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Comment by ThePhysicist | Hacker News Reader

Maxwell didn't have the nice differential geometric notations that we use today, which allow us to write his equations in a very concise and easy to understand form. His original paper is way more convoluted, so at the time it must have been really difficult to understand for everyone except the subject matter experts. And he was of course building on the work of Faraday, Ampere and others.

But like with other theories, people find ways to simplify the notation and formalism and explain it better. Quantum mechanics, special and general relativity are similar in that regard.

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True, but he did use quaternions (by 1873), which allow the field properties to be written as a single equation. It's kind of sad that more physicists don't use or teach quaternions, while math and CS have fully adopted them.

I really liked Kathy Joseph's historical reviews of vector physics and the people who developed it, which explain some of the reason's for how it's taught. Most texts don't even develop electrodynamics from relativistic electrostatics as a demonstration.

https://youtu.be/CdwxpSInhvU

I think I fell down the rabbit hole from Freya Holmer's "why you can't multiply vectors".

https://youtu.be/htYh-Tq7ZBI

The key being that all of the Hamiltonian fields can be found in a single quaternion equation, which is just what happens when you start multiplying vectors together.

Unfortunately he didn't use quaternions in his initial formulation (that was all split into xyz coordinates) and in his later revision he took apart the quaternions into scalar and vectors parts. It could have been so much prettier....but luckily we have geometric algebra for that today.

On the other hand he did derive the electric and magnetic fields from a scalar and potential field. In that sense Heaviside made a step backwards.

Faraday didn't even know trigonometry, allegedly (he never studied mathematics). It's interesting that his student (Maxwell) who did have the mathematical background would extend his theories and figure out the math to explain it all

Maxwell was deeply influenced by Faraday's work but he was not his student: he first noticed Faraday’s work while he was at Cambridge in the 1850s. He found a way to translate Faraday’s experimental findings (expressed as the interaction of "lines of force") into a mathematical model (with fields), also taking into account Coulomb's and Ampère's laws. Maxwell then extended that model to take into account the conservation of charge / the continuity of currents.

While Maxwell’s work was inspired by Faraday's, it was also built upon the contributions of many other scientists (Coulomb, Ampère, Thomson, Neumann, Lenz, ...)

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