Last time on this series, I talked about the word manifold. Today, we’re going to add a modifier.
In fact, 代数 appears to be a prefix that means algebraic, and is used in many other situations. Here, the two kanji are actually pretty straightforward in why they make something algebraic.
The first is 代, which here is pronounced dai, and has a great many other pronounciations. It also has a great many different shades of meaning. But the obviously relevant one here is “substitute” or “replace.”
The second kanji, 数, is pronounced
kazu su here, again among many other things. The meanings are “number,” “law,” “figures,” and the like. (According to a commenter, only “number” and “to count” are common meanings, the others may be archaic)
So together, they mean something like “substituting numbers” or “laws of substitution,” which mean algebra. As last time, we discussed the word “tayoutai,” or manifold, this means that daisutayoutai translates as “algebraic manifold.”