I would like to understand why and when polynomial algorithms became of interest.
When did people realize the role and importance of efficient versus non-efficient algorithms? Did that happen when the concept of an algorithm was discovered, or the the term algorithm used.
For instance, I've looked at some textbook of Algorithms such as the one by Cover, Leiserson, Rivest, and Stein "Introduction to Algorithms" 3rd ed. they states in the Preface "Before there were computers, there were algorithms. But now that there are computers, there are even more algorithms, and algorithms lie at the heart of computing".
Would it be the case that, before computers were invented, we were more interested in finding new ideas for solving problems, and were not so concerned with the time it took.
So I am interested in knowing when people became conscious of the importance of efficiency, started to study it more systematically.
Are there some reference papers on the subject, on the history of algorithms and their motivations, and on the concern with efficiency.
[note from the translator] The topic of the question may seem a bit wide, as I tried to keep the meaning without betraying the author. But it seems a good and useful general question that can be adressed with a few general remarks and some facts and examples