Mammillaria celsiana?

In flower today 11-5-08

I think this is the right name. It is an old plant which has been grown in the bed for many years. Hunt believes this is referable to either M.muehlenpfordtii or M.dixanthocentron, if so then it must be a extreme form. I have seen a plant of this in the past which had divided dichotomously into four heads.

M. celsiana - yes maybe, but the original celsiana was actually given to a plant with long central spines, a form of neopositana that is synonymous with muehlenpfordtii.
It has also been applied to forms of dixanthocentron, in particular a form recollected by Lau under his number 1087.
So which is your plant? perhaps a short spined version of muehlenpfordtii would be my best guess, based upon the bristle like radial spines primarily. I have a Lau 1087 and it has much more defined, and fewer, radial spines, and the central spines are somewhat longer, although not as long as some dixanthocentron forms.
But celsiana according to our Dr Hunt is a name best dispensed with, because of the confusion with which it seems to be applied. In Craig the type locality of celsiana is said to be San Luis Potosi, and Mexico state, and Oaxaca. Hmmm........
It is difficult to see what Lemaire original description was based upon, as none of my literature contains that text, only references to it.