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?