The bulk of professor McNees's thread, minus images, quoted below for the convenience of people who can't unroll or view the twitter thread:

begin @mcnees quote

On a Heuristic Point of View Concerning the Production and Transformation of Light," Einstein's paper that asserted the reality of quanta to explain the photoelectric effect, was published #OTD in 1905.
https://einsteinpapers.press.princeton.edu/vol2-doc/185

Five years earlier, Planck proposed the emission and absorption of radiation in finite chunks as a way of explaining the emission spectrum of a black-body. But he didn’t think it was a fundamental property of light! He thought it was a consequence of how matter & light interact.

Einstein opens the paper by acknowledging that the existing theory of light – continuous waves governed by Maxwell's equations – provides an immensely satisfying and probably irreplaceable description of optical phenomena as they were understood at the time.

But he then points out that there wasn't such strong evidence for the wave picture when it comes to processes involving the emission and absorbtion of light. So maybe light isn't really continuous waves, after all.

This is a big claim! 100 years earlier, Young's double-slit experiment stuck a dagger in Newton's corpuscular theory of light. And Maxwell's equations, considered one of the great triumphs of 19th century physics, were only 40 years old. Einstein needed to make quite a case.

So Einstein considers the thermodynamics of radiation in a black-body cavity, and shows that when you let the system expand or contract a bit, the entropy changes in just the way you'd expect for a gas made of independent particles.

He then zooms in on a narrow band of frequencies, a tiny sliver around some arbitrary value f, and shows that those particles should each carry energy h*f, where h is Planck's constant.

At this point, a skeptical reader might challenge him. (Most physicists at the time would have been pretty skeptical.) Where are you going with this? Why assume it's real? Herr Planck told us it was a trick! Everyone knows that radiation is continuous, not discrete.

But you know Einstein. He takes the result seriously, and asks "What phenomena can we explain if we assume that light really is composed of quanta?" Einstein presents what he considers to be three pieces of evidence for his claim.

The first is "Stokes's Rule" for photoluminescence: The frequency of the emitted light never has greater frequency than the absorbed light. Einstein explains this in terms of quanta and conservation of energy.

The second is the big one: the photoelectric effect. Hertz, Lenard, and others had observed that light incident on various metals and gasses caused electrons to be emitted. For a given substance, the light must be above some specific frequency before any charges are liberated

Increasing the intensity of the light frees *more* charges from the substance. But the *energy* carried by each charge increases linearly with the frequency of the light, not the intensity. At the time, no one understood why.

Einstein explains this straight away. Light of frequency f is made up of quanta with energy hf. For a given substance, freeing an electron requires some amount of energy W. When f > W/h, each quanta frees an electron which carries off the leftover energy hf - W.

More intense light means more quanta, so more charges are freed from the substance. But each one still carries the same amount of energy. And if f < W/h then the quanta simply don't have enough energy to free a charge.

Einstein points out that one could measure the electric potential needed to stop these electrons, plot it versus the frequency of the incident light, and the result should should be a straight line: V = hf/e - W/e, where e is the electron charge. The slope gives the value of h.

Robert Millikan thought this was nonsense, and set out to prove Einstein wrong. He ended up verifying Einstein's prediction and producing exquisite measurements of Planck's constant.

The third and final piece of evidence offered by Einstein involved the photoionization of gas. He showed that his proposed quanta more or less agreed with all the experimental data.

And that's it. It was a stunning claim that was both outrageous and true: Radiation is quantized. The paper would lead to a Nobel prize, and was one of the core results that prompted the development of quantum mechanics.