Solving 2D equations using color, a story of winding numbers and composition

The video introduces an algorithm for solving 2D equations, including those with complex numbers. It begins with a simple 1D function example and extends the concept to 2D functions, using color mapping for visualization. The development of an efficient algorithm is discussed, focusing on winding numbers to find zeros. The video concludes with applications of the algorithm and introduces new team members.

What challenges are faced when applying the algorithm to two-dimensional functions?

Summarize the overall process of the 2D equation solver as described in the text.

How does the algorithm ensure efficiency in finding zeros of functions?

What is the fundamental theorem of algebra as mentioned in the text?