Algebraic geometry has been at the center of much of mathematics for hundreds of years. Its applications range from number theory to modern physics. Yet, it begins quite humbly with the study of conic sections: circles, ellipses, hyperbolas, and parabolas. What is algebraic geometry and how did it grow beyond the scope of these familiar curves to become one of the most important branches of mathematics today?

In this talk, which will not be able to completely answer these questions, we will focus on its growth from the study of conic sections to the exploration of algebraic varieties.