Why is the destruction of the Great Library of Alexandria considered to be one of the greatest tragedies of the academic world?

Because it was the loss of the ancient world's single greatest archive of knowledge.

Explanation:

Alexandria was founded in Egypt by Alexander the Great. His successor as Pharaoh, Ptolemy I Soter, founded the Museum (also called Museum of Alexandria, Greek Mouseion, "Seat of the Muses") or Royal Library of Alexandria in 283 BC. The Museum was a shrine of the Muses modeled after the Lyceum of Aristotle in Athens. The Museum was a place of study which included lecture areas, gardens, a zoo, and shrines for each of the nine muses as well as the Library itself. It has been estimated that at one time the Library of Alexandria held over half a million documents from Assyria, Greece, Persia, Egypt, India and many other nations. Over 100 scholars lived at the Museum full time to perform research, write, lecture or translate and copy documents. The library was so large it actually had another branch or "daughter" library at the Temple of Serapis.

The ancient library of Alexandria was part of an institution of higher learning known as the Alexandrian Museum. The library was intended as a resource for the scholars who did research at the Museum.