Please allow me one more comment:
It seems that C. Reid is not the primary (printed) source: Her _Hilbert_
was first published in 1970, while, according to Mike Deakin, the phrase
appears also in Robert Jungk's book: _Heller als tausend Sonnen_
Scherz & Goverts Verlag, 1956.
Has anyone access to this book (or its English translation) ?
In what context the phrase appears in Jungk's book?
In one of my previous messages on this thread, I mentioned a fiction story
by a Greek mathematician where we find a version of the Hilbert's
phrase (RH instead of FLT). The context in this book is about proving theorems
(Galois was trying to solve the quintic eq. and discovered Group Theory.
And the author comments "as Hilbert said...".)
Antreas