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Surely, it is an overstatement to say that "It is customary to say that the work of David Hilbert, put an end to classical invariant theory". The statement I remember hearing when I studied invariant theory in college was "Hilbert's proof of the Fundamental Theorem for Form Invariants almost killed the whole subject" (I forget whether that was Weyl himself or Gian Carlo Rota).
BTW: what does "related in fact to" in the phrase "what was actually studied in the classical phase of invariant theory related in fact to" really mean? Why not tell us what the relation IS?
Reply. On the first point, perhaps it would be better to say it was at one time customary to say....
On the second point: obviously a full treatment of the topic would delve into the classical language (of contragredient variables, or whatever they were called). It's kind of a big job to get everything in: why the old guys were studying invariants, and how what they did fits in with a modern point of view.
Charles Matthews 21:08, 5 Apr 2004 (UTC)
I find it unnecessary and highly-annoying to come across these Wikipedia articles that have nothing in them decipherable to someone who does not happen to be in the field under consideration. It's a pointless exercise whose sole objective is for the author to get people to go along with the author's actual objective: "Everybody look at me and recognize how smart I am!!!" If the author had wanted to convey information, then he or she would have bothered to include at least a short summary explaining what "invariant theory" is actually all about, and what it's useful for.