History of manifolds and varieties

The history of manifolds and varieties is a rich and evolving narrative within mathematics, particularly in the fields of geometry, topology, and algebraic geometry. Here’s an overview of their development: ### Early Concepts 1. **Geometry and Curves (Ancient to Renaissance)**: Early thinkers like Euclid focused on geometric shapes, while the study of curves began to take shape during the Renaissance with the work of mathematicians like Descartes and Fermat.