The Algorithm is Rémi Gallego, an electronic music composer from Toulouse, Midi-Pyrénées, France. Born October 7, 1989, he began releasing music under this name in 2009 following the dissolution of his former band Dying Breath. It's a fusion of several styles of electronic music with progressive metal, mathcore, and djent. For live performances, he uses an Akai APC40, a MIDI controller produced by the company Akai, co-developed with the German company Ableton, connected to a laptop running Ableton Live. He initially sought to form a mathcore band, taking inspiration from The Dillinger Escape Plan, but after a futile search for band members, with the help of his guitar and a digital audio workstation, he began producing his own music.

The debut Algorithm releases were the demos The Doppler Effect and CRITICAL.ERROR, released for free via his own website in December 2009 and July 2010 respectively. In October 2011 he appeared at the Euroblast Festival in Cologne alongside bands such as Textures, TesseracT, and Vildhjarta. A month later Mike Malyan, the drummer of Monuments, uploaded a drum cover of "Isometry" to YouTube. After seeing this, Gallego was convinced that it would be possible to play his songs on a real drum kit and Malyan became his live drummer. Gallego stated, "Before he put his Isometry drum cover online, one year ago, I had no idea that someone could ever play my drum programmings with such dedication, musicality and tightness. He was really thrilled to play live with me and so we decided to make it happen. I can’t be more happy to work with such a great friend/musician." In the same month, The Algorithm signed to British label Basick Records.

In January 2012, The Algorithm released the digital single "Tr0jans." It was followed by appearances in festivals such as Djentival in Karlsruhe, Germany, as well as the UK Tech-Metal Fest held in Alton. On November 19, 2012, the debut album Polymorphic Code was released.

On June 17, 2013 The Algorithm received a Metal Hammer Golden God award as best underground artist, decided by Metal Hammer readers' votes.

The Algorithm released its second album, OCTOPUS4, on June 2, 2014. The track "_MOS" is the first ever collaboration between Mike Malyan and Rémi Gallego on an album and is, according to Gallego, "the result of a mutual love for old-school C64 sounds."