Not only do I doubt that "anyone" can write these programs, most of them do not look particularly interesting or fun. Many if not all of the non-mathematical ones are simply replicating off-the-shelf utilities or tools; what is the point of reinventing the wheel? Even if you are looking to hone your skills in a new language, creating something genuinely new seems like it would be more useful and motivational.
I was writing a chess app a while back and a non-programmer friend mocked me for re-making something that already ships for free on every computer in the world. This took me by surprise! Why do people complete crossword puzzles that millions of people have also completed? Why do people learn to play songs on the piano that millions before them have learned? Why do people learn math proofs that have been known to othe…
> Why do people learn to play songs on the piano that millions before them have learned?
I honestly asked myself that same question when I was a teenager, and I decided to quit piano lessons. It felt like a waste of time and a useless skill now that we have MIDI and self-playing pianos. So I switched to jazz and improvisation, and tried to compose my own music (although I'm not very good.) But I enjoy the creativity a lot more than playing songs from sheet music.