As for his substantive points, I don't see why math is any different. After all, scientists make frequent use of math. But maybe I misunderstand.
...............
He addresses this in the interview:
DENNING: It seemed to me that if we are a science, we should be able to explain our fundamental principles. I began to ask what they are. I discovered that neither my colleagues nor I could say. I grew up with the definition that computer science is the study of phenomena surrounding computers. This definition puts the computer at the center. It holds that computation is what computers do. In 2001, when Biology Nobel Laureate David Baltimore said that cellular mechanisms are natural computational means to read DNA and construct new living cells, I saw that our definition, and the thinking behind it, is backwards. Computation is the principle, the computer is simply the tool.
UBIQUITY: But how can you have computation without a computer?
DENNING: Our older definition is like saying that biology is the study of phenomena surrounding the microscope, or astronomy is the study of phenomena surrounding the telescope. How odd this sounds! It sounds odd because we recognize that the microscope and the telescope as tools to study life and the universe. So it is with computation. Suppose that information processes already exist in nature, and the computer is our tool for studying them? David Baltimore is one of first scientists to say that computation occurs naturally; many have since followed.
[...]
There's an even easier way to say it: just as we copied birds by inventing airplanes; we're mimicking natural computation through computers.
Computation, as a principle, isn't a human invention and brains aren't the only or best example found in nature.
We've just started to realize this.
In a recent interview, Rudy Rucker (Wikipedia.com all ye who are curious) wondered about the natural computational power manifested when trees produce leaves. Of course, that's not all that's happening but it's surely an important component of the process.
Denning is after the fundamental principles of computation which exist *outside* of their current machine expression. And this is a curious thing really. To return to the bird example - we spent generations dreaming and thinking about birds and theorizing concepts of flight long before aircraft ever left the ground. The history of computing machinery placed the cart before the horse. Powerful, basic operational principles were developed and we've made the most of them. But no natural analogs seemed evident (I wonder if Babbage and Lovelace thought of this...I'll have to refresh my reading).
The utility of the machines we've fashioned from these ideas and methods took center stage, causing most of us to mistake the machine for the computing principle which, now that we're looking more carefully, we're beginning to see all around us in unexpected places.
.d.