Just how "unreasonably effective" is mathematics, anyway? First, why does math accomplish so much for us in (apparently, in practice at least) understanding the "real world" around us? Then, what are the limits of what it can accomplish? Can it tell us why there is anything substantial at all, and why the world is the way it is? Here I argue related theses. First, mathematics is good at judging relative consistency (such as, whether a given model universe will be able to satisfy conservation of mass-energy.) This is demonstrated through a novel argument explaining why our universe must have three large spatial dimensions, in terms of the self-consistency of electromagnetic relations. Then, I argue that math has no ability to explain its own effectiveness in a "real world," or to explain the particular foundational properties of our world. Furthermore, math cannot explain why some possible worlds have "concrete" or "real existence" and others do not. Indeed, the very idea there is such a distinction is surprisingly problematic and questionable, as argued by Max Tegmark and others. Finally: any such existential distinction would be inaccessible to computational (AI-theoretical) intelligences.
Neil Bates