One biographical curiosity has loomed large in discussion of the musician formerly known as Manitoba and now recording under the name Caribou: his mathematics PhD. While studying at Imperial College, London, Dan Snaith submitted a thesis titled Overconvergent Siegel Modular Symbols, a contribution to the field of complex analysis. He was, in effect, joining the family business: his father Victor is a professor of maths at Sheffield and his sister Nina is a reader in the same subject at Bristol, though Snaith himself grew up in Canada. This is exotic stuff in the world of electronic music, or at least the world of electronic music with an audience, so interviewers and reviewers can hardly be blamed for using it as a peg for their articles.
They might, for instance, suggest that the stylistic restlessness of his output has something to do with his analytical training or ask him how the satisfactions of manipulating notes and numbers compare. Then again, they might get carried away. The British website The Quietus wrote that Snaith's work was an "investigation into the mathematical structures of music", a statement which is either trivially true (all music has a mathematical structure, and all musicianship might be thought of as investigating it) or else very doubtful. Is the idea that Caribou records represent a sort of catalogue of possible sonic forms? Odd that Snaith should have lingered so long over the psych-rock end of things, in that case. From the casual listener's perspective, his output is about as credibly the product of a rational research programme as Hawkwind's.
Snaith, for his part, indulges his questioners. "I started enjoying math at the point where it became more abstract and much more imaginative," he told The Sunday Times recently, in a story headlined "Caribou cracks the equation". "Say you're trying to piece these two ideas together, and you're kind of fumbling around with these mental structures, and you only have a glimpse of what you're working with - and then you get a flash where everything makes sense. It's that same sense of searching for congruences that you get with music."
Up until fairly recently, this wasn't a sense that you got very strongly with Snaith's music. Back when he was Manitoba - before, that is, Handsome Dick Manitoba of the New York Punk band The Dictators threatened him with legal action and forced him to change his name - he specialised in a kind of soft-focus style that has steadily shifted from minimalism to maximalism. His 2001 debut album Start Breaking My Heart was a suite of gently bucolic electronica. But by the time of his 2003 breakthrough LP Up In Flames, Snaith's sound had become dense with foggy guitars, banks of percussion, squiggles of synth and flute and the sighing, backwards-reverbed vocals made popular by My Bloody Valentine. Up In Flames was a shaggy, shambling thing, looping contentedly through its clouds of noise, free of any trace of premeditation.
A couple of albums later Snaith was experimenting with a more deliberately classic approach to popular music. Andorra is billed as his tribute to the sharply arranged guitar pop of the 1960s: it is an LP of intros, verses, choruses, bridges - all the traditional virtues. Snaith, by now trading as Caribou, even managed a serviceable Brian Wilson impression. For long stretches it is only the teeming production, as thick with detail as the sample-collages of The Avalanches, that places it in its correct decade. The last couple of tracks, however, move into more ambiguous territory. Somewhere between Irene's wobbly synthesizer ostinatos and Niobe's stealthy pulse, the pull of the dancefloor is felt.
This is where Snaith's fourth and latest album, Swim, picks up, but before we get onto that, it's worth noting a couple of points. Firstly, even if the relatively sophisticated songwriting of Andorra bears comparison with the "fumbling around with mental structures" that Snaith associates with maths, it clearly isn't the kind of thing you need a maths PhD to do. After all, Snaith learnt it from 1960s bands like the Zombies, and none of the Zombies have one. QED.
Secondly, and more importantly, it doesn't seem to have much to do with his previous work either. And if you leave aside its anomalous last couple of tracks, Andorra doesn't sound like it has much to do with the record that followed it. In his unassuming way, Snaith is shaping up to be something of a chameleon - not a master of reinvention in the theatrical manner of Bowie and Madonna, but a man who seems content to move from task to task without getting too caught up in any of them. He learns how to make glitchy electronica and fuzzy psychedelic rock on his laptop, then he learns some classic songwriting moves, at some point he figures out what he thinks about Overconvergent Siegel Modular Symbols, and then he goes dancing.
Thus Swim. The album opens with Odessa, a disco-funk track that sounds like it was recorded in a refrigerated hangar. The bassline slops about like a waterbed, cowbells echo and Snaith's vocals imitate the late avant-garde cellist and alt-disco pioneer Arthur Russell at his most glumly ethereal, which if nothing else demonstrates good taste. Snaith has put it about that the record was inspired by the swimming lessons his wife bought him recently. He told the music website Pitchfork: "Everybody's familiar with how the sonic sense is different underwater and above water, and so you're in this weird kind of sonic space that rocks back and forth. And I thought, that's an interesting idea to do that with some sounds on the record."
Yet it's not so much the faintly aqueous effects as the empty space that distinguishes this track from Caribou's past output, and as the album progresses it becomes clear that Swim is, well, awash with it. Sun opens with a sampled vocal singing the word "sun" five times a bar, rising and falling in the mix as a jazzy house beat comes in and organs borrowed from Joy Orbison swell to a crescendo that doesn't quite come. That's it, barring a few broken synth chords and a bit of filter modulation. It is one of Snaith's most restrained performances, and if the rest of the album doesn't quite live up to its spartan example, its point is still well made.
Along with the economy of means displayed on Swim, Snaith reveals an unexpectedly sinuous rhythmic sense. Found Out revisits Russell's sighs and cello tones, but skips along on bitcrushed high-hats and out-of-sync Afropop guitars. Bowls samples the sound of two Tibetan singing bowls knocking together, fills the room with a cascading harp and then settles into a brooding techno riff that throbs along for several enjoyable minutes.
One could guess that Snaith has been spending time with his friend and mentor Kieran Hebden, better known as Four Tet. Hebden persuaded Snaith to start making music in the first place and Four Tet's recent album, There Is Love In You, is full of soulish vocal samples, grainy synths and hypnotic drum loops, achieving a similar tone of sultry abandon to Swim. Alas, Four Tet's love of protracted grooves too often succumbs to tedium; something that Snaith's maximalist streak seems not to permit. Instead, the ravey chords of Kaili give way to squalls of brass and saxophone; Leave House, a menacing disco cut for most of its duration, includes a woodwind interlude that could have been lifted from late-1990s Mercury Rev.
Swim's closing masterstroke marries all of Snaith's accomplishments - the spareness, the poise, and the willingness to sacrifice both in the interest of fun. The closing Jamelia features an attractive, Vampire Weekend-style vocal from Luke LaLonde of the Born Ruffians, jazzy arpeggios from the left-hand side of an electric piano, a ticking drum track and, to use a phrase from the recurrently influential Russell (who, incidentally, recorded a song titled Let's Go Swimming), a world of echo. Bursts of orchestral noise float in and out, then the track lifts off in a whirl of luminous keyboards. It is Caribou's most striking moment yet. I don't think there's any science to it, though. Snaith is just a guy with a very low tolerance for boredom.
Ed Lake is The National's arts critic.