I have always considered computer science to be information science and be a part of mathematics and not a separate science. But then again, as a physicist i might be wrong. It's not meant to be diminutive at all (i am after all a programmer) but i consider programming to be a tool, like maths (and consider the two to be inseparable).

I really wish we in the English-speaking world would stop calling it computer science and call it informatics, as is done in some parts of the world. Linear algebra, when applied to any practical problem, is almost always done by computer, yet linear algebra isn't called computer matrix equation science. The terms linear algebra and informatics make it clear that these are mathematical fields that can be studied for their own sake or as tools for practical applications in other fields.

People who majored in informatics would study such things as information theory, approaches to AI/machine learning, models of human cognition, communications (as in signal/noise, data compression, etc.), and so on, and would undoubtedly be required to take programming classes, where programming would be considered a tool to help people learn informatics.

People who majored in programming (wherever that was done, including industrial training and apprenticeships), would be required to take some informatics classes, where informatics was treated as a tool to help them learn to be better programmers.

Just changing the name to informatics would go a long way, in my opinion, toward clearing up the mess. Employers who demand CS degrees as if the degree meant "better-trained programmer" might think differently if they were called informatics degrees and stand in contrast to programming degrees (or certifications) that emphasized practical industrial software dev. And informatics departments would be freed up to be a more general resource to more than just programmers.

Mathematics ("the systematic study of quantity, structure, space, and change") and computer science are both formal sciences (http://en.wikipedia.org/wiki/Formal_science). You can always broaden the definition of mathematics to encompass all formal sciences but it's useful in practice to be able to differentiate them: a mathematician is a different thing from a computer scientist, even if they both spend all day pushing symbols around inside imaginary formal systems instead of predicting and measuring the physical universe.

I have always considered mathematics to be a part of philosophy and not a separate science.

It's all down to definitions.

You could argue that mathematics is philosophy done right: With rigour.

Well, if you take attitude, then you'd have to reject all science because it relies on induction.

Oh, nothing wrong with induction. Just with waffling around.

I think Hume would disagree.

I wasn't permitted to study CS formally (no school would accept me), but I've never found the study itself to be particularly inaccessible. There is a lot of great information out there that anyone can access.

I think people are just apt to become discouraged. There is the prevailing idea that only CS students can learn CS, especially on places like HN, which causes people, who would otherwise be more than capable, to shy away from studying the topic.