Dear Jim,
As you note, physics is a science that deals with "matter and energy and their interactions." (I consider the "matter" in this definition to include "anti-matter".) If one, barefooted, kicks a stone, one is left with a very strong feeling that the physical world is real - it matters! But you further note that the union of math and physics "offers more substance"; supplying proofs, furnishing structure, providing order, and clarifying and vivifying quests." Very well put!
You then focus on the Euler's identity. If I were ever tempted to be a Platonist, believing that mathematics existed in some realm outside time and space, I would probably use Euler's identity to prove my point. It is truly remarkable.
Instead, I tend to view it as follows. I see the essence of math as derived from physical reality and as a formal mapping or map overlaying abstract symbols in such a way as to reflect the order or structure of physical reality, say for example, a helix. If one then extracts the underlying reality from the mapped physical structure, one is left with only the map, which, apparently has existence only in our minds. Writing Euler's equation on paper would seem to mean nothing, if no one ever saw the paper.
I found your analogy of an interest formula, that shows the growth one expects from combining math, physics, and brains to be useful and to contain more than a grain of truth.
You tackle the big projects, like the LHC and the Human Genome Project. [I was present at the initial meeting, and you'd be amazed at how many of the participants were against the project - "big science" was foreign to biologists at the time.]
Your European Robin example is extremely interesting. As you know, from reading my essay, the study of one particle's spin interacting with a non-homogeneous magnetic field is overwhelmingly complex, and is currently quite controversial. My own opinion is that if we cannot understand and agree on this simple physics, it is quite a stretch to attribute bird navigation to entanglement in cytochrome. But that's what this essay contest is focused on.
You have written a wide-ranging, enjoyable essay, and I wish you the best. I certainly agree with your major points.
My very best regards,
Edwin Eugene Klingman