The French mathematician Évariste Galois is primarily known for his work in which?

The story behind the answer

Galois Theory is correct because Évariste Galois created a deep link between polynomial equations and the symmetries of their roots, captured by the “Galois group.” He showed that whether an equation can be solved by radicals depends on whether its associated group is “solvable”—foundational work that essentially launched group theory and modern field theory.

Context: Galois (1811–1832) wrote his breakthroughs as a teenager and died in a duel at 20; his notes were published posthumously, reshaping algebra. Memory tip: think “Galois Group” and “solvability”—both start with G. Galois gauges equations by groups.