Multi-purpose Device for Understanding Mathematics and its Development, or Empty Generalization?
“Embedding” as a technical concept comes from linguistics, more precisely from grammar. The present paper investigates whether it can be applied fruitfully to certain questions that have been investigated by historians (and sometimes philosophers) of mathematics: 1. The construction of numeral systems, in particular place-value and quasi place-value systems. 2. The development of algebraic symbolisms. 3. The discussion whether “scientific revolutions” ever take place in mathematics, or new conceptualizations always include what preceded them. A final section investigates the relation between spatial and linguistic embedding and concludes that the spatio-linguistic notion of embedding can be meaningfully applied to the former two discussions, whereas the apparent embedding of older within new theories is rather an ideological mirage.