After 2000 years of hard work, Descriptive Geometry allows us to study the Apollonian problem in space; we are able to establish the exact number of possible solutions and geometric relationships between the data and the solutions (Louis De Gaultier). And yet it does not provide a complete representation of the spheres that solve the problem, presumably because the classical construction is so complex it goes beyond the limits of precision of our graphic tools. Thanks to mathematical representation it is now possible to achieve two new results: the first involves the complete visualization of the solutions; the second, more important result, consists in a general geometric solution, valid, in other words, in the plane as well as in space, whatever the given data are: points, planes or spheres.