Armstrong was born on February 18, 1974, in New Canaan, Connecticut, and has continued to perform often in cities along the Connecticut coast. He began piano lessons at age seven, at first only because he was jealous of his older sister, Jane, who had been offered them. He took to the instrument, and his father, a pianist, noticed how he began to carefully shape the music he played. In his teens, Armstrong was sent to the Hoff-Berthelson School in Scarsdale, New York, for studies with Miyoko Nakaya. He began to win prizes, 25 of them in all, and as a freshman at Columbia University (he paid his tuition largely with prize money), he entered the Van Cliburn Competition in Fort Worth, Texas. Earning plaudits from Cliburn himself, Armstrong won a Jury Discretionary Award. After that, though, the prizes dried up, and a first-round washout at the next Cliburn Competition caused Armstrong to think he was prioritizing prize-winning over musicality. He dropped out of Columbia, left his teacher, and began to study concertos on his own, taking engagements with orchestras large and small that wanted to have him. The strategy proved fruitful: he met Columbus (OH) Symphony conductor Günther Herbig, who invited him to perform with the orchestra.
In 2000, he married violinist Ayako Yoshida, for whom he had served as accompanist; the marriage ended in divorce (he has since remarried and had four children), but it marked the beginning of a successful chamber music career marked by frequent collaborations with star violinist James Ehnes. He has also performed with the Alexander, Manhattan, and American String Quartets. Armstrong has appeared at many major American venues, including Alice Tully Hall and Carnegie Hall in New York, and the Kennedy Center in Washington, as well as across Europe (including at the Grand Hall of the Moscow Conservatory), Latin America, and Asia. He has a strong interest in music education and often performs concerts for children.
After releasing two recital albums in the early 2000s, Armstrong was highly visible on recordings in the 2010s, accompanying Ehnes on a cycle of Bartók violin-and-piano works on the Chandos label. The pair moved to Onyx in 2015 for an album of violin sonatas by Franck and Strauss, and in 2019 began a cycle of Beethoven's works for violin and piano. Armstrong also backed cellist Robert deMaine on an album of works by Fauré, Grieg, and Rachmaninov. Armstrong serves as Artistic Director of Columbia Museum of Art’s Chamber Music on Main series in South Carolina. ~ James Manheim, Rovi