A mathematical phenomenon or event is the publicationPublication of a mathematical document—letters, manuscripts, articles, books. The foundation of the history of mathematicsHistory of Mathematics is a scientific biography and bibliography. For two millennia, the history of mathematics presented as a chronologically ordered sequence of mathematical phenomenaPhenomena: “who is after whom.” The belief reigned that mathematics is an unshakable body of knowledge, given to us by a Greek miracle. The history of mathematicsHistory of Mathematics reached a scientific level in the Age of Enlightenment. A doctrine appeared about historical documents, about the signs of their reliability, ways to distinguish falsificationFalsification, about ancient written instruments and materials, about styles. For the first timeTime, an understanding of the progress of mathematics arose. The history of mathematicsHistory of Mathematics began to be presented by professional mathematicians as the history of concepts, ideasIdeas, theories. The article focuses on the evolvement of the history of mathematicsHistory of Mathematics as a science and the development of its methodology from the fourth century B.C. to the age of Enlightenment. We consider works of Eudemus of Rhodes[aut]Eudemus of Rhodes, Pappus[aut]Pappus, Thabit ibn Qurra[aut]Thabit ibn Qurra, Johannes Buteo[aut]Buteo, Johannes, Pierre de la Ramée[aut]de la Ramée Pierre, Joseph[aut]Ramée, Pierre de la Justus Scaliger[aut]Scaliger, Joseph Justus, Dionisius Petavius[aut]Petavius, Dionisius, Bernardino Baldi[aut]Baldi, Bernardino, Joseph Blancanus[aut]Blancanus, Joseph, Gerardus Johann Voss, [aut]de Chales Claude-FrancoisClaude-Francois de Chales[aut]Chales, Claude-François de, Jean Mabillon[aut]Mabillon, Jean, John Wallis[aut]Wallis John, Edward Bernard[aut]Bernard, Edward, Joseph Raphson[aut]Raphson, Joseph, Christian von Wolff[aut]Wolff, Christian von and Johann Heilbronner[aut]Heilbronner, Johann.