Journey through one of mathematics' most beautiful theories via 24 interactive demonstrations. Trace the 4000-year quest from Babylonian quadratics to Abel and Galois, build field extensions, explore the fundamental correspondence between subgroups and subfields, and see why the quintic cannot be solved by radicals.
See also: Rings & Fields for the field extensions that Galois theory classifies, Group Theory for the subgroup-subfield correspondence at its heart, and Number Theory for the classical problems Galois theory finally settled.
From Babylon to Galois -- the 4000-year quest to solve polynomial equations by radicals
Building number systems by adjoining roots -- from the rationals to algebraic number fields
The smallest field containing all roots of a polynomial -- where symmetry lives
Symmetries that shuffle roots while respecting arithmetic -- the heart of the theory
The crown jewel -- a perfect correspondence between subfields and subgroups
The profound link between extracting roots and group structure -- and why it breaks for quintics
Ruler-and-compass geometry, roots of unity, and the deep algebra beneath classical problems
Open questions and modern directions -- from inverse Galois to algebraic number theory