I want to start out by making this clear: I'm NOT looking for the modern proofs and rigorous statements of things.
What I am looking for are references for classical enumerative geometry, back before Hilbert's 15th Problem asked people to actually make it work as rigorous mathematics. Are there good references for the original (flawed!) arguments? I'd prefer perhaps something more recent than the original papers and books (many are hard to find, and even when I can, I tend to be a bit uncomfortable just handling 150 year old books if there's another option.)
More specifically, are there modern expositions of the original arguments by Schubert, Zeuthen and their contemporaries? And if not, are there translations or modern (20th century, say…) reprints of their work available, or are scanned copies available online (I couldn't find much, though I admit my German is awful enough that I might have missed them by not having the right search terms, so I'm hoping for English review papers or the like, though I'll deal with it if I need to.)
Best Answer
I do know of one article taking a historical approach to Schubert calculus:
Kleiman, Steven L. Problem 15: rigorous foundation of Schubert's enumerative calculus. Mathematical developments arising from Hilbert problems (Proc. Sympos. Pure Math., Northern Illinois Univ., De Kalb, Ill., 1974), pp. 445--482. Proc. Sympos. Pure Math., Vol. XXVIII, Amer. Math. Soc., Providence, R. I., 1976.
I am much less of a Schubertist than the average Berkeley/Harvard-educated mathematician with research interests in algebraic geometry, but nevertheless I found this article to be fascinating reading.