on for eternity (though if it had, would anyone have minded?). The ensemble-playing wasn’t overly exact but there was magic in its casual spontaneity. It felt like overhearing thoughtless conversation between two extraordinary minds.

More broadly, though, the concert was an odd piece of programming, with the entire second half given over to an orchestral medley of Wagner’s Greatest Hits. A lack of luminous depth in the playing signalled the fact that this West-East ensemble is in truth an overgrown youth orchestra that’s been lucky enough to receive privileged mentoring from a great musician. But it’s a seriously good youth orchestra.

Just as classy in its way was the Proms at the Roundhouse, Camden, that other iconic circular venue. Proms were often relocated here during the 1970s under Pierre Boulez. Now, after a too-long interval, they’re back. And it’s an atmospheric space for them, suited to edgy projects that require surround-sound, as a number of the pieces did here.

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