>The first one "Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians." just sounds like bragging between academic camps.
From a mathematical/proofs point of view, computer science is much harder then many forms of applied math. Sure, basic programming isn't all that difficult, but algorithm design and some of the more complex fields, like computer vision? Proofs of correctness are harder on algorithms (you need more in your head, state wise, then you do to a simple inductive proof), and even basic edge detection (Let's say 'Canny', because that's a particular algorithm) requires a deep, intuitive understanding of multivariable calculus.
From a mathematical/proofs point of view, computer science is much harder then many forms of applied math. Sure, basic programming isn't all that difficult, but algorithm design and some of the more complex fields, like computer vision? Proofs of correctness are harder on algorithms (you need more in your head, state wise, then you do to a simple inductive proof), and even basic edge detection (Let's say 'Canny', because that's a particular algorithm) requires a deep, intuitive understanding of multivariable calculus.