Cut into its simplest terms, Torah Umadda means that knowledge of non Torah subjects is a worthwhile pursuit for its own sake.
More conventional yeshivishe Torah hashkafa is that it is permitted to pursue secular knowledge for a specific purpose, as a kardom lachpor bah. But to study the sciences, humanities, philosophy or whatever in chachmas chitzonios, lishmah, as it were, would not be permitted. That would explain why the Rambam was involved in other chachmos, as they related to the various specific positions that he held, whether in Torah, medicine, community leadership, or government.