It is not, especially not in the sense of math as what mathematicians study, but, again, math as an academic discipline is also not that. Math as an academic discipline says nothing about matter. Physics and chemistry (as academic disciplines) do.

Maybe a better phrasing would be that math is another paradigm of matter, another way of visualizing matter. Still i stand by what i said, even if mathematician studies are seemingly abstract, it is only because we have developed math to a higher stage of development than other disciplines and thus have lost the forest for the trees.

It’s the other way around, however. Math as what mathematicians study is not dependent on matter in any way.

Math does not exist in a vacuum, this is a big difference between metaphysics and Marxism, things do not exist in a vacuum… Math studies have to converge to the currently developed laws of math or it is not math but nonsense.

“Contrary to metaphysics, dialectics does not regard nature as an accidental agglomeration of things, of phenomena, unconnected with, isolated from, and independent of, each other, but as a connected and integral whole, in which things, phenomena are organically connected with, dependent on, and determined by, each other.” (Dialectical and Historical Materialism)

What do you mean by ‘material’?

Nevermind, I saw your comment below.

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

Marxists don’t study things, they study relations and processes. So when Marxists talk of ‘material’, they’re speaking of ‘material relations’. This includes physical objects, of course, and also social relations and e.g. gravity or magnetic fields. Money or value as social relations are as material as gravity or a flower; such relations have very real, very tangible effects on the world even if you can’t see or touch the relations.

You seem to be transposing your own definition of ‘material’ onto historical and dialectical materialists who hold a very different definition. You’re just going to speak past people if you do that.

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? You say that you’re:

yet to encounter any conflicts in … [t]he entire foundation of Marxism (dialectical materialism) [and] the foundation of idealism[.]

Personally, I haven’t come across a single Marxist who treats materialism and idealism as compatible. Even those who admit that ideas can shape reality (including Marx himself) do so from a position of rejecting idealism. In that sense, just as material does not equate to (physical) matter, idealism does not equate to ideas simpliciter.

All these debates are rooted in historic philosophical traditions. You can’t dismiss the essence of Marxism on the basis of modern, dare I say idealistically universalised, notions of what these terms mean; you have to go back to the beginning and situate the terms in their historical context. That is another aspect of Marxism—insisting that relations are historically contingent, meaning that e.g. definitions can change through the epochs.

That pure mathematics has a validity which is independent of the particular experience of each individual is, for that matter, correct, and this is true of all established facts in every science, and indeed of all facts whatsoever. The magnetic poles, the fact that water is composed of hydrogen and oxygen, the fact that Hegel is dead and Herr Dühring alive, hold good independently of my own experience or that of any other individual, and even independently of Herr Dühring’s experience, when he begins to sleep the sleep of the just. But it is not at all true that in pure mathematics the mind deals only with its own creations and imaginations. The concepts of number and figure have not been derived from any source other than the world of reality. The ten fingers on which men learnt to count, that is, to perform the first arithmetical operation, are anything but a free creation of the mind. Counting requires not only objects that can be counted, but also the ability to exclude all properties of the objects considered except their number — and this ability is the product of a long historical development based on experience. Like the idea of number, so the idea of figure is borrowed exclusively from the external world, and does not arise in the mind out of pure thought. There must have been things which had shape and whose shapes were compared before anyone could arrive at the idea of figure. Pure mathematics deals with the space forms and quantity relations of the real world — that is, with material which is very real indeed. The fact that this material appears in an extremely abstract form can only superficially conceal its origin from the external world. But in order to make it possible to investigate these forms and relations in their pure state, it is necessary to separate them entirely from their content, to put the content aside as irrelevant; thus we get points without dimensions, lines without breadth and thickness, a and b and x and y, constants and variables; and only at the very end do we reach the free creations and imaginations of the mind itself, that is to say, imaginary magnitudes. Even the apparent derivation of mathematical magnitudes from each other does not prove their a priori origin, but only their rational connection. Before one came upon the idea of deducing the form of a cylinder from the rotation of a rectangle about one of its sides, a number of real rectangles and cylinders, however imperfect in form, must have been examined. Like all other sciences, mathematics arose out of the needs of men: from the measurement of land and the content of vessels, from the computation of time and from mechanics. But, as in every department of thought, at a certain stage of development the laws, which were abstracted from the real world, become divorced from the real world, and are set up against it as something independent, as laws coming from outside, to which the world has to conform. That is how things happened in society and in the state, and in this way, and not otherwise, pure mathematics was subsequently applied to the world, although it is borrowed from this same world and represents only one part of its forms of interconnection — and it is only just because of this that it can be applied at all.

• Friedrich Engels, Anti Dühring

Yup. I should have added that part but forgot.

I think the true utility of dialectics to Marx was that it allowed him to intuit how change actually occurs in our material world without relying on the science of thermodynamics which didn’t exist yet.

It’s more than just thermodynamics. I don’t think dialects can simply be reduced to science (that is positivism, which marx rejected). It might be better to say that dialects is the philosophy of science.

Plus, marx was well aware of thermodynamics. In fact, the whole idea of labor-power was inspired by horse-power. And value was conceived of as the economic analogue of work.

I think it’s more correct to say dialectical materialism is a subset of materialist philosophy. It’s not a dualist philosophy because the mental realm is not conceived of as a separate thing

This line of thinking indicates the assumption that the only type of idealism is the sort that posits that only matter and ‘mental’ non-material stuff exists. There are other types, including ones that do not consider said ‘mental’ stuff to exist.
I myself, for example, fall under the camp of considering non-material non-mental stuff to exist, in addition to mental stuff. I consider some, but not all, of the former to have no dependencies on material stuff, with material stuff being dependent on such, and that all mental stuff depends on material stuff. I am yet to find any sort of conflicts with Marxism on these grounds (or in general, sans, perhaps, some wording that is used by Marx or other people).

Because Marxists think of ideas as themselves being material things. Marxism is not a dualist philosophy. For us, ideas exist as brains, books, TV programs and so on. There is thus even some interesting theories about how the medium itself changes the ideas. Furthermore, in marxist theories, ideas are not given equal weight to the rest of the system. Ideas are only a small part of material reality.

Again, for example, I am a mathematical Platonist. What beliefs of mine in that regard contradict with Marxism?

Well for one you see math as something independent, you see math existing in a vacuum.

"Contrary to metaphysics, dialectics does not regard nature as an accidental agglomeration of things, of phenomena, unconnected with, isolated from, and independent of, each other, but as a connected and integral whole, in which things, phenomena are organically connected with, dependent on, and determined by, each other.

The dialectical method therefore holds that no phenomenon in nature can be understood if taken by itself, isolated from surrounding phenomena, inasmuch as any phenomenon in any realm of nature may become meaningless to us if it is not considered in connection with the surrounding conditions, but divorced from them; and that, vice versa, any phenomenon can be understood and explained if considered in its inseparable connection with surrounding phenomena, as one conditioned by surrounding phenomena." (Dialectical and Historical Materialism)

This is my understanding of your views from what you wrote in other replies, i haven’t read and don’t plan to read about mathematical Platonism, we already have developed much further than whatever Plato worked with.

The production of ideas, of conceptions, of consciousness, is at first directly interwoven with the material activity and the material intercourse of men, the language of real life. Conceiving, thinking, the mental intercourse of men, appear at this stage as the direct efflux of their material behaviour. The same applies to mental production as expressed in the language of politics, laws, morality, religion, metaphysics, etc., of a people. Men are the producers of their conceptions, ideas, etc. – real, active men, as they are conditioned by a definite development of their productive forces and of the intercourse corresponding to these, up to its furthest forms. Consciousness can never be anything else than conscious existence, and the existence of men is their actual life-process. If in all ideology men and their circumstances appear upside-down as in a camera obscura, this phenomenon arises just as much from their historical life-process as the inversion of objects on the retina does from their physical life-process.

In direct contrast to German philosophy which descends from heaven to earth, here we ascend from earth to heaven. That is to say, we do not set out from what men say, imagine, conceive, nor from men as narrated, thought of, imagined, conceived, in order to arrive at men in the flesh. We set out from real, active men, and on the basis of their real life-process we demonstrate the development of the ideological reflexes and echoes of this life-process. The phantoms formed in the human brain are also, necessarily, sublimates of their material life-process, which is empirically verifiable and bound to material premises. Morality, religion, metaphysics, all the rest of ideology and their corresponding forms of consciousness, thus no longer retain the semblance of independence. They have no history, no development; but men, developing their material production and their material intercourse, alter, along with this their real existence, their thinking and the products of their thinking. Life is not determined by consciousness, but consciousness by life. In the first method of approach the starting-point is consciousness taken as the living individual; in the second method, which conforms to real life, it is the real living individuals themselves, and consciousness is considered solely as their consciousness.

This method of approach is not devoid of premises. It starts out from the real premises and does not abandon them for a moment. Its premises are men, not in any fantastic isolation and rigidity, but in their actual, empirically perceptible process of development under definite conditions. As soon as this active life-process is described, history ceases to be a collection of dead facts as it is with the empiricists (themselves still abstract), or an imagined activity of imagined subjects, as with the idealists.

Karl Marx - The German Ideology
https://www.marxists.org/archive/marx/works/1845/german-ideology/ch01a.htm

My understanding of this passage is that in idealist thinking, ideas shape reality but in materialist thinking, material reality shapes ideas.

Look into historical materialism. Marx’s materialist method of understanding how human societies evolved hinged on giving primacy to factors like energy, production, population and ecology. It allowed him to construct an understanding of anthropology so advanced for his time that when I was being taught anthropology by my uni professors I legit thought he was a Marxist. Only later did I realise that marx’s method is today being rediscovered and being touted as some new revolutionary thinking.

Another point in which materialism is important to Marxism is with economics. Whole today’s economic theories on value consider it to be subjective, marx analysed value through constraints on labour in an economy. The method that he used was a kind of primitive linear programming. It then inspired the creation of actual linear programming, which won Nobel prizes and forms the backbone of economic planning even in capitalist firms.

Really, marx’s dialectical materialism was one of the first scientific approaches to fields and political movements (economics, history, socialism) dominated by idealism and hodgepodge theories. It is the reason why marx was so influential beyond his years and beyond his contemporaries like proudhon and fruerbach

Does Marxism draw any [relevant] conclusions from materialism?

Of course. One of the tenets of Marxism is that social being determines social consciousness, not vice versa. This is textbook materialism. Anything else simply leads to liberalism, religion, etc.

the idealist schools of thought that only recognise material and non-material mental stuff

You seem confused. There are two main currents in philosophy - materialism, which posits that nature is primary to spirit, being is primary to thought, and idealism, which posits the opposite. In between the two there are agnostics, who claim this question is impossible to answer. This has nothing to do with whether a philosophy “recognizes non-material stuff”.