Galois theory
Quick Summary
Galois theory is a branch of mathematics concerned with the conditions under which polynomial equations can be solved using radicals, such as square roots and cube roots. Developed by the French mathematician Évariste Galois, it provides a way to determine if an algebraic equation of any degree can be solved by radicals. Galois's work established a connection between the solvability of equations and the properties of abstract mathematical structures called groups. This theory not only solved a long-standing problem in algebra but also laid the groundwork for the study of abstract structures, fundamentally reshaping the field.1234
Ask Britannica AI about this topic
Britannica doesn't have a full article on this topic, so we've curated a list of our relevant coverage.
algebraNoether and Artin…for the latter’s reformulation of Galois theory. Rather than speaking of the Galois group of a polynomial equation with coefficients in a particular field, Artin focused on the group of automorphisms of the coefficients’ splitting field (the smallest extension of the field such that the polynomial could be factored into…
Read More…for the latter’s reformulation of Galois theory. Rather than speaking of the Galois group of a polynomial equation with coefficients in a particular field, Artin focused on the group of automorphisms of the coefficients’ splitting field (the smallest extension of the field such that the polynomial could be factored into…
Read More- Camille Jordan
…of the importance of the theories of the eminent mathematician Évariste Galois, who had died in 1832.
Read More…of the importance of the theories of the eminent mathematician Évariste Galois, who had died in 1832.
Read More