Spoken language has a lot going for it. I note the featured article and it's discussion are all words not maths.

By the way looking at Maxwell's paper it seems awful complicated https://royalsocietypublishing.org/doi/pdf/10.1098/rstl.1865...

compared to the modern form of the equations https://ethw.org/w/images/d/d6/Maxwell_image_02.jpg

>compared to the modern form of the equations

Are the Geometric Algebra...

    ∇F = μ₀cJ

..and Differential Form...

    dF = 0
    d⋆F = J

...equivalents post-modern?

https://en.wikipedia.org/wiki/Mathematical_descriptions_of_t...

Heaviside thought that too which is why he invented the modern form. Not that he just used a different set of math to describe the problem, he invented the math too.

The modern form of the equations was worked out by commoners, so had to be filtered through the work of others before it could be taught.

You're really caught up on this commoner/non-commoner dynamic (from your other comments). Was it really that important? - many of the well known scientists of that time were 'commoners'.

I'm not, but they were. But it was not discussed openly in print at the time, and so must be inferred.

I just read his Wikipedia and he was sponsored by his uncle Sir Charles Wheatstone of Wheatstone bridge fame and ended up a Fellow of the Royal Society so was not so badly situated.

Wasted implies the solution is somehow obvious but that’s hindsite bias. Looking at lotto winners it feels easy. But, the reality is a lot of effort went to things both promising and wacky to get those steps forward. And other less major progress is being glossed over.

Maxwell unified electromagnetism into a propagating wave. That was the big leap. Before that, things were disparate.

Hertz proved it experimentally, and Heaviside turned it into an engineering discipline.

This is true of the mathematics, but it's worth noting that Faraday had already proposed EM waves ~30 years earlier based on his intuitive understanding.

And had rejected the aether, on the basis that it was unimaginable that any medium could propagate transverse waves in all directions but not allow longitudinal waves.

> Pupin went first to Cambridge and enrolled as a student, hoping to learn the theory from Maxwell himself. He did not know that Maxwe ll had died four years earlier. After learning that Maxwell was dead, he stayed on in Cambridge and was assigned to a college tutor.

It wasn't that people spend all those years actually working on this problem. There wasn't an internet nor modern travel to share/disseminate/argue about these ideas.

> So basically ~70 years wasted.

to call those years wasted implies that we shouldn't have had to wait for them. it suggests that we should look for a way to bypass them.

I’d rephrase it as: we would probably do ourselves good by coming up with better mathematical intuition and tools of understanding math.

They were wasted if people toiled fruitlessly on the problem. Not necessarily wasted if they were making progress on other problems.

In truth, it generally takes significant time to arrive at fundamental theories. Most people don't realize this because in a physics class, at best, you might get taught when so-and-so published an equation.

[retracted]

Lord? Faraday was no lord. He was also dead by the time Maxwell gave this presentation.