For most practical applications this is not necessary at all. Common Lisp has countless mathematical applications which make use of its various numeric data types.
We are using different notions of type. For me, a type is a static guarantee about the meaning of a syntactic term in the program, rather than a mere labelling of values during the runtine process. In the sense of type that I use, Common Lisp does not have but just one type, and it is not even a type of numbers - it is a type of everything.
All in all, I did not intend to overly diss Common Lisp. It is a very flexible, expressive and powerful language. I am just saying that, at least from my point of view, Common Lisp does not look particularly inspired by mathematics.
