# Who discovered Maxwell-Faraday equation, $\nabla\times E=-\frac{\partial B}{\partial t}$? Was it Maxwell or Neumann?

I have been trying to find out who discovered Maxwell-Faraday equation, $$\nabla\times E=-\frac{\partial B}{\partial t}$$. Was it Maxwell himself, or was it Franz Ernst Neumann who derived it?

The equation means that a time varying magnetic field induces a spatially varying electric field.

While searching for the answer I stumbled upon an important piece which is given below.

"Maxwell's unique contribution was his "Ampère's" circuital law (both forms: with and without the displacement current term). Faraday's Law was derived by Franz Neumann in $$1845$$. Gauss (and Lagrange before him) knew the compatibility between Coulomb's law and "Gauss"'s law. I'm not sure who was the first to derive $$\nabla\cdot B=0$$".– Geremia Source: Why is Maxwell and not Ampère credited for unifying electricity and magnetism?

Faraday's law in itself was more about voltage generated as a result of magnetic field. To confuse things more, it is said that it was Neumann who first put the result of Faraday's experiment into a mathematical form somewhere around $$1845$$. Why did it take so long to mathematize the result of an experiment? Why didn't Faraday himself converted the result of his experiment(s) into a mathematical form?

Related discussion: Who discovered the magnetic vector potential, $\vec{A}$? "The laws of induction of electric currents in mathematical form was established by Franz Ernst Neumann in 1845." -https://en.wikipedia.org/wiki/Faraday%27s_law_of_induction