On Mathematical Sophistication

Whenever you study a theoretical textbook, the author usually will specify what kind of mathematical maturity or sophistication he/she is expecting. Luce and Raiffa have the following say, which I find interesting and honest:

Probably the most important prerequisite is that ill-defined quality: mathematical
sophistication. We hope that this is an ingredient not required in large
measure, but that it is needed to some degree there can be no doubt. The
reader must be able to accept conditional statements, even though he feels the
suppositions to be false; he must be willing to make concessions to mathematical
simplicity; he must be patient enough to follow along with the peculiar kind
of construction that mathematics is; and, above all, he must have sympathy
with the method — a sympathy based upon his knowledge of its past successes
in various of the empirical sciences and upon his realization of the necessity for
rigorous deduction in science as we know it.