Aaron Goldberg was born in Boston on April 30, 1974, the son of two scientists: his father Alfred L. Goldberg was a biochemist, his mother Joan Helpern Goldberg a hematologist. He started piano lessons at seven and came to jazz at fourteen, at Milton Academy, through the school's jazz program and its bassist-teacher Bob Sinicrope. Sinicrope's account of their first meeting has become the standard opening of every Goldberg profile: asked to play a C chord, the new student played a piece of Rachmaninoff in C instead. At sixteen he began formal study with saxophonist Jerry Bergonzi. He won the National Foundation for Advancement in the Arts Recognition and Talent Search and the International Association of Jazz Educators' Clifford Brown/Stan Getz Fellowship, and at seventeen he moved to New York for the New School for Jazz and Contemporary Music. The class he landed in there, in 1991, is the reason half of his discography looks the way it does: his fellow students included bassist Omer Avital, drummer Ali Jackson, trumpeter Avishai Cohen and pianist Brad Mehldau.

He did not stay a conservatory student. He transferred to Harvard College and graduated magna cum laude in 1996 in History and Science, with a concentration in Mind, Brain and Behavior, writing a thesis on scientific theories of consciousness under the philosopher Robert Nozick. While he was still an undergraduate, Betty Carter picked him as a founding member of her Jazz Ahead workshop. His earliest documented recording predates all of it: Guillermo Klein's large ensemble Big Van, taped live to two-track at Master Sound in Astoria on December 17, 1994, with Klein conducting and Mark Turner and Chris Cheek in the saxophone section.

After Harvard he settled in New York and worked as a sideman for Al Foster, Freddie Hubbard, Nicholas Payton and Stefon Harris, among others. In late 1997 he formed the trio that carried him for the next two decades, with bassist Reuben Rogers and drummer Eric Harland. From 1998 he held the piano chair in the Joshua Redman Quartet alongside Rogers and drummer Gregory Hutchinson, a band that recorded Beyond (cut at Avatar Studios in May 1999, issued by Warner Bros. in 2000) and Passage Of Time (2001), and that reconvened eighteen years later for Come What May on Nonesuch, released March 29, 2019. His own debut, Turning Point, came out on the small New York label J-Curve in 1999: the Rogers and Harland trio, with Redman and Mark Turner both guesting on tenor, Carla Cook singing on one track and Karsh Kale adding tabla. Unfolding, the straight trio record, followed on the same label in 2001.

The other band of those years was the OAM Trio, the initials of Omer Avital, Aaron Goldberg and the Catalan drummer Marc Miralta. It made four records across a decade: Trilingual (Fresh Sound New Talent, recorded in Paramus, New Jersey in 1999), Live In Sevilla with Mark Turner (taped at the Teatro Central in Seville on November 17, 2001, released by Lola Records in 2003), Flow (recorded in Hoboken in 2000 but held until November 2004) and Now & Here, again with Turner, for the Spanish label Nuba in 2009. Goldberg's association with the Israeli musicians around the Greenwich Village club Smalls ran through the same period. He is the pianist on Avital's quintet date The Ancient Art Of Giving, recorded live at Fat Cat in New York on January 14, 2006 and issued by Smalls Records later that year, with Mark Turner on tenor, Avishai Cohen on trumpet and Ali Jackson on drums. He also played on both of the 3 Cohens records that put Anat Cohen, Yuval Cohen and their brother in a front line together, Braid (recorded in Brooklyn in September 2006, with Avital on bass) and Family (2011), and on two early albums by saxophonist Eli Degibri, for whose 2003 debut he also wrote part of the liner notes.

From 2004 to 2008 he worked in Kurt Rosenwinkel's group, documented on The Remedy, recorded at the Village Vanguard in January 2006 with Turner, Joe Martin and Harland. In 2005 he toured with Wynton Marsalis's quintet and the Lincoln Center Jazz Orchestra; he had already recorded with Marsalis two years earlier, on the Ali Jackson Quartet's Big Brown Getdown, taped live at Fat Cat on August 29 and 30, 2003. His first Sunnyside album, Worlds, arrived on May 9, 2006, and gave him the widest audience he has had by an accident of software licensing: its track "OAM's Blues" was one of the sample recordings bundled with Windows Vista. In the same stretch he and saxophonist John Ellis built the Baby Loves Jazz Band, a children's-record project that ran to nine volumes for Penguin's Price Stern Sloan imprint between 2006 and 2007, with Goldberg producing.

He then did something few working pianists attempt in mid-career: he went back to school. He took the GRE at thirty-one, around the time the Marsalis work began, and enrolled at Tufts University to study analytic philosophy with Daniel Dennett. It was meant to take two years and took five, finishing with an M.A. in 2010. His first semester overlapped with the Rosenwinkel and Marsalis bands at once, which he has described as unsustainable. The records kept coming through it: Home (April 13, 2010), the Rogers and Harland trio with Mark Turner added on tenor; Bienestan, a two-piano collaboration with Guillermo Klein cut at Systems Two in Brooklyn on May 13 and 14, 2009 and mixed more than a year later; and Yes!, recorded at the same studio on December 29, 2009 with Avital on bass and Ali Jackson on drums, released January 17, 2012. Its title track is an Avital composition that closes The Ancient Art Of Giving, which the same three men had recorded together three years earlier. The Now (2014) brought the original trio back with Rosenwinkel guesting on one track.

At The Edge Of The World, recorded on September 16 and 21, 2016 and released in 2018, introduced a new trio: bassist Matt Penman, whom Goldberg had known since Penman arrived from New Zealand in 1994, and drummer Leon Parker, back from years of near-invisibility in France. Parker plays a stripped kit and a self-devised body-percussion system he calls EmbodiRhythm, and on "Poinciana" keeps time under Goldberg's solo without touching the drums at all. The record is deliberately quieter and less dense than its predecessors: Goldberg has said he wanted to get away from "overly informational playing, where there's too much to listen to." Since then the Yes! Trio has become his main recording outlet. Groove Du Jour, cut in Meudon outside Paris on October 29 and 30, 2018 and released by the French label Jazz&People on October 11, 2019, won the Grand Prix de l'Académie du Jazz for album of the year. Spring Sings, recorded April 21 and 22, 2022 and issued February 26, 2024, is the trio's third. Alongside the playing he teaches at the New School and at William Paterson University, produced fundraising concerts for the Kerry, Obama, Clinton and Biden presidential campaigns between 2004 and 2020, and received an honorary doctorate in music from the University of the Arts Helsinki in 2019. He is a Steinway Artist and keeps a Mason and Hamlin baby grand at home.

Goldberg is a swinging, harmonically dense post-bop pianist whose default setting is the piano trio and whose repertoire choices are unusually catholic: Abdullah Ibrahim, Thelonious Monk, Duke Ellington, McCoy Tyner, Bobby Hutcherson, Brazilian and Argentine songs, and a steady supply of his own tunes. He speaks Spanish, French, Italian and Portuguese, learned the same way he says he learned jazz, by ear, and the Latin American strand in his playing is a consequence rather than a decoration: his closest musical partner outside his own trios has been the Argentine pianist and composer Guillermo Klein. He is explicit about the risk of derivative playing and about the discipline that keeps him clear of it, arguing that the useful discoveries come on the bandstand rather than in the practice room and that the standard they have to clear is set by Bud Powell, Charlie Parker and Mulgrew Miller. Asked whether a philosophy degree makes his music analytical, he has pushed back hard: clarity of ideas and logical development are things he aspires to at the piano, but jazz is physical and emotional in a way that analytic philosophy deliberately is not. The New York Times has called him a post-bop pianist of exemplary taste and range, and JazzTimes one of the most scintillating performers in jazz.