Mammillaria baumii is known for over 80 years, originally placed to artificial genus Dolichothele. It is a nice and distinct plant, with larger flowers. It is a popular species in cultivation, but not as much as you would expect for such a nice plant. My guess is that it may be somewhat difficult plant to grow when traditional soil-based mixes and tight pots are used, due to it's huge taproots. This plant in the picture had split it's clay pot once, and now is in bowl-shaped pot for that reason.
In my conditions it presents no problems and treated as everything else. It is somewhat less tolerant to full sun when temperatures are over 40C, but so are many other plants I grow.
Mammillaria baumii comes from mountain areas of Mexican state Taumaulipas and moderately frost-hardy when dry. Flowering is diurnal and repeating over the summer.