Short answers, pulled from the story.
Johann Matthias Gesner (the 9th of April 1691 - the 3rd of August 1761) was a German classical scholar, schoolmaster, and professor who became a major figure in Latin scholarship and educational reform. He held positions at Weimar, Ansbach, Leipzig, and Göttingen, where he produced influential reference works on the Latin language and founded the Deutsche Gesellschaft to promote German literature.
Gesner and Bach became good friends during Gesner's time as librarian and vice-principal at Weimar, where he worked from 1715. Bach later dedicated his Canon a 2 perpetuus, BWV 1075, to Gesner. The two men were also colleagues when Gesner served as rector of the Thomasschule at Leipzig, where Bach had been cantor since 1723.
The Novus Linguae et Eruditionis Romanae Thesaurus, meaning New Thesaurus of the Roman Language and Learning, was Gesner's major scholarly work, published in 1747 and continued under a related title in 1749. Gotthold Ephraim Lessing noted that passages from Horace, Virgil, Catullus, Juvenalis, and Cicero quoted in Baumgarten's Aesthetics of 1750 were drawn from Gesner's Thesaurus.
Gesner studied at the University of Jena as a theology student, working under Johann Franz Buddeus, who befriended him and allowed him to live in his own house. Before that, he attended the Ansbach Gymnasium, where rector Georg Nikolaus Köhler provided him with special instruction, loaned him Greek texts, and devised exercises in reconstructing texts from fragments.
Gesner founded the Deutsche Gesellschaft at Göttingen in 1738, an organization devoted to the advancement of German literature. He had likely become familiar with a similar organization during his earlier years in Leipzig.
Gesner served as librarian and vice-principal at Weimar from 1715, rector of the gymnasium at Ansbach from 1729, rector of the Thomasschule at Leipzig from 1730, and from 1734 as Professor of Poetry and Eloquence at the University of Göttingen, where he also served as librarian until his death in 1761.