Was the Septuagint Destroyed When the Alexandrian Library Burnt Down in 48 BC?

Many Jewish apologists dislike the disproportionate competition between the more recent masoretic text (of which the oldest known complete copy dates to the 11th century AD) and the much older Septuagint text (the oldest mss. of which include 2nd-century-BCE fragments of Leviticus and Deuteronomy), and so they often criticize the latter in an attempt to discredit it. One of the more bizarre claims in their repertoire is that the Septuagint does not exist because it was destroyed when the Library of Alexandria was burnt down in 48 BC. This paper is a response to that claim.