The idea of fields was first introduced into mathematics in the early 19th
century by French mathematician Évariste Galois and Norwegian
mathematician Niels Henrik Abel in their studies of the roots of
polynomials (
see Equations, Theory of). Fields were used to
show that, although there is a quadratic formula for solving second-degree
polynomials, there is no analogous formula for the general solution of
fifth-degree or higher polynomials. The word
field was first used at the
end of the 19th century by German mathematician Julius Dedekind who, along with
his colleague Leopold Kronecker, developed abstract field theory and its
application to the theory of numbers.
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