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In school, I did not excel in any academic area, prompting my father to suggest that I become a gardener or a craftsman.

Though I eventually developed into both a skilled mathematician and specialist in Sanskrit literature, I never held a position of prominence higher than that of being a secondary school mathematics teacher.

To complement Cayley's work on geometry in n-dimensions, I published my Ausdehnungslehre as a way to build a calculus of "extensive magnitudes."

Unfortunately, my Ausdehnungslehre was not accepted because it had "forbiddingly novel notation and obscure exposition,"...but it eventually was recognized in the U.S. by Gibbs as an algebra of 3-D vectors.

My Ausdehnungslehre also was published the year after Hamilton discovered non-commutative quaternion multiplication, so I received no credit for my discovery of a similar noncommutative operation for vector multiplication (which also was not associative).

Answer: Hermann Grassmann (1809-1877)