I remember reading what Lenat did with early versions of Eurisco: he ran it on some axioms from number theory and observed discovery of some number theory theor

I remember reading what Lenat did with early versions of Eurisco: he ran it on some axioms from number theory and observed discovery of some number theory theorems, some of them pretty fundamental. As "time" progressed, the "theorems" Eurisco kept getting discovered became duller and duller, like expansion of square of sum into sum of products (I can't remember exact example from the book, but level of dulliness is about right). I believe this can be served as example of combination of existing concepts in novel ways, applied to math, which is very formal and, on the other hand, is the basis of many other areas of human knowledge. If this can serve as a such example, then you are wrong. Also, what you have shown as your examples are not very much interesting outside of entertainment.