The Best Math Rock Albums of the 2000s

Four men, one mirrored Brooklyn room, and John Stanier playing beneath a crash cymbal mounted so absurdly high that he has to reach up for it — you can watch him do it in the video. 'Atlas' turned into an actual hit, a stomping thing with Tyondai Braxton's voice pitched up into cartoon territory, and it dragged the genre briefly into daylight.

Damon Che drums as though arguing with the rest of the band, and this is where Ian Williams' two-handed tapping stopped being a party trick and became the actual songwriting. Steve Albini recorded it, and the group came apart soon after a van accident on tour. 'Fire Back About Your New Baby's Sex' opens and sets the terms immediately.

Two people from Sacramento: Zach Hill hitting drums faster than seems structurally advisable, Spencer Seim answering on guitar with no bass player anywhere in the building. 'Biblical Violence' is ninety-odd seconds that sound like a machine disassembling itself at speed. There is no low end on the entire record and you stop noticing about four minutes in.

A Providence duo who set up on the floor rather than the stage so the crowd has to form around them, with Brian Chippendale singing through a telephone receiver taped inside a mask. 'Dracula Mountain' is the one everybody plays first: bass distorted past recognition, drums at a tempo nobody should be able to hold. Load Records, no compromise anywhere.

Tokyo, four players, and a drummer in Takashi Kashikura who treats jazz brushes as a perfectly legitimate math rock instrument, which alone sets them apart from everything American here. 'tremolo+delay' is precisely what its title promises and somehow also lovely. The band kept day jobs for years, which explains the unhurried feel of everything they make.

Their first with Greg Puciato singing after Dimitri Minakakis left, and their first since an EP with Mike Patton convinced them melody was not a betrayal. 'Panasonic Youth' opens with thirty seconds of undiluted hostility before the record starts doing far stranger things. Ben Weinman writes riffs counted in numbers I long ago stopped trying to follow.

The four members of Cap'n Jazz back in a room together, Albini at the desk, five years after that band imploded — and what they made sounds almost nothing like it. 'Everyone Is My Friend' has Tim Kinsella talking more than singing over guitar lines that keep sidestepping. Spotify shouts the artist name in capitals; the album cover just says Owls.

Seattle, ex-Botch guitarist Dave Knudson, and a song-titling policy seemingly designed to stop anyone taking them seriously: 'Thanks For The Killer Game Of Crisco Twister' is track one and not even the silliest. Underneath the jokes sit finger-tapped guitar figures, programmed-sounding drums and real hooks. The band who made this stuff danceable, for better and worse.

Here is a filing problem worth flagging: the Sacramento trio's debut sits on streaming as 'Untitled', dated 2010 for the Sargent House reissue, when the record itself came out in 2005. Eight instrumentals, numbered rather than named. 'Melody 4' is where the seasick tuning and the stop-start editing stop feeling like exercises and start feeling composed.

Three lads from Wexford, one of whom performed in a full-head mask, with an album title that tells you the tone before a note has played. 'Snakehips' closes proceedings in a blaze of major-key guitar with more in common with video game music than with anything gloomy. Eight tracks and gone before you have properly settled.

Belfast, four members, and a decision to make instrumental music that behaves like a punk band rather than a landscape painter. 'Set Guitars to Kill' opens their debut with a riff that apologises for nothing. Note the credit oddity while you are here: the artist name uses a small f in 'from', the album title capitalises it, and nobody has ever explained why.

Every song named after an animal, guitar tunings nobody else was using, and a rhythm section holding parts together while they change shape underneath. 'Baboon' did the rounds on early YouTube guitar-cover channels and effectively taught a generation how to tap. Credited as TTNG on streaming now; back then they were still called This Town Needs Guns.

Chicago art students, tapping with both hands, and Dave Davison singing in a warble that people either love on contact or never get past. 'Everyplace Is a House' opens seven tracks that streaming calls an album and everyone else calls a mini-LP. Note the title too: singular tree, and dated 2007 here rather than the 2008 you will often see printed.

Dischord, Washington DC, Ian MacKaye at the desk, and four kids who had absorbed Fugazi and decided to make it jerkier. 'Line In The Sand' opens with a guitar figure that refuses to resolve for the length of the song. They lost the bass player after this and went stranger; this is still the one worth keeping.

A Tokyo trio built around two pianos and a drum kit, which ought not to work as math rock and absolutely does. 'spectres de mouse' hammers a repeating figure into something closer to Steve Reich than to any guitar band on this list. The members came out of the hardcore scene and you can hear it in how hard the keys get hit.

Before the stadium choruses arrived, Oxford's Foals made a record of interlocking clipped guitar lines owing far more to Battles than to any indie contemporary. 'Cassius' came back from Dave Sitek's New York mix sounding, by the band's own account, like it had been recorded in the Grand Canyon, so they remixed the album themselves. The UK running order is the one to hear.