My claim is not that software engineering is related to computer science, it is that software engineering IS PART of computer science. And being part of it, me

My claim is not that software engineering is related to computer science, it is that software engineering IS PART of computer science. And being part of it, means that computer science is not merely an applied subfield of mathematics. A truth that mathematicians and computer scientists accepted decades ago when computer science split off from mathematics into its own department. AS for your example of LAPACK, "The existence of evening, my dear Boswell, does not mean that day is the same as night." Numerical linear algebra is on a boundary between mathematics and computer science. There is a large boundary between math and computer science. But then again the same can be said of, say, math and physics. But by the time you're worried about how to use caching effectively, and make that work in a distributed computation, you're pretty far on the computer science side. Also your idea of grouping them because of research methods is problematic at best. For example machine learning research has a highly experimental flavor that does not fit in mathematics at all. Quantum computing contains a lot that is closer to a field of applied physics than of mathematics. And so on.