@helenS Tunneling has nothing to do with Maxwell, but his work certainly embodies "Physics is cool!" I think of Maxwell's equations as sort of the gateway to relativity, because they beg the question "wave velocity relative to what?" But I can't tie them into the ultraviolet catastrophe or the photoelectric effect or the other precursors of quantum physics.
@ElwoodBlues Isn't quantum mechanics a critic of classical electrodynamics? According to the equations above, the H atom should not exist. The electron should spiral into the core while emitting radiation of ever-increasing frequency.
@helenS Sure, and yet classical electrodynamics describes antennas and waveguides and radar and EM emissions of circuit boards so accurately. Each theory has its place. Even though relativity supplanted Newton's laws over a century ago, I bet you haven't abandoned F=ma.
Einstein made that assertion about fundamental randomness vs determinism, but all his attempts to substantiate it failed. In fact, while Einstein was trying to demonstrate the errors of quantum mechanics, he (& Podolsky & Rosen) discovered that QM implies entanglement.
Entanglement was never observed in Einstein's lifetime, and he called it "spooky action at a distance" but that attempt didn't falsify or damage QM. Einstein spent many years working intermittently on so called "hidden variable" theories to explain away the apparent fundamental randomness of the universe, but never produced a workable theory.
For the last 9 decades or so, our most accurate measurements and predictions have come out of quantum mechanics which, counter to Einstein, assumes fundamental randomness.