On Peter Freyd's substantial simplification of Frobenius's theorem on finite dimensional real division algebras.

**Abstract:** A well-known theorem of Frobenius states that a finite
dimensional real division algebra is either the reals, complex
numbers, or the quaternions. The standard proofs are fairly
complicated (see
Wikipedia
for example). By a clever use of conjugation, Peter reduced the result
to a simple argument that is so pretty I would like to present it. I
will also explain the centrality of centrality in the argument, why
the result fails if the reals are not centrally embedded in the
algebra, which goes back to Gerstenhaber and Fine in my student days.