Originally Posted by Wikipedia

Math rock is a rhythmically complex, often guitar-based, style of experimental rock[1] that emerged in the late 1990s, influenced by progressive rock bands like King Crimson, as well as 20th century minimalist composers such as Steve Reich. It is characterized by complex, atypical rhythmic structures (including irregular stopping and starting), counterpoint, odd time signatures, angular melodies, and extended, often dissonant, chords.

Originally Posted by RYM

Math Rock is a genre that developed in the late 1980s to early 1990s via the influence of bands such as Slint, Drive Like Jehu and Shellac who added to the already established sounds of Noise Rock and Post-Hardcore a sense of rhythmic variety and complexity that was claimed by many critics to sound almost mathematical, eventually being coined "Math Rock". It became a large influence on some underground movements in the US and became a common instrumental style of certain genres including many bands of the Midwestern Indie Emo and Indie Rock scene.

By the dawn of the 21st century the sound of Math Rock was even more riff focused. Emphasised by polyrhythmic and winding yet consonant guitar riffs with the bass often used as a counter melody, vocals were usually used as a secondary instrument to the guitar or not at all. The genre took further influences from Jazz-Rock and Post-Rock often sounding both accessible and experimental with the dissonance of earlier Math Rock groups being far less dominant. Modern Math Rock groups include Don Caballero, 65daysofstatic and Tera Melos. Some modern groups have also acquired mainstream success whilst using Math Rock influences. These bands include Battles, Minus the Bear and Foals that further show Math Rock's gradual divergence from the underground.