To Engels’s mind, there was nothing in math that was not already in nature; mathematics was simply a reflection and an explanation of the physical world. As a result, he attempted to crowbar all sorts of mathematical models into his system of dialectics. “Let us take an arbitrary algebraic magnitude, namely a,” begins one passage in Dialectics of Nature. “Let us negate it, then we have -a (minus a). Let us negate this negation by multiplying -a by -a, then we have +a, that is the original positive magnitude, but to a higher degree, namely to the second power.” As the Trotskyist scholar Jean van Heijenoort points out, this is all horribly confused: to take just one example, ”negation” in Engels’s usage can refer to any number of differing mathematical operations. Worse was to come as Engels, playing the reductive philistine, dismissed complex numbers and theoretical mathematics—those parts of theoretical science that went beyond a reflection of natural phenomena—as akin to quackery: “When one has once become accustomed to ascribe to the [square root of] -1 or to the fourth dimension some kind of reality outside of our own heads, it is not a matter of much importance if one goes a step further and also accepts the spirit world of the mediums.”

Tristam Hunt, Marx’s General: The Revolutionary Life of Friedrich Engels, New York, 2009, pp. 286-287