fractal_shark

How does an atheistic/materialistic view of the natural world account for pure mathematics?

Many contemporary atheists are materialists, believing that everything is reducible to the physical. This seems especially true of those who come from a scientific background. At the same time, much in modern mathematics doesn't seem to be rooted in the physical world. Prima facie, abstract topological spaces, Grothendieck universes, nonstandard models of arithmetic, large cardinals, and many more objects of mathematical study seem to not be about physical objects. Many of these have not seen application in scientific theories.

How does an atheistic materialistic worldview account for these abstract mathematical objects?

Edit: Some context to this question for readers in this thread. One of the things championed by contempory atheists/skeptics/whatever one chooses to call them is the importance of science education. This plays into the broader push for STEM---Science, Technology, Engineering, and Math---education. Yet the view of materialism advanced by these people doesn't seem amicable to a significant chunk of mathematics. To those of us in the M of STEM, it can seem as though we are being asked to support something that compromises the foundation of our discipline. Should we support this materialist skeptic push for science and empiricism? I think the answer is no if mathematics is one of the targets. My question is trying to get at whether this approach puts mathematics in a 'handmaiden to the sciences' role, or whether that's just a surface appearance. Judging by the answer I got, it appears to be more than just a surface appearance.

How does that account for mathematical objects that don't seem to be about the physical world (such as the ones I listed, the ones my question was about)? If mathematics is a language for describing the world, are these things not part of mathematics? Actually about the world despite appearances otherwise?

Sure, but that's not what my question is about.

My question is how a certain worldview accounts for the parts of mathematics that aren't a 'language for science'. I'm well aware that much of mathematics has application to the sciences. My question isn't about those parts of math.

This analogy is awful, but it's the best I could come up with in a few seconds: it's as if I asked for Krauss's opinion on apples and he replied by talking about oranges. They're both fruit, but I'm asking about apples.