# Definition:Galois Theory

## Definition

**Galois theory** is a subfield of abstract algebra which provides a connection between field theory and group theory.

## Also see

- Results about
**Galois theory**can be found**here**.

## Source of Name

This entry was named for Évariste Galois.

## Historical Note

The discipline of **Galois theory** dates back as far as $1600$ BCE, when the mathematicians of ancient Babylon worked out how to solve the quadratic equation.

In the $16$th century, the technique leaked out into the public that the cubic equation was also soluble.

Soon after that, Lodovico Ferrari extended this method to show how to solve the quartic.

The quintic remained unsolved until the early $19$th century, at which point Paolo Ruffini and Niels Henrik Abel proved it insoluble.

At around the same time, Évariste Galois produced his own approach to the problem, whose elegance initiated the field of study known now as **Galois theory**.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**Galois theory** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Galois theory**