I've heard the opinion repeated many times that if the Library hadn't been destroyed, we'd probably all be colonizing Alpha Centauri by now. While the idea has a certain tragic romanticism, it also strikes me as absurd on ground of Eurocentrism alone- after all, it's not like the Greeks were the only ones who knew anything. I also know that a lot of the works survived in other places, especially in Baghdad.
On the other hand, I recently read a couple journal articles attempting to piece together a partial inventory of the works we know to have been destroyed or lost, and I found it deeply compelling (I know it's insanely stupid, but it nearly brought me to tears). Histories, ethnologies and maps of parts of the world/world history we know very little about, to my knowledge; mathematical, astronomical, and mechanical treatises that were at least centuries ahead of their time (unless I'm wildly off base, a decently predictive heliocentric model of the solar system wasn't re-introduced until 1543); even poetry and literature that, while not directly applying to the colonizing-Mars-thesis, had to contain information about the cultures it came from.
I know this is a pretty open-ended question, but I think what I'm really trying to get at is whether the meme of a tragic and dramatic blow to the stockpile of accumulated human knowledge is really accurate, whether it's accurate in a limited context (i.e. it sucked for Greece but didn't matter much in the long run), or whether it's a total myth and really nothing too critical or unique was lost due to duplication/transportation/etc.
My current gut instinct is that in terms of scientific/mathematical knowledge the loss was likely minimal due to duplication in other parts of the world, but that the historic/anthropological/literary loss was immense, perhaps uniquely (or at least very exceptionally) so.
I'd be interested to know what journal articles you were reading that tried to list the lost works. This effort would be extremely difficult, if not impossible, since as far as I know we don't have a record of all the books that were stored at the Library when it burned as the Index was lost. We also don’t know when the Library was burned for sure, or whether the destruction was complete or partial. Some sources say that Julius Ceaser destroyed it by accident in 48BC, while others say that it was destroyed when Aurelion captured the city in 270AD.
There was also a second, smaller library,that may or may not have survived, the Serapeum, which some sources claim was destroyed at the same time as the larger Library, by Ceaser, though Socrates of Constantinople claimed that the Serapeum was destroyed by riots after paganism was declared illegal in 391AD. But Scholars of the fourth century never mentioned it existing, and if it did, it is unknown how many books it did contain, if any. Even Caesar’s burning may not have been as tragic as we think, since the Library had long since passed its heyday under the Ptolemies. In the early 2nd century BC scholars began to abandon Alexandria for safer cities with better patrons. In 145BC Ptolemy VIII expelled all of the foreign scholars as well. Furthermore, the Library made copies of all the books it could, and kept the originals, sending the copies back to their owners.
I suppose what could have been done by the authors of your articles, is to compile a list of books that are referenced in other works, which we don't have any more. If the last reference to them is just before the Library burned then it can be argued that it is possible that they were destroyed in the fire, though it will always be uncertain.
One thing to keep in mind however is that the Greeks were not modern scientists. They had some interesting ideas, and a pretty good culture of philosophic debate, but they often came up with completely wrong ideas such as Plato who claimed that the eye emitted light, or Megasthenes who claimed that lambs grew from trees, or Aristotle who claimed that the heart was the source of the mind, and the brain was just a cooling device. Their theories were later developed and many had to be completely replaced over the centuries, before we reached modern scientific accomplishments. Indeed some later scientists had to fight to break away from their influence in order to make progress. Science advances not from carefully preserving ancient ideas, but discovering new ones. It would definitely be academically interesting if we had more ancient texts that had survived to the modern day, but whether their survival would have advanced the progress of scientific understanding in any way is extremely debateable, even if we do assume that there were vast stocks of scientifically literate works that were lost, which is complete supposition in itself.
/u/rosemary85 has written several responses on this before (I, II, III) and perhaps might show up here to add onto his previous answers, but the sum of what you'll find there is that while we definitely lost some interesting stuff, to quote, "in overall terms it didn't really set European culture back at all: it was a single incident in a very large world, and there were many other good libraries around the Roman world."
This question has been asked a lot.
http://www.reddit.com/r/AskHistorians/comments/14h7qx/how_far_did_the_destruction_of_the_library_at/
Those were just from a quick search in the subreddit. It's also in the FAQ.
mathematical, astronomical, and mechanical treatises that were at least centuries ahead of their time
I am frankly a bit skeptical on this point. Any book of this kind by its nature would have been pretty useful, and so it would have been widely distributed.
More generally, it is not that Alexandria was some incredibly special place were people wrote incredibly advanced book and treatises and those were stored there in the library and only there.
Alexandria was certainly a very important place, but the strength of the library was that it gathered books from all over the world. It was after all at the center of a very important trade network.