In his ground-breaking 1901 paper, published from his Dec. 14th, 1900 lecture at the German Society of Physics, the great Max Planck made public his discovery about the discretness of the energy of a single electromagnetic wave, by expressing that his energy E =hf was a fundamental quantum of action, and that no other value of energy for a single EM wave could be lower than such value.
With this simple assertion he created, single-handedly, the basis for Quantum Physics, which perdure as a branch of physics as of today.
This simple paper, which solves for good the problem of black body cavity radiation in 8 pages, is crystal clear about what he meant with his quantum of action.
Nevertheless, in the times after this publication, he went to the subject and remarked:
"Light travels as an electromagnetic wave, but is emitted and absorpted in discrete units of energy".
Blinded by ambition and being shameless, in 1905 Einstein sequestered the works of Planck, von Lenard and others (like Newton, Boyle, Matus, Biot, Hertz, etc.), and wrote a paper about the corpuscular theory of light and his quanta of energy (he even plagiarized Planck's definitions). By 1910, Einstein was parroting around, at different conferences and meetings, flanked many times by Planck (he had issues with Einstein since 1905 and, probably, before that year), about the need to accept the existence of a dual nature of light. Of course, as with relativity, Einstein was marketing himself (with a little help from his friends) in order to SELL the absolutely un-needed corpuscular theory of light (either in propagation or in actions over matter).
It was the great James Clerk Maxwell who, 40 years before, had clearly defined the wave nature of light:
"Light is composed by orthogonal self-sustaining electrical and magnetic fields, which oscillates in quadrature and travel along the space at a velocity given by (e0.u0)-1/2."
Even Maxwell, in his incredible power of mind, had envisioned a travelling point-like entity, with sinusoidal behavior (which is described by a propagating sinewave, when math is used or a graph is made to represent it).
When you merge Maxwell's definition of what light is with Planck's definition about the minimum amount of energy by which it interact with matter (atoms), no other explanation like a corpuscular (photonic) theory of light is needed.
But ambitions for lefting marks in the history of science degenerated these pure concepts, creating confussion and a false need for a photonic theory.
The real problem in the last 114 years is not that light has a dual behavior: It has only one, and is expressed in two paragraphs belonging to two of the greatest minds in the XIX century: Planck and Maxwell.
The real problem is the inability or lack of imagination to use mathematics to express, in a compact way, the action of light with matter.
Is very easy and convenient to have an alternate corpuscular theory of point-like massless particles (photons), which also captures the imagination of laymen and the lesser gifted scientists.
There is an abysmal difference using the simplification of the "figure of a photon" carrying a hf (or hbar w)quanta of energy, and the figure of a single wave represented by:
hbar w e-jwt
With the generalized use of photons with hf energy, troubles arise immediately when it has to be explained what is the frequency f.
The semi-classic expression of a single wave of light carrying a quanta of hf energy and oscillating like a point-like, with the expression hbarw e-jwt solves any differences between wave and corpuscular behavior of light.
The only thing missing, as these expressions are pre-atomic age, is to incorporate the delay in the emission and absorption processes which, by the way, were not solved by the photonic theory.
What is the problem, then: Physical or mathematical?
For me, the need for a dual theory of light is originated in the inexistence of proper mathematical models to solve this problem at once and for good.
And once again: Thanks, Einstein, for messing everything that you were able to access to publish (because you were protected).
To prevent any comment about how light is affected with the "inverse square of the distance" law when it depart from a distant source, like
a star, I have to remark that every expression above, either photonic or "thermo-electro-dynamical", correspond to a single unit of energy
emitted by an atom or molecule. Light that departs from a source at deep space does it in spherical shells, which creates the attenuation
law of the inverse square of the distance (due to the surface of the spherical shell).
Light emitted ommidirectionally from a distant source adds up a huge amount of energy, which is decomposed in such elementary units.
Then, as distance increases, what decay is the FLUX of point-like entities per unit surface, not its individual intensity.
With this aditional definition, the problem of attenuation with distance is equated either for "photons" or ELEMENTARY waves.