TITLE: Original proof of Hilbert's syzygy theorem
QUESTION [8 upvotes]: Does anyone know an English reference for the original proof of Hilbert's syzygy theorem? The three proofs that I know use either:

the theory of projective dimension and change of rings (plus a step to go from projective to free resolutions)
the symmetry of the Tor functors
Groebner bases

None of these tools would have been available to Hilbert, and I guess his original proof was much more direct. But, unfortunately, the original reference is in German. Is there an English proof somewhere?

REPLY [9 votes]: Actually, there is an English translation of Hilbert's
"Über die Theorie der algebraischen Formen" (Mathematische Annalen 36, 473--530, 1890), where the theorem is in Part III of that five-part paper. The translation is in pages 143--224 of "Hilbert's Invariant Theory Papers", Volume VIII of R. Hermann's "Lie Groups: History, Frontiers and Applications", Math. Sci. Press, Brookline, MA, 1978. I don't know if the book is available on-line.