[1] Merzbach was born in Berlin, where her mother was a philologist and her father was an economist who worked for the Reich Association of Jews in Germany during World War II.
[1][2] The Merzbachs survived the war and the camp, and after living for a year in a refugee camp in Deggendorf they moved to Georgetown, Texas in 1946, where her father found a faculty position at Southwestern University.
[1] Merzbach became a school teacher, but soon returned to graduate study at Harvard University.
Her dissertation, Quantity of Structure: Development of Modern Algebraic Concepts from Leibniz to Dedekind, combined mathematics and the history of science; it was jointly supervised by mathematician Garrett Birkhoff and historian of science I. Bernard Cohen.
[1] In 1991, she co-authored the second edition of A History of Mathematics, originally published in 1968 by Carl Benjamin Boyer.