"Madness" is an electronic rock,synthpop,soft rock, and R&B song. According to NME, "Madness" draws influences from Queen's "I Want to Break Free", George Michael's "Faith" and some instrumental elements of his other hit "I Want Your Sex". During a preview of The 2nd Law on French site Jeuxactu, the song was said to resemble Depeche Mode and described as "calm, languid and sweet".Matthew Bellamy stated that the song started as a personal reflection after a fight with his girlfriend Kate Hudson, and how, after she had gone to her mother's house, he began to realise "yeah, she was right, wasn't she?" In a separate interview, Bellamy stated the song was the band's attempt to strip down the sound of the album, and that the song has its roots in 12 bar blues with gospel, soul and R&B influences. He went on to conclude that, "It's the song I'm probably most proud of on the album for sure."
The song was released as a digital download on 20 August 2012, with an accompanying lyric video for the song being uploaded shortly after.NME described the song as "taking the defining noise of 'bass music' and using it to create slinky, soft rock sex music." The track review goes on to call it a brilliant single and jokingly states that Muse have tamed the shark (following their declaration that Muse had jumped the shark with "Survival"). Diffuser.fm noted that the single "doesn't sound like the Muse that established itself as one of the worlds biggest rock bands" but that "the unusual blend of sounds works far better than it probably should"; giving the track 8/10.Rolling Stone stated that the single sees Muse "swap bombastic bass brutality with wubby subtleties as Matthew Bellamy croons over a surprisingly gentle pop track."Radio Times described it as "George Michael's "Faith" underwater". In a negative review of the song, Robert Myers of The Village Voice wrote that "the band's U2 imitation has finally caught up to Achtung Baby and Zooropa". He further added that Muse "gets the surface details right but lacks the emotional and intellectual foundation to get at their inspiration's essence."Rolling Stone named the song the 37th best song of 2012.Chris Martin of Coldplay described the single as "Muse's best song yet".
"Madness" had a positive commercial performance, charting in several countries and peaking within the top ten in Belgium (Wallonia), Iceland, Israel, Italy, Japan, Portugal, and South Korea. In the band's home country of the United Kingdom, the song peaked at number 25 on the UK Singles Chart. In the United States, the song peaked at number 45 on the Hot 100 and number 3 on the Hot Rock Songs chart. It topped the Alternative Songs chart for 19 weeks, breaking the record for the longest-reigning number-one song on the chart, which was previously held by "The Pretender" by Foo Fighters. That record later got overtaken by Portugal. The Man's "Feel It Still in 2017 which spent 20 weeks at the number 1 spot. "Madness" has been certified gold by the IFPI in Switzerland, platinum by the MC in Canada and FIMI in Italy, and double-platinum by the RIAA in the United States.