Optimal path to swim across river in least time - Math Puzzle (HARD)

The video tutorial explores the problem of crossing a river with variable water speed in the least time. It breaks down the velocity into horizontal and vertical components, derives equations for time minimization, and applies the Euler-Lagrange equation to find the optimal path. The solution involves calculating a Lagrange multiplier numerically, and the video concludes with a Matlab script verifying the optimal path.

What new insight or understanding did you gain from this video?