TITLE: Serre's theorem about regularity and homological dimension
QUESTION [23 upvotes]: One of the nicest results I know of is (Auslander-Buchsbaum-)Serre's theorem asserting that a (commutative!) local ring is regular iff it has finite global dimensional.
I'd like to ask a somewhat vague question: 

what is the history and what was the context of this result? 

By this I mean: presumably the above characterization did not come out of thin air (or just out of Serre's mind!), and there was a buildup of ideas which lead to such an elegant and, I guess, surprising characterization of regularity. Nowadays, such a thing appears almost natural to our minds brought up in the nice set-up constructed by the founders of homological algebra and tended to by a few generations already, but I suspect it was less «evident» at the time.

REPLY [45 votes]: In 1953-54 E. Artin asked me to describe homological algebra to him. In addition to Ext and Tor, I decided to show him the "homological proof" of the Hilbert Basis Theorem and indicated that the same proof showed that a regular local ring had finite global dimension. Artin then mentioned the open localization problem, and I said that if the converse of the theorem I just showed him were true, the localization result would be trivial. He asked if I could prove the converse, I said no, and we both agreed that it would be nice to prove it. The question of factoriality in regular local rings also came up in that conversation, and so I set myself the goal of proving those two theorems. I persuaded Auslander to join me in that project. When Auslander and I had almost all the results, and an outline of the string of inequalities needed, Eilenberg asked to see them, we wrote them up for him, and he went to Paris with them. It was there that Serre saw the outline of our project, and he beat us to the final proof by around a week (or the time it took an air mail letter to travel from Paris to Princeton). This may clear up the questions initially posed.