Springer GTM Series statement of purpose (early editions) Earlier editions of the Springer Graduate Texts in Mathematics series include a motivating statement about the purpose of the series.  The current statement of purpose is as follows:

Graduate Texts in Mathematics bridge the gap between passive study and
creative understanding, offering graduate-level introductions to
advanced topics in mathematics. The volumes are carefully written as
teaching aids and highlight characteristic features of the theory.
Although these books are frequently used as textbooks in graduate
courses, they are also suitable for individual study.

I believe the earlier statement of purpose, from the paper books, is somewhat more colorful.  Does someone have access to an early GTM book to check?  I believe the statement is found just inside the cover; it isn't present in digitized versions that I've seen online.
 A: Aha, found it, via a footnote to my own PhD thesis :-)

“A student approaching mathematical research is often discouraged by the sheer volume of the literature
and the long history of the subject, even when the actual problems are readily understandable. Graduate Texts
in Mathematics, is intended to bridge the gap between passive study and creative understanding; it offers introductions on a suitably advanced level to areas of current research. These introductions are neither complete
surveys, nor brief accounts of the latest results only. They are textbooks carefully designed as teaching aids;
the purpose of the authors is, in every case, to highlight the characteristic features of the theory. Graduate
Texts in Mathematics can serve as the basis for advanced courses. They can either be the main or subsidiary
sources for seminars, and they can be used for private study. Their guiding principle is to convince the student
that mathematics is a living science.”

You can also find a copy of the text in the linked backmatter of Advanced Mathematical Analysis (1973), GTM #12, as digitized on SpringerLink. Looking around, some early versions of the text have as the second sentence "The new series, Graduate Texts in Mathematics...". Presumably the author was Paul Halmos?
