Mathematics, as defined at this source: Princeton.edu is "a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement."
I like your "God's copyright" concept, but I do not quite understand what you mean by "unreasonable" effectiveness of mathematics in the natural sciences, as mathematics involves quantitative measurements and "unreasonableness" by contrast is a rather subjective, non-quantitative metric.
Mathematics claims logical proofs. Science can make no such claim.
Where mathematics is defined as it is above, I believe science can indeed make such a claim.
The reason I teed you up to this comment was because I happened upon a thread the other day that I had saved from back in 2005, which I found quite fascinating at the time entitled, 'Theory of everything' tying researchers up in knots" , and I found your writing throughout the thread to be quite profound. So, I do definitely have an appreciation for your perspective on this topic:
This was an interesting article revealing a bit of infighting among physicists wrt string theory.
IMHO, it points to an ideological difference which would stem from the priority given to pure mathematics in physics. Indeed we've seen similar disputes here on the forum between those of us who center on the mathematics (information theory, complexity, etc.) related to evolution and those who center on the sciences (biology, chemistry, genetics, paleontology).
It is a philosophical difference which I believe we would all benefit from exploring.
Personally, I fall on the “math first” side of the debate – I put mathematics above all sciences - and physics at the top of the science heap because of its integration with the mathematics.
The thing I like about dialog with you is that while we agree on much, where we disagree with respect to whether Schroeder's view of Genesis days is correct or our respective inclusions or exclusions where it comes to the meaning of the term,"science," is concerned we are able to do so pleasantly.
Be well, Sister!
The "unreasonable effectiveness of mathematics in the natural sciences" is the title of a major essay by Wigner. If you'd like, you can read it here
Wigner and his essay are also cited by Cumrun Vafa in a lecture he gave on geometric physics raising even more examples of the phenomenon.
As to mathematics not being science, that's the claim most of the scientists around here have made for years. And the meaning of the term "science" has also changed over time. Originally it was philosophy, but now of course scientists insist that philosophy is not science.
Beginning of Modern Science and Modern Philosophy