Ilya Lipovsky (lipovsky@cs.bu.edu) on 2/18/08 wrote:
---------------------------
>Yes, and some parts are definitely pure mathematics. [...]
>He was a "computer scientist," but he actually was a mathematician,
>studying and proving theorems regarding computability, reductions, complexity, and
>general information theory. But, in my humble personal opinion he isn't quite a computer **scientist**.

>By the way, my other post mentions briefly that I don't consider computer science
>to be science. I just don't know if studying man-made abstract structures can be
>considered a science. Science entails experimentation with subsequent discovery
>of natural laws with subsequent fitting of various phenomena to these laws. Physics and chemistry are prime examples.

I think your definition of "science" is too restrictive. Wikipedia has a reasonable overview:

http://en.wikipedia.org/wiki/Science
http://en.wikipedia.org/wiki/Formal_science

I view formal science as a science not just because it fits in with the older definition of the word, meaning "knowledge", but because I see abstract notions like the halting problem as being fundamentally real and waiting to be discovered and not simply accidental artefacts of the way we construct our formal systems. In that sense proofs and deductions are an analogue of experiments. If we were to eliminate anything that was not based on empirical study from the umbrella "science" then large chunks of the theoretical branches of the various sciences are going to be demoted as well, including physics. (String theory, abiogenesis, and cosmology are just a few areas of investigation that will have serious difficulty, either because experiments to test them can't be constructed at all at the moment, or because experiments conducted now don't really prove what happened then, and there isn't much evidence about what happened then.)

On that basis, I see mathematics as a science. Theoretical computer science is very much a branch of pure mathematics, but qualitatively different to other branches -- Turing Machines and Gödel's Incompleteness Theorem are really the same thing, but Turing's Universal Turing Machine and conclusions about computability definitely have a unique flavour to them.

My research was in artificial intelligence, and I think that is also a science, with important questions that impact on the nature of biological systems as well.

>Accordingly, *if* computer science is a science, it is as much a science as, say,
>number theory - there are always new abstract relationships and properties to be
>discovered/modeled, but they are "out there," in the abstract.

Yes -- but that doesn't make them any less real. Any sentient life form in the universe should make the same discoveries. They shouldn't conclude, for example, that the halting problem doesn't exist, just as they shouldn't conclude that the ratio of the circumference of a circle to its diameter is anything other than pi (which is derived mathematically, not by getting increasingly accurate tape measures and placing them around increasingly large circles).