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?

Introduction to Projective Varietiescontains an elementary proof by induction on the number of variables. $\endgroup$ – Joshua Mundinger Aug 26 '20 at 16:27