In 1844, the Prussian schoolmaster Hermann Grassmann (1809-77) published Die Lineale Ausdehnungslehre (also reissued in the Cambridge Library Collection). This revolutionary work anticipated the modern theory of vector spaces and exterior algebras. It was little understood at the time and the few sympathetic mathematicians, rather than trying harder to comprehend it, urged Grassmann to write an extended version of his theories. The present work is that version, first published in 1862. However, this also proved too far ahead of its time and Grassmann turned to historical linguistics, in which field his contributions are still remembered. His mathematical work eventually found champions such as Hankel, Peano, Whitehead and Elie Cartan, and it is now recognised for the brilliant achievement that it was in the history of mathematics.

The Prussian schoolmaster Hermann Grassmann (1809-77) taught a range of subjects including mathematics, science and Latin and wrote several secondary-school textbooks. Although he was never appointed to a university post, he devoted much energy to mathematical research and developed revolutionary new insights. Die lineale Ausdehnungslehre, published in 1844, is an astonishing work which was not understood by the mathematicians of its time but which anticipated developments that took a century to come to fruition - vector spaces, dimension, exterior products and many other ideas. Admired rather than read by the next generation, it was only fully appreciated by mathematicians such as Peano and Whitehead.