Abraham was born in Danzig, Imperial Germany (now Gdańsk in Poland) to a family of Jewish merchants.

[2] In 1909 Abraham travelled to the United States to accept a position at the University of Illinois, but ended up returning to Göttingen after a few months.

He was later invited to Italy by Tullio Levi-Civita, and found work as the professor of rational mechanics at the Politecnico di Milano university until 1914.

After the war, he still was not allowed back into Milan, so until 1921 he worked at Stuttgart as the professor of physics at Technische Hochschule.

After his death, Max Born and Max von Laue wrote about him in an obituary: He loved his absolute aether, his field equations, his rigid electron just as a youth loves his first flame, whose memory no later experience can extinguish.