As no-wave veered off from punk-rock, taking its revolutionary tendencies into atonal, arrhythmic, so, too, did math-rock veer off from hardcore, taking hardcore's essential elements —speed, precision, volume— and using them in new ways. But, where no-wave prized a complete lack of musical training, math-rockers were monsters of technical proficiency. The movement, which flourished in the early-'90s, featured jagged edges: angular guitar, stop-start rhythms, songs built from shards of sound. Here are ten albums that helped define the genre's complex calculus.

01 of 10 Bastro 'Diablo Guapo' (1989) Homestead Come the '90s, David Grubbs and John McEntire would explore the farthest reaches of contemplative, chin-scratchin' sound in Gastr del Sol and Tortoise, respectively. But, in the '80s, the pair were still bound to their punk roots. Bastro was formed in the wake of Squirrel Bait, the teenage hardcore outfit in which Grubbs and bassist Clark Johnson (and the future members of Slint) cut their teeth. Teaming up with Johnny Mac, the three set about creating a delirious, dizzying form of noisy, speedy, busy post-hardcore built on frenetic tempos, chaotic meters, and ridiculous, stop-on-a-dime precision. In 1989, when the trio released their debut LP, no one thought to call it math-rock. But Diablo Guapo is the first true example of the genre.

02 of 10 Breadwinner 'Burner' (1994) Merge By the time Merge assembled this singles compilation by Virginia's Breadwinner, the band had broken up. But they'd already cemented a reputation as a seminal, definitive example of math-rock. The Richmond, Virginia instrumentalists wielded their standard power-trio instruments —guitar, bass, drums— like weapons; sometimes with parrying, rapier precision; other times as blunt and bludgeoning. Their multi-metered music is alive with crazy complexity. At times, Breadwinner sound like a band in perfect concert; moving together like pieces of interlocking machinery. Other times, they sound like three dudes attempting to play three different songs simultaneously.

03 of 10 Shellac 'At Action Park' (1994) Touch and Go Notoriously cranky audio engineer Steve Albini is, in effect, the patron saint of math-rock. Essentially for his role as a producer; rolling (analog!) tape on countless combos operating somewhere within the genre. Musically, his first two bands —Big Black and Rapeman— were spiritual influences on the genre, but not actually math-rock bands at all. After all, Big Black's Roland drum-machine wasn't exactly rolling out polyrhythms in 11/8. Shellac was the first Albini outfit who made math-rock music: all acute angularity, stop-start precision, and wound-up tension. Their debut LP, At Action Park, arrived when Albini was at his most in/famous —fresh off recording Nirvana's In Utero, and delivered a band fully-formed: noisy, ornery and pissed off.

04 of 10 U.S. Maple 'Long Hair in Three Stages' (1995) Skin Graft Hugely influenced by Captain Beefheart —and his 'exploding note theory'— Chicago's U.S. Maple played an exploded form of rock'n'roll in which ​guitars fell and tumbled over each other in collapsing measures, whilst super-loud bass and urgent, insistent drums played a more traditionally 'rocking' sound; albeit in short, spastic, clanging bursts. Their debut album, the Jim O'Rourke-produced Long Hair in Three Stages, arrived right when math-rock was starting to develop its identity. The LP was generally received as a noisy, chaotic mess, but listening to songs like "Magic Job" —whose guitars sound like a swarm of hornets— reveals a band that, in their Beefheartian way, were so well-drilled every seeming accident was precisely timed.

05 of 10 Don Caballero 'Don Caballero 2' (1995) Touch and Go Don Caballero are the ne plus ultra of math-rock; the definitive, the exemplar, the beginning and end, the nerdiest of the nerdy, the undefeatable. Don Cab, as the kids called 'em, boasted Ian Williams, tapping out crazy guitar patterns like some human player-piano, and Damon Che, a percussionist powerhouse whose everywhere-at-once playing suggested, to play-at-home listeners, that he perhaps had extra arms. But Don Cab wasn't just dudes who could play: their four 'classic lineup' LPs, issued between 1993 to 2000, were works of punk-rock purity and ambient uneasiness. For all its hyperactive instrumentalist workouts, Don Caballero 2 is as much a mood piece as anything; long stretches devoted to noise, drone, discordance, and strangeness.

06 of 10 A Minor Forest 'Flemish Altruism (Constituent Parts 1993–1996)' (1996) Thrill Jockey For math-rock nerds (which math-rock fans are by definition), the debut LP for San Francisco's A Minor Forest played a hilarious game with Shellac's twin audio-engineers: half was recorded with Steve Albini, half with Bob Weston, with the track-list ping-ponging each song between the two. There was just as much volleying compare/contrast in A Minor Forest's music, which used differences in tone —between dissonant and clean guitars— and volume as well as math-rock tricks of changing keys and shifting time-signatures. The centerpiece of Flemish Altruism (Constituent Parts 1993–1996) is the epic "So Jesus Was at the Last Supper...," the outfit's chops on never-ending display across a 14-minute masterwork that reinvents itself dozens of times.

07 of 10 Storm and Stress 'Under Thunder and Fluorescent Light' (2000) Touch and Go After years of hyper-precision in Don Caballero, six-string virtuoso Ian Williams cut loose (truly) in the much-more-messy Storm and Stress. Their '97 debut was a free-jazz-ish wreck of smashing the glass, guitar, spasmodic bass, absurdist lyricism, and erratic percussion. But, where that first S&S LP made a dynamic, almost violent spectacle out of cacophonous arrhythmia, 2000's Under Thunder & Fluorescent Light found the band was doing something more unexpected: using rhythmic discordance as a study in isolation. As melancholy guitar flutters, doleful vocals, eerie keyboards, and Tourettic drum tics float by like ships passing in the night, there's an exquisite loneliness in the way these individual parts never quite come together.

08 of 10 Hella 'Hold Your Horse Is' (2002) 5 Rue Christine If you're just listening at home, it's hard to believe that Hold Your Horse Is is the work of just two dudes. There are literally notes flying everywhere: a million dots, dashes, and slashes of guitar sound tapped out. It sounds like drums falling down stairs forever. This ridiculous noise was the work of Sacramento pair Spencer Seim (on guitar) and Zach Hill (on drums). After math-rock had started to lag as a movement, their Hella debut —issued on Kill Rock Stars sister imprint 5 Rue Christine— provided a fresh shot in the arm for fans of ridiculous rhythmic complexity and stop-start instrumental mayhem.

09 of 10 Lite 'Filmlets' (2006) Transduction There have been scores experimental Japanese bands whose music has aligned with the math-rock movement. But Lite openly identify with the genre; they're students of sonic soundscapes steeped in a million math-rock and post-rock records. Though they favor the quiet-to-loud swells and 'atmospheric' intent of post-rock, the Tokyo quartet plays so clean, precise, and nerdy that math-rock devotees adore them. Over a rhythm-section that never drops a non-4/4 note, guitarist Nobuyuki Takeda and Kozo Kusumoto weave interlocking patterns that create chiming harmonies and giddy polyrhythms. The effect is, in contrast to many bands here, more pleasing than provocative.