algorithms can be pointless too

It's easy to write useless silly algorithms, that are essentially little more than a bunch of random symbols on a page. This does not distinguish mathematical algorithms from computer programs at all. While you may tend to think of such things as "not really algorithms", you can equally classify programs as useless, useful, and.or original (and think of the useless ones as being "not really programs" if you like). In both cases, there is a complete continuum between the extremes - with the middle occupied by algorithms/programs that are a mixture of utility and flaws.