I. ˈgalˌwä- noun
Usage: usually capitalized G
: a part of the theory of mathematical groups that is applied especially to showing which algebraic equations can be solved by sequences of rational operations and by the extraction of integral roots of already known quantities and to proving that a quintic equation exists that cannot be solved by such procedures
II. (ˈ)gal¦wä- noun
Usage: usually capitalized G
Etymology: after Evariste Galois died 1832 French mathematician
: a part of the theory of mathematical groups concerned especially with the conditions under which a solution to a polynomial equation with coefficients in a given mathematical field can be obtained in the field by the repetition of operations and the extraction of nth roots