Question

Proof of the Rienmann hypothesis.

Answer 1

Right then, now I’ve got your attention: What is the difference between the gradient and divergence, and in what situations are either used?

Answer 2

lol

Answer 3

The gradient is the a vector that represents the maximum rate change relative to a function. If that function is a surface it is perpendicular to it.
\[E=-\nabla V\]is a good natural example
the electric field is given by the gradient of electric potential, and points perpendicular to every point on an equipotential surface

Answer 4

Divergence is not something I have used too much in physics yet, but I know that, for instance, an incompressible fluid like water has a divergence of zero. It also comes up in Maxwell's equations
Here is Faraday's law in differential form\[\nabla\times E=-\frac{\partial B}{\partial t}\]This may bot be such an intuitive concept though.