A wave is already what we call a manifestation of a field, maybe I skimmed too quickly but I don't get the author's breakthrough point.

I am not sure there’s any breakthrough here, but this article is about a different QM interpretation (as opposed to Copenhagen or Many Worlds). Interesting but seems irrelevant to the discussion here of particles and fields.

Yes, the field is the substrate.

"I insist upon the view that 'all is waves'."

    Letter to John Lighton Synge (9 November 1959), as quoted by Walter Moore in Schrödinger: Life and Thought (1989) ISBN 0521437679 
It is not a breakthrough, it is just something we refuse to see, something that was known for a century.

"All is a wave" is the unifying principle. I am no mathematician, but the math needs to start with that fundamental principle.

The very notion of calling it "qunatum" physics is probably wrong since quantum is "a discrete quantity of energy proportional in magnitude to the frequency of the radiation it represents."

And if everything is a wave there are no discrete quantities beyond our definition of what constitutes the end, or borders, of the wave.

> I am no mathematician, but the math needs to start with that fundamental principle.

This is a weird sort of hubris. “I’m not qualified to do this job but I can certainly tell you how it needs to be done.”

> And if everything is a wave there are no discrete quantities beyond our definition of what constitutes the end, or borders, of the wave.

This is not true in multiple ways. First, it’s known that these particles exhibit quantum behavior. This is measured and confirmed over and over. Many measures are in fact quantized.

Second, existing as a wave does not mean no discrete quantities. Even in everyday materials we observe situations like standing waves that are effectively quantized.

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

> This is a weird sort of hubris. “I’m not qualified to do this job but I can certainly tell you how it needs to be done.”

A quantum state is a mathematical entity that represents a physical system. Since waves are not physical can you see where I can assume that the math needs to start from a different place? If it is even useful at all?

> it’s known that these particles exhibit quantum behavior. Many measures are in fact quantized.

To measure is to quantize, so this is circular reasoning. If particles are always waves we would still see the quantum behavior.

> Second, existing as a wave does not mean no discrete quantities.

Where is the precise point a standing wave ends and begins? The best we can do is guess with calculus and differential equations. Again, yoiu are quantifying things that in and of themselves are not quantized outside of our conception.