I was a student of Riemann andf a professor of mathematics at Leipzig.
In my 1867 text, I proposed the ideas that real numbers had to be recognized as "intellectual structures," not Euclid's magnitudes.
In 1867, I was able to prove that the algebra of complex numbers is the most general algebra possible under the fundamental laws of arithmetic.
I am best known for my quote: "In most sciences one generation tears down what another has built and what one has established another undoes. In Mathematics alone each generation builds a new story to the old structure."
Hermann Hankel, 1839-1873