memes

I apologise for disappearing for a few days. Dealing with stress, in particular due to this discussion, and with more 'professional' stuff. I have not read everything in the thread that got posted since I last replied here yet, and will probably not be able to do so quite right now.

Maybe a better phrasing would be that math is another paradigm of matter

In what sense? If by the word 'paradigm' you just mean 'a collection of ideas' (where an 'idea' is any non-material object), then the expression 'a collection of ideas of matter' doesn't make sense in this context without further clarification.
If you mean that it is some sort of a collection of theories about matter, then there are, again, problems. Math-as-what-mathematicians-study is not a theory, not a collection of thought patterns, research methods or anything like that - it exists independently of our minds. Also, not particularly relevant, but math as the body of knowledge about what mathematicians study tells us nothing about matter without application of the sort that physicists and chemists engage in.

another way of visualizing matter

Math-as-what-mathematicians-study is not any sort of way of visualising anything, though. We can use knowledge about that stuff in order to help us visualise things, both material and non-material, like we know how to draw an annulus and we know that a Laurent series generally converges for z within a metric annulus on the complex plane, meaning that we can visualise the region of convergence of such a series with a relevant drawing (or imagine a relevant drawing), or like how we can use our knowledge of the fact that roughly half of uranium-238 decays into uranium-234 within 4.5 billion years or so to make a relevant drawing (or, again, imagine one).

Math does not exist in a vacuum, this is a big difference between metaphysics and Marxism, things do not exist in a vacuum

Not sure what you mean by 'existing in a vacuum'. In the literal sense, it is incorrect, as math is not a material thing, and does not have a location in any reasonable sense in this context.
If by that you mean that it depends on matter, then that seems to be an assumption/axiom that you subscribe to. That assumption does not seem to have a good basis. How would matter have to be different in order to, for example, eliminate the idea of the field of rational numbers? Or do you have another example of a dependency of math-as-what-mathematicians-study in mind?

Math studies have to converge to the currently developed laws of math or it is not math but nonsense

What do you mean by 'converge' here, and what relevance does this sentence have to this topic?
What mathematicians study can be said to be 'the laws of math'. The study of math can't be said to 'converge' in any sense that I can think of, other than colloquial and imprecise, in which case I'm not sure what exactly it is that you mean.

Furthermore, are there any conclusions that Marxism draws from materialism about society, economics, politics, communist praxis, epistemology or some human activity that I have failed to consider here? Because if not, it seems that we are in the same boat with the exception that I say that some non-material things are non-mental and are not dependent on matter, while matter has dependencies on it, and you say that there are no such things.

I apologise for disappearing for a few days. Dealing with stress, in particular due to this discussion, and with more 'professional' stuff. I have not read everything in the thread that got posted since I last replied here yet, and will probably not be able to do so quite right now.

I think the misstep that you're taking is equating 'material' with 'physical' or relating to '(physical) matter'

But then what you mean by 'material' also encompasses non-material things, which doesn't align with how the word 'material' is used in philosophy. This also supports the thoughts that I have been left with for a while at this point that there is no conflict between Marxism and idealism. Just between Marxism and some forms of idealism that are often presented to encompass all of idealist schools of thought.

Also, can you provide a source for your definition of the word 'material'? Also, as of right now, I do not understand what exactly it is that you mean by it if not that a 'material' object is one that consists of matter (and, perhaps, that a 'material' process is one that involves material objects, etc.).

I could be wrong: are you referring to any particular Marxists as a source for your definition of materialism and it's coincidence with idealism?

I never claimed that materialism 'coincides' with idealism. What I have claimed is that Marxism doesn't conflict with idealism (in particular, with the views that I subscribe to).
Strictly speaking, my claim is incorrect, because at least usually Marxists do seem to take as an axiom that all ideas depend on matter in some way, but

1. I don't see any significant conclusions that are drawn from that assumption that conflict with idealism.
2. Judging by how often Marxists who criticise/reject idealism don't actually mean idealism in general, but just some idealist schools of thought. More specifically, ones that only distinguish mental stuff out of non-material. These would be people like, for example, (some of) idealist mathematical intuitionists seem to believe (as opposed to materialist mathematical intuitionists).

Personally, I haven't come across a single Marxist who treats materialism and idealism as compatible

I do not treat them as compatible, except in the sense that there are types of materialism of different strictness. I don't think that anybody here subscribes to strict materialism that posits that nothing but matter exists, for example.
What I am saying is that Marxism is fundamentally 'agnostic' in this sense. All of the relevant conclusions can be made in various idealist and materialist frameworks, especially if we allow for some basic rewording. Again, at the very least currently I am not aware of any relevant conflicts.

Although, I think that all the 'idealism vs materialism' arguments do lack an evaluation of a view that neither matter nor ideas have any sort of 'primacy' in any reasonable sense, considering that idealism and materialism are often defined through specifically the 'primacy' thing (as opposed to through what is labelled as 'existing', which is how the relevant terms are defined in at least some traditions), and, bizarrely, I have not encountered the position that I just outlined yet.

idealism does not equate to ideas simpliciter

Not sure what you are trying to say here.

1. If you mean that, literally, that words 'idealism' and 'ideas' are not synonymous, then that is obviously correct.
2. If you mean that idealist schools of thought do not generally say that ideas are the only thing that exists, then yes, that is correct. In particular, I do say that matter exists.
3. If you mean that idealism does not necessarily claim that ideas have primacy over matter, then there is an issue. While, for example, I claim that there are ideas (such as what mathematicians study) that are independent of matter but not vice versa, and that I also claim that there are ideas (like, for example, our imagination and perception of things, including what is studied by mathematicians as well as how that stone that you just threw skimmed over the water) that either have dependency on matter but not vice versa or, at least, that matter has some sort of 'primacy' over those, I do claim that some ideas do have some sort of 'primacy' over matter. If you do not define 'idealism' and 'materialism' through some sort of 'primacy' or even existence of relevant objects, then how do you define those?

In any case, my main point is that, so far, I do not see any significant conflicts between Marxism and idealism.

Science doesn’t not have to be positivist. I think most scientists actually understand that. For example the laws of thermodynamics break down at a quantum level and we’re still trying to come up with and test better models that can incorporate that new information.

What I mean to say about the laws of thermodynamics is they are incredibly useful in describing how and why things change. These were not all worked out when Marx was developing his theories. Yes, Marx and Engels were up to date with the science of their time and they make reference to work and power. However they lacked an understanding of entropy if only because scientists had only begun to experiment with the concept. That’s very clear especially if you read Engels’s Dialectic of Nature. In it he explicitly argues against ideas that would come to be core to the science of thermodynamics.

That’s all to say I suspect if those developments in physics had occurred maybe 40 years earlier, Marx would have formulated a much more precise concept of value. Then maybe he wouldn’t have needed to write so much about linen coats.