  It appears that, along with many of my friends and colleagues, I had been
brainwashed by the great and tragic lives of Abel and Galois to believe that no
general formulas are possible for roots of equations higher than quartic. This
seemed to be confirmed by the brilliant and arduous solution of the general
quintic by Hermite. Yet, below we find a formula giving a root to any algebraic
equation of degree 2-5 and any reduced equation (see below) of higher degree.
This algorithm, which must have been familiar to Lagrange, resulted when I was
working on a paper on the asymptotics of hypergeometric functions where Gauss'
multiplication formula for the gamma function is used to reduce certain
infinite series, and by a happy accident my copy of Whittaker and Watson opened
at p. 133.
