| Abstract:
This question was asked by little William Edwin and his Papa was Sir William
Rowan Hamilton. His thirteen years of research eventually led to the discovery
of the now famous quaternions. It was Frobenius (also Hurwitz) who first proved
the impossibility of multiplying two triples and having the usual properties
enjoyed by the "real associative algebras". Their proofs employed Brower's
Fixed Point Theorem of algebraic topology. Subsequently, several simpler proofs
have appeared in the literature. In this talk, we mention some of these proofs
which are accessible to advanced students of linear algebra.
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