Galois theory
In the year 300 BCE, the Greek mathematician Euclid (pronounded yook-lid) wrote a book on geometry titled Elements. The text contained thirteen books, all on how to solve problems in geometry. Euclid was able to find ways to bisect any angle; that is, he was able to find an angle that was half of any other angle. Euclid was able to do much more, too. He could construct with a straightedge and compass shapes like circles, triangles, squares, pentagons, and others. However, he was unable to find a way to make every possible polygon. For example, Euclid was unable to make a regular 9-gon, a shape with 9 equal sides, using only ruler and compass. Mathematicians, like Euclid, tried to solve other problems as well. If they could cut any angle in two halves, then was there a way to cut any angle into three equal angles? Similarly, was there a way to square the circle (find a square with area equal to π, or a square with side length equal to  ), or double the cube(find a cube with twice the volume of another, by constructing a side of the cube with length  )? These questions remained unanswered for over 2000 years.