I have looked really hard, in vain, for a statistics textbook that condescends to explain (to the non-expert) how the $t$-distribution was arrived at.
By this I mean a well-motivated mathematical derivation that connects the $t$-distribution to the original problem that Gosset, Fisher, and others were grappling with when they settled on it.
Statistics textbooks treat this subject as if it were pure kryptonite. Just shocking.
If someone knows of such a book, please let me know.
NOTE: this question is a reference request. I'm not looking for such well-motivated mathematical derivation here. Rather, I'm looking for a pointer to such a derivation in a book or article.