It’s unfortunate Marx was so bad at maths. Well, bad isn’t quite the right word, as he often expends a great deal of effort and creativity establishing the various mathematical conclusions he needs to establish, even when the conclusions are obvious. It’s rather wearing slogging through a whole chapter to finally get to the conclusion and realize what Marx has been trying to point out is the difference between the mean and the median. I do wonder what mathematical education was like in 19th century Prussia; Marx was an educated man, but seems to know less maths than you’ld expect from an 11 year old today.
Except, this mathematical inability turns out to reveal something important about Marx’s method. One of the most important aspects of skill in maths, I think, is a certain facility with abstraction, recognizing that the same thing can bear many different roles, and shuffling between these roles. The number 2, for example, can be a numerator or a denominator, or both, while still remaining the number 2. This kind of abstraction seems something Marx is incapable of. Perhaps the most obvious example is the way Marx doesn’t distinguish between a property and the way it is measured , and so rather than talking about, say, labor time and price as two different ways of representing the value of a commodity (in the way that, say, centigrade and and fahrenheit are two different ways of representing a temperature that exists separately from the representation), he discusses these as two separate things, which must be worked on to transform one to the other.
This resistance to a too-easy abstraction is, though, rather the point for Marx, because one of the things he wants to demonstrate in Capital is that capitalism is a system of real abstractions. Abstraction, that is, is not simply a mental process which leaves the world being abstracted unchanged. Instead, abstraction involves the production of social relations such that the abstraction can be acted on, and only then grasped by the mind. Abstract labor might be Marx’s best example of this, as he argues that the idea of work in general, as opposed to some particular type of work, depends on the whole process of primitive accumulation which brought about the existence of a class of wage laborers. It’s this idea that abstractions always arise from particular social relations which we can see at work in Marx’s laborious operations on the mathematics he discusses. Given the way that the abstractions of mathematical economics increasingly serve to evacuate any discussion of or resistance to social relations, Marx’s mathematics of suspicion, as we might call it, is salutory.