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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.
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