Scientists at Bell Labs build the Isograph, a precision instrument that calculates roots of polynomials up to degree 15.

Emil Artin (1898-1962) uses field theory to develop the modern theory of algebraic equations.

Vladimir Arnol'd, using results of Andrei Kolmogorov (1903-1987), shows that it is possible to express the roots of the reduced 7th degree polynomial in continuous functions of two variables, answering Hilbert's 13th problem in the negative.

Hiroshi Umemura expresses the roots of an arbitrary polynomial through elliptic Siegel functions.

Peter Doyle and Curt McMullen construct a generally convergent, purely iterative algorithm for the numerical solution of a reduced quintic, relying on the icosahedral equation.

David Dummit and (independently) Sigeru Kobayashi and Hiroshi Nakagawa give methods for finding the roots of a general solvable quintic in radicals.