Hermann Günther Grassmann was a gifted German thinker whose work spanned the fields of mathematics and linguistics, theology, and botany. His decision to focus on mathematics came when he was 31, but he abandoned the field 20 years later when his formulation of a geometric calculus did not receive the recognition it deserved. Grassmann's conception of n-dimensional vector spaceand multi-linear algebra, laid out in his monumental work Die Lineale Ausdehnungslehre, were ahead of his time but had great impact once they were grasped by late 19th- and early 20th-century mathematicians.

Grassmann was born on April 15, 1809, in Stettin, Prussia (present-day Szczecin, Poland), the third of 12 children. His father, Justus Günther Grassmann, taught mathematics and physics at the local gymnasium and wrote several basic-level mathematics textbooks. The Grassmann family was a religious one: Justus had briefly served as a Protestant minister before becoming a teacher, and Grassmann's...