Josiah Alexander Sila was born in Denpasar, on the Indonesian island of Bali, on June 25, 2003. His parents, Denny Sila and Farah Leonora Urbach, ran an adventure tourism business and were both jazz listeners, and the records in the house were the boy's entire curriculum. At six he was given a small electric keyboard and worked out Thelonious Monk's "Well, You Needn't" by ear from his father's collection. He never had a formal jazz teacher. Because Bali offered no jazz education, the family gave up the tourism business and moved to Jakarta so that he could sit in with the country's working players, and by eight he was a regular at jam sessions in both cities. That year Herbie Hancock came to Jakarta as a UNESCO goodwill ambassador and Alexander played for him. Hancock told the boy that he believed in him, and Alexander has described the encounter as the day he decided to give his childhood to jazz. In 2013 he took the Grand Prix at the Master-Jam Fest, an all-ages improvisation competition in Odesa, Ukraine.

A friend showed Wynton Marsalis a video clip of the child playing Monk, John Coltrane and Chick Corea, and Marsalis invited him to the Jazz at Lincoln Center gala in May 2014. He was ten, it was his American debut, and his unaccompanied "'Round Midnight" made him famous overnight. Allen Morrison wrote in DownBeat that if the word genius still meant anything it applied to this prodigy. The family relocated to New York later that year. Jeanne Moutoussamy-Ashe put him on the bill of the Arthur Ashe Learning Center gala, where he played for Bill Clinton, and a benefit concert with students from Juilliard drew enough national attention to secure him an O-1B visa, the category reserved for individuals of extraordinary ability. He also appeared that year at the Copenhagen Jazz Festival and at the Java Jazz Festival in Jakarta.

His debut album, My Favorite Things, was recorded at Avatar Studios in New York over three days in October 2014 and released by the Harlem label Motéma on May 12, 2015, when he was eleven. He arranged all of it. Larry Grenadier and Ulysses Owens Jr. play the first half of the record, Russell Hall and Sammy Miller the second, and Alphonso Horne adds a trumpet to "Tour de Force"; the one original is "Ma Blues", written under the spell of Bobby Timmons's "Moanin'". It reached number 59 on the Billboard 200 and topped the jazz chart. In December 2015 it brought him two Grammy nominations, Best Jazz Instrumental Album for the record and Best Improvised Jazz Solo for "Giant Steps", and he played at the pre-telecast ceremony of the 58th Grammy Awards in February 2016, at twelve, to a standing ovation. He was the first Indonesian musician nominated for a Grammy. That summer he worked the main festival circuit for the first time, at Montreal and at Newport, where the producer George Wein had broken his own rule about child prodigies after hearing him play in a Manhattan apartment.

Countdown followed on Motéma in September 2016, cut at Avatar in January with Dan Chmielinski and Grenadier splitting the bass chair, Owens on drums and Chris Potter guesting on soprano saxophone; its title track, Coltrane's, earned a third Grammy nomination the following year. In June 2017 he recorded seven Monk pieces live in the Appel Room at Jazz at Lincoln Center with Scott Colley and Willie Jones III, issued as Joey.Monk.Live! for the Monk centenary. That same year he turned up as the guest soloist on "Very Early" on the Jazz at Lincoln Center Orchestra's Handful of Keys, a survey of the piano in the big band recorded across three nights in 2016, sharing the feature with the tenor saxophonist Walter Blanding. Eclipse, taped at Dreamland in Hurley, New York in August 2017 with Reuben Rogers and Eric Harland and released in May 2018, was his first record built around his own writing, with Joshua Redman on three tracks. He played the opening ceremony of the Asian Games in Jakarta that August, and appeared on the singer and songwriter Lori Henriques's Legion of Peace, a Motéma song cycle about Nobel laureates on which he shares tracks with Pedrito Martinez and the clarinettist Oran Etkin.

Verve signed him in 2019, and Warna, the Indonesian word for colour, arrived on January 31, 2020. It was his first album of almost entirely original music, with Grenadier and the drummer Kendrick Scott as the working trio and guest turns from the flautist Anne Drummond and the Venezuelan percussionist Luisito Quintero. Three singles followed in 2021, and one of them, "SALT", put him on Fender Rhodes on record for the first time. He moved again in 2022, to Mack Avenue, where Origin became the first album made entirely of his own compositions. Recorded with the Warna rhythm section and released on May 20, 2022, it added two guests, Potter on both saxophones and the guitarist Gilad Hekselman, who plays on "Winter Blues", "Summer Rising" and "Rise Up". Continuance, made in two days at The Bunker in Brooklyn in March 2023 with Kris Funn and John Davis and the trumpeter Theo Croker on four of the seven pieces, found him adding Rhodes and Mellotron to the acoustic piano and producing the session with his father.

Through the middle of the decade he toured with a trio of Funn and the drummer Jonathan Barber and moved back to Bali, and that return shaped his eighth album. Celestial Keeper was issued by Mack Avenue on July 17, 2026, reuniting him with Jason Olaine, who had produced his first four records. It opens and closes on solo improvisations, sets the alto saxophonist Jaleel Shaw against the trio on three pieces, and brings in two singers, Alita Moses and Lisa Fischer, the latter on a reading of "My Funny Valentine" in odd metre. Asia Society had named him among its 2016 Asia Game Changers, where he also performed, and in 2018 the Anugerah Musik Indonesia gave him its award for best jazz instrumental artist.

Alexander learned the music the way a pre-war musician would have, off records and off bandstands, and what that produced is a player whose sense of time and harmony arrived intact and unusually early rather than one who sounds studious. Marsalis, asked about the ten-year-old, said there had never been anyone who could play like that at his age and singled out the rhythm and the confidence; George Wein, who had spent fifty years declining to book children, said what distinguished him was the maturity of his harmonic approach. The listening behind it is specific and largely pianistic: Bill Evans, Hancock, Monk and Duke Ellington first, then Brad Mehldau and McCoy Tyner, with a stated affinity for trumpet players, Clifford Brown, Lee Morgan, Miles Davis and Marsalis, that shows in how he shapes a line. Coltrane is the fixed point, supplying the two tunes on which his Grammy nominations turned. The interesting part of his career is what happened after the prodigy story stopped being the story. From Eclipse onward the standards receded and the writing took over, until Origin carried nothing but his own pieces, several of them in asymmetrical metres, and by Continuance he had put the Fender Rhodes and a Mellotron next to the acoustic piano. His own account of the later music turns on restraint rather than fluency: he talks about leaving space between the notes and about the pull of the sacred, and a hymn or a spiritual has closed or nearly closed each of his last three albums.