Claudius Ptolemy's famous "Almagest" has long attracted the attention of astronomers and historians. It is believed to have been created in the 2nd century CE. It turns out that this is a mistake. Using the methods of geometry and statistics, the authors date the famous star catalog of Almagest to the era of the 7th - 13th centuries AD. The final edition of the whole Almagest was made, apparently, only in the 16th - 17th centuries AD. The method developed by the authors is applicable to any ancient star catalogs.