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Of course we'll never know for sure, but do historians have some reasonable ideas about what knowledge may have been lost at the Library of Serapeum of Alexandria, when it was destroyed by the Decree of Theodosius in 391?

From the movie "Agora" it is shown that the pagan occupants attempted to save whatever they could, and suggests that there may have been philosophical, mathematical, and astronomical research. However, Wikipedia information suggests that at this time the library may not have had such information:

The Serapeum housed part of the Great Library, but it is not known how many, if any, books were contained in it at the time of destruction. Notably, the passage by Socrates makes no clear reference to a library or its contents, only to religious objects. An earlier text by the historian Ammianus Marcellinus indicates that, whatever books might earlier have been housed at the Serapeum, none was there in the last decade of the 4th century. The pagan author Eunapius of Sardis witnessed the demolition, and though he detested Christians, and was a scholar, his account of the Serapeum's destruction makes no mention of any library.

So, my question is: in this or other destructive events, did the Library of Alexandria house information that was lost, and caused for lack of a better term, a setback for the progress of human knowledge?

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Agora, while a nice film, is not historically accurate but a story based on some historical facts. See maria Dzielska's Hypatia of Alexandria for a better source: amazon.co.uk/Hypatia-Alexandria-Revealing-Antiquity-Dzielska/dp/… –  Sardathrion Oct 31 '11 at 8:26
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The Serapeum is actually a smaller "branch" of the original library, formally part of the Temple of Serapis. The temple was converted to a Christian church by Theophilus around 390 AD, and it appears this is the reference you have noted above. This "branch" was not actually destroyed, but there is no doubt that many documents were destroyed during the conversion.

The official library, known as the Royal Library of Alexandria, was much larger and housed over half a million documents at the height of its glory. There are three different claims to having destroyed the original library, but we may never know exactly who was responsible.

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Italian author Lucio Russo in his book "Forgotten revolution" argues that a large part of the scientific knowledge of Hellenistic world has been lost. I find his arguments very convincing.

Exact sciences in the modern sense of this word originated in Ptolemaic Egypt and other Hellenistic states, and reached very high degree of development. Few first class works survived, like Euclid, Apollonius and Archimedes, but there is a lot of evidence that this is just a tip of the iceberg. For example, almost all writings of Hipparchus, "the father of astronomy" are lost. We know about them from the account of C. Ptolemy who lived 3 centuries later. Or look at the "Antikythera mechanism" on Wikipedia and elsewhere, to get some evidence of what was lost.

L. Russo is a mathematician, and on his opinion, the level of development in some areas of mathematics in Hellenistic time was not really surpassed until XIX century. I am also a mathematician, and I confirm this.

This does not only apply to exact sciences. Critical scientific study of ancient texts, as we understand it now, also apparently originated in these Hellenistic states.

A legend says that one of the Ptolemy rulers tried to buy (from Athens) original texts of Aeschylus, Sophocles and Euripides. Athenians refused. Then he asked to borrow them to copy. Athenians agreed, but required an enormous security deposit. He payed the deposit, and did not return the original manuscripts:-)

The same Ptolemy issued the order that all ships arriving to Alexandria must be inspected and searched for books. All books found must be copied.

So we really lost a lot with Alexandrian library. When exactly it disappeared and how, is also subject to discussion. Some blame Julius Caesar who started a fire during a battle that destroyed a large part of the library. Other people say that it still existed at the time of the Arab conquest, and was destroyed by the conquerors. And many events in between are also mentioned.

The fact is that Claudius Ptolemy (astronomer, who probably worked in Alexandria in 2 century AD) could read Hipparchus. And we cannot.

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