An illness thwarted Michael's plans to attend Harvard, and instead in 1871 he traveled to Europe with his parents and decided to study in Germany.
[5] At Tufts College, Michael met and married, in 1888, one of his own science students, Helen Cecilia De Silver Abbott.
Following several years in England, during which the couple worked in a self-constructed laboratory on the Isle of Wight, they returned to the United States in 1894 where Arthur Michael again taught at Tufts, leaving in 1907 as an emeritus professor.
Throughout his career, Michael worked with some of the foremost chemists of his day, obtained chemistry professorships, and achieved fame among his peers.
As originally defined by Michael, the reaction involves the combination of an enolate ion of a ketone or aldehyde to an α,β-unsaturated carbonyl compound at the β carbon.