Have you ever come across something like: "This course has no prerequisites except a certain level of mathematical maturity." To me this sounds just as awful as: "It is easy to see that..." or "Proof: trivial." What is mathematical maturity anyway? As far as I know, the concept of maturity is only used in relation to mathematics. Doesn't it simply means knowing a LOT about mathematics? Anyway, If I would have to describe my own mathematical development then I would not use the words mature or maturity. I would probably say that "I am learning how little I know and how little I will ever know". It is as though if I set one step towards my goal, my goal takes two steps back. I keep walking and learning but I will clearly never reach that final goal. You are never done in mathematics.

Krantz (left) Lederman (right ) |

Stephen G. Krantz wrote a book about mathematical maturity called "A Mathematician comes of Age.". Sol Lederman interviewed Krantz in his series 'Wild about Math'. Krantz has a website too and I happened to found that he left a copy of his book on it: here ( PDF ). There may be a zillion reasons why he left it there so let's not speculate about it. Get the book while you still can and read it if you are interested in the concept of mathematical maturity.

Link to A Mathematician Comes of Age on Amazon.