The shift in meaning for mathema is likely a result of the rapid categorization during the time of Plato and Aristotle of their mathemata in terms of education: arithmetic, geometry, astronomy, and music (the quadrivium), which the Greeks found to create a "natural grouping" of mathematical (in the modern usage; "doctrina mathematica" in the ancient usage) precepts.
In a philosophical dialogue, King James penned the character Philomathes to debate on arguments of whether the ancient religious concepts of witchcraft should be punished in a politically fueled Christian society. The arguments King James poses through the character Epistemon are based on concepts of theological reasoning regarding society's belief, as his opponent, Philomathes, takes a philosophical stance on society's legal aspects but seeks to obtain the knowledge of Epistemon. This philosophical approach signified a philomath seeking to obtain greater knowledge through epistemology. The dialogue was used by King James to educate society on various concepts including the history and etymology of the subjects debated.2
"Philomath". Lexico UK English Dictionary. Oxford University Press. Archived from the original on 2021-05-07. https://web.archive.org/web/20210507072519/https://www.lexico.com/definition/philomath ↩
King James (2016) [1597]. Daemonologie (critical ed.). ISBN 1-5329-6891-4. 1-5329-6891-4 ↩