Brad Mehldau, Barbican Hall

Brad Mehldau is a cool cat. An intellectual one, introverted to the point of semi-autism, precise and clear. A strong mystique based on critic-proof good taste and hardly talking to anyone, least of all many music journalists (I’ve tried). At least that’s what I used to think before last night’s extraordinary show. He still looks a bit of a nerd, hunched over his piano and pale as a baby polar bear locked in the attic for too long, but this was a warm, enveloping trip of a gig. The 21st century is the century the nerds took over - Gates, Zuckerberg, Mehldau. The jocks, the lookers, the sexy ones: your time is up - you really should have been concentrating in algebra, after all.

This gig (part of the London Jazz Festival) was the premiere performance of Mehldau’s madly eclectic and ambitious album Highway Rider, in which he attempts a path that many have stumbled on - a jazz-classical fusion. It may well be that the worst music ever made has been jazz attempts at fusion. It appeals to all the worst instincts of jazzers who want to be taken seriously as artists. They or their forebears have suffered for decades in smoky bars where people didn’t listen to every note, possibly because they were actually having fun. Those days of smoky bars and having fun are over. But Mehldau’s pretention turns out to be rather enjoyable anyway.

Highway Rider is that despised thing, a concept album. It’s a quest, a cyclical journey with an actual chamber orchestra on it - last night the Britten Sinfonia, conducted by Scott Yoo, in the first of six concerts across Europe. Mehldau has opened up and is having a bash at being a proper composer, and the risk more or less paid off. As my late colleague and friend Robert Sandall put it when we made it CD of the Month in March - one of Robert’s last pieces - “By the end, you're not quite sure what it is you've witnessed - a compelling jostle of contemporary classical, chamber jazz and ingenious post-rock pianissimo - but you know that it's an addictive mix that you're going to have to revisit again and again.”

Live, the passages with just the Sinfonia were all over the place. Normally that would be a criticism. A little bit of the chaos may be due to lack of rehearsal, but Mehldau’s wild eclecticism is evident - at various times you were listening to echoes of film music, Brahms, Berg, Nick Drake or The Beatles and all points in between. It also may be that Mehldau is still finding his voice as an orchestrator.

But Mehldau’s piano-playing - and he is a master of his instrument - brought it all together. That and his strong band, fronted by one the best saxists we have, Joshua Redman, whose lines were like a lead vocalist for much of the evening (several passages cry out to be sung, actually). Mehldau knows restraint, as we know, but often during the evening he was positively wigging out, tripping the light fantastic on his keyboard. We had waltzes, blues, meditative music, and at one point he seemed to be channelling the steamy piano of New Orleans jazz great Professor Longhair, even if it was Prof Longhair with a PhD in Higher Mathematics. Those fiendish time-signatures would send a dervish into orbit.

He is a wonderfully ambidextrous pianist - his left hand seems to be just as fluid as his right. “Into the City” started with a left-hand vamp, with various virtuoso flourishes - we were in a Post-Modern-film car chase. In others it was more Schubertian. A wonderful tune, “The Old West”, was a masterful duet between Mehldau and Redman, both alternating, semi-improvised, between lyricism and rapid-fire rhythm. Other pieces on the journey were pictures of highways with space and speed and mountains, with elements of cragginess and dizzying vertigo. There were surprising sweeps of Romanticism and even the odd flash of muscular near-funk.

The snatches of atonality were like a splash of cold water to stop this becoming too sentimental - although it turns out that Mehldau is a bit of softie, after all. The lack of perfection and perfect tonality were rather human. We are all flawed, and so was this. It reminded me of the Islamic carpet-makers who always include a deliberate mistake or two because to be perfect would be to ape Allah and thus be blasphemous. The human scale was emphasised by the small drums, the handclaps, the handmade nature of some of the percussion.

As a premiere it had the virtue of great freshness and the downside of problems to be worked out in sound balance. The last number “Always Departing, Always Returning” should have been a "Hey Jude"-like uplifting mantra, with its lift-off repetitive chords, but on this one the Sinfonia sounded a bit bolted-on. This will improve in further concerts. It was, anyway, a warmer, more vulnerable Mehldau we saw last night. And all the better for it.

• Find Highway Rider on Amazon
• London Jazz Festival information