He went to the University of Leipzig in 1757 and took courses in medicine, philosophy, Latin, Greek, physics, mathematics, and aesthetics.
[2] Hindenburg's first published mathematical publication, Beschreibung einer ganz neuen Art, nach einem bekannten Gesetze fortgehende Zahlen, durch Abzahlen oder Abmessen bequem und sicher zu finden, originated as a project to extend then-existing prime tables up to 5 million.
In the book, he mechanically realizes, independent of the work done by Felkel,[3] the sieve of Eratosthenes, which he then proceeds with rules to both optimize and organize.
[5] In 1796, he edited the Sammlung combinatorisch-analytischer Abhandlungen, which contained a claim that de Moivre's multinomial theorem was “the most important proposition in all of mathematical analysis”.
[6] Another student, Johann Karl Burckhardt published the book Theorie der Kettenbrüche after being encouraged by Hindenburg to work on continued fractions.