If we were to destroy all written documents existing today, human knowledge would be reduced in at least these two ways: first, some knowledge would be permanently forgotten if the world's scholarly community did not remember it well enough to write it down again. Second, the loss of all records would harm the ability of future historians to gauge the state of human civilization and knowledge in our time and in all prior times.
The burning of the Library of Alexandria tends to be portrayed in terms of irreplaceable books being destroyed and their contents lost forever. Would contemporaries of the library have thought similarly? Or would they adopt an attitude like we would to the news that all calculus textbooks have been lost - regret that it has happened, but indifference considering that the mathematicians of today could surely write new texts.
Would your answer be the same for other libraries from the same era? How about for libraries outside Europe and the Mediterranean?
Although I encourage you to check out Searocksantrees link, I think the best way to sum up the true impact of the destruction of the Library is by pointing out that we have no idea when it was actually destroyed, because no one bothered to mention it except off-hand.
The destruction is probably the most "overrated" historical event of all time.
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