Apelt graduated from secondary school in Zittau and entered the University of Jena in 1831.
[1][2] Apelt was a student of Jakob Friedrich Fries,[3] succeeding him at the University of Jena.
He was the principal contributor to the Abhandlungen der Fries'sche Schule, which he founded with Matthias Jakob Schleiden.
[4] He was also one of the early scholars of the life and work of Johannes Kepler, a precursor of Alexandre Koyré.
[5] His son Otto Friedrich Apelt made important contributions to the debate on the nature of the categories of Aristotle.