The raw mathematics isn't the hardest; most of this is settled by the end of the second year of undergraduate physics—things like Taylor series, ODEs, PDEs, special functions, a bit of linear algebra (no proofs needed, just use the results); perhaps complex analysis which leads to Fourier transforms and all. Maybe a treatment of tensors.

The issue is the sheer complexity of micro systems, and the unintuitive nature of going deeper than 'EM wave reflects off electrons'.

Consider metal-light interaction. Exactly how does a visible-light EM wave interact with a conduction band of superposed free valence electrons? How does the massive superposition elevate each valence electron up energy levels? Why do only metallic and semi-metallic crystals have no band gap? Why are electrons filled in the order of s, p, d, f, g, h orbitals? Why do these orbitals have these shapes? Why are electrons so much less massive than protons and neutrons? Why does the nucleus not tear itself apart since it only contains positive and neutral particles? Why are protons and neutrons made of three quarks each, and how does the strong interaction appear? Why are the three quarks' mass defect so much more than the individual masses of each quark? How does the mass-energy equivalence appear? Why does an accelerating electric charge produce and interact with a magnetic field, and thus emit EM radiation? What is mass, charge, and magnetism in the first place?

Each question is more 'first principles' than the last, and the answers get more complex. In these questions we have explored everything from classical EM, to solid state physics, to quantum electro- and chromodynamics, to particle physics and the Standard Model, and are now verging on special and general relativity.

> The raw mathematics isn't the hardest; most of this is settled by the end of the second year of undergraduate physics—things like Taylor series, ODEs, PDEs, special functions, a bit of linear algebra (no proofs needed, just use the results); perhaps complex analysis which leads to Fourier transforms and all. Maybe a treatment of tensors.

It sounds like the OP is saying you could tackle the article if you just know a little high school calculus and trig, and you're here saying that you need years of post-secondary mathematical education. I think you're making his case that he's dramatically simplified understanding how to compute these things for someone who doesn't have a post-secondary education.