The mathematical entities studied range from algorithms, where computer scientists reduce their properties to discover similarities and qualify different algorithms under different algorithmic classes according to the way said algorithms tackle a problem; all the different kinds of automata, to discover numerical, combinatorial and computational properties of language processing automata, such as mathematically analysing and discovering the computational possibilities of different classes of automata, as well as the qualification of different languages according to the kind of automathon that can compute them, and other theorems regarding the nature of automata themselves (such as the theorem that states that for any NFA an equivalent DFA exists); computational complexity classes, discovering different properties that make problems belong to certain classes under a certain computational model, but tp other complexity classes under other theoretical computational models, discovering the patterns and properties of different computational problems situated in ranges of their complexity classes (an important theorem in this subject is Shaefer’s dichotomy Theorem); and finally, the study of mathematical abstractions of computational models, including, but not limited to turing machines, quantum computers and other theoretical non-deterministic impossible “oracles”.

By saying that “the computational world is already mathematically described” you’re completely taking for granted the structures cited above, which are studied and researched by Computer Scientists to reduce new conclusions about the immutable properties surrounding computation in our reality. It might be that algorithms (mathematical imperative statements) existed for a long time already, but an in-depth study on their true nature was never done before Alan Turing, who created Theoretical Computer Science. Automata, complexity classes, computational classes of combinatorial languages and the properties of theoretical computational models are all mathematical structures that had to be reduced and researched by computer science, and they have their immutable properties, theorems and definitions, just like any other mathematical entities, not merely “inventions to serve a purpose”, but actual “mathematical structures reduced by the study of the underlying properties of computation”.

So, in fact, as you can see above, there was A LOT that still had to be reduced in computer science.

You might argue that this all is mathematics, not science, but nor is it engineering.

tl;dr version: Stop being so narrow-minded.

Man, I agree on your point that computer science is the “engineering arm of mathematics” in that it bends mathematics to fulfull certain tasks, but I wouldn’t use the wording you did, I’d definitely not say computer science is “mathematical engineering”.

So, Computer Science is about bending mathematics to specific tasks, but so is Operations Research, which is considered an applied mathematics discipline rather than an engineering discipline. Computer Science is not much different from Operations Research at all, and I think it should qualify as Applied Mathematics too.

Someone stated that Computer Science should be called Software Engineering, and that’s just wrong. Software Engineering is concerned with working under the limitations of technology to create digital software and systems according to specifications, and Computer Science, on the other hand, is more concerned with the mathematics underlying the computation of results, not restrained to the existing computer technology. Software Engineering suffers from engineering-type constraints of feasibility, viability, etc. while Computer Science’s constraints are mathematical possibility and human imagination.

My suspicion is that you seem to have your own very narrow understanding of what is computer science rather than accepting the fact that a lot of what is computer science, is exactly that, science. On the other hand, there are a lot of computer scientists that are not doing science in any shape or form of science. That does not however extend to all computer scientists. Such a claim would be so bad that it isn’t even wrong… .

Unless you also support the claim that medicine isn’t science (there is not scientific method behind modern medicine, just approximations of it), any social or political science is also out, in fact Newton wasn’t a scientist (he certainly didn’t experimentally prove all his theorems), that goes for Einstein and in fact a lot of the classical scientists. A lot of theoretical science does not fullfil your criteria, so which is wrong. You or the world?

But it kind of begs the question – is mathematics a science?

Does science require that evidence come from nature?

Interesting article here:

http://www.arachnoid.com/is_math_a_science/index.html

if you look closely at other sciences, such as chemistry, we sometimes dont study nature directly. we figure out that ‘50ml of chemical A with a smaller molecules/atoms mixed with 50ml of chemical B with a bigger molecules/atoms does not give you a 100ml’. how do we model it to study them? well, back in my class, we teacher gave let us mix 5ml of green bean and 5ml of perhaps rice to show how it does not give us a 10ml worth of mixture. i think computer science is very similar, we not only study natural phenomenon with the aid of one or more tools, we also follows the scientific methods.

however, i acknowledges that not all computer scientists agree with whether computer science is a science or not. that might probably depend on their aim to study computer science. some studies computer science with notations for expressing computations, while the others study it for the finding of the absolute truth of the world.

what say you? im actually writing a report on computer science, will be glad to take in some propagation and debunking.

But, just off the top of my head, I can think of several fields in artificial intelligence that fit even your definition of science.

Since your whole argument is about the definitions of computer science and science, I think you’d be better off to start with formalized definitions of each that are generally accepted. And you’ll want to spend the bulk of your work explaining why those definitions are correct. Above you merely state your definition of science, then agree it’s incorrect, but continue to use it anyway. You never attempt to define computer science, but it’s fairly clear from the text that you think it’s the act of typing code into an IDE.