Armstrong's boyhood home, 1032 Warburton Avenue, overlooking the Hudson River in Yonkers, New York, c. 1975. It was demolished in November 1982 due to fire damage.
Armstrong was born in the Chelsea district of New York City, the oldest of John and Emily (Smith) Armstrong's three children. His father began working at a young age at the American branch of the Oxford University Press, which published bibles and standard classical works, eventually advancing to the position of vice president. His parents first met at the North Presbyterian Church, located at 31st Street and Ninth Avenue. His mother's family had strong ties to Chelsea, and an active role in church functions. When the church moved north, the Smiths and Armstrongs followed, and in 1895 the Armstrong family moved from their brownstone row house at 347 West 29th Street to a similar house at 26 West 97th Street in the Upper West Side. The family was comfortably middle class.
At the age of eight, Armstrong contracted Sydenham's chorea (then known as St. Vitus' Dance), an infrequent but serious neurological disorder precipitated by rheumatic fever. For the rest of his life, Armstrong was afflicted with a physical tic exacerbated by excitement or stress. Due to this illness, he withdrew from public school and was home-tutored for two years. To improve his health, the Armstrong family moved to a house overlooking the Hudson River, at 1032 Warburton Avenue in Yonkers. The Smith family subsequently moved next door. Armstrong's tic and the time missed from school led him to become socially withdrawn.
From an early age, Armstrong showed an interest in electrical and mechanical devices, particularly trains. He loved heights and constructed a makeshift backyard antenna tower that included a bosun's chair for hoisting himself up and down its length, to the concern of neighbors. Much of his early research was conducted in the attic of his parents’ house.
In 1909, Armstrong enrolled at Columbia University in New York City, where he became a member of the Epsilon Chapter of the Theta Xi engineering fraternity, and studied under Professor Michael Pupin at the Hartley Laboratories, a separate research unit at Columbia. Another of his instructors, Professor John H. Morecroft, later remembered Armstrong as being intensely focused on the topics that interested him, but somewhat indifferent to the rest of his studies. Armstrong challenged conventional wisdom and was quick to question the opinions of both professors and peers. In one case, he recounted how he tricked an instructor he disliked into receiving a severe electrical shock. He also stressed the practical over the theoretical, stating that progress was more likely the product of experimentation and reasoning than on mathematical calculation and the formulae of "mathematical physics".
Armstrong graduated from Columbia in 1913, earning an electrical engineering degree.
During World War I, Armstrong served in the Signal Corps as a captain and later a major.
Following college graduation, he received a $600 one-year appointment as a laboratory assistant at Columbia, after which he nominally worked as a research assistant, for a salary of $1 a year, under Professor Pupin. Unlike most engineers, Armstrong never became a corporate employee. He set up a self-financed independent research and development laboratory at Columbia, and owned his patents outright.
In 1934, he filled the vacancy left by John H. Morecroft's death, receiving an appointment as a Professor of Electrical Engineering at Columbia, a position he held the remainder of his life.