The interaction between mathematics and technology

Scholars have paid little attention to the links between mathematics and technology, despite their practical relevance. Beginning with the use of basic aide-mémoires for counting and arithmetic, the article traces the evolution of the relationship between technology and mathematics, moving on to its application in weaving, construction, and other trades, the introduction of calculus to address technological issues, and finally, to the use of computers to address mathematical and technological problems simultaneously. An examination of this historical résumé reveals three significant philosophical concerns: the reliance of mathematical knowledge on technology, the clarification of the hybrid notion of a (technical) computation, and the (maybe unexpected) practical application of mathematics in technology. An overview of each of these topics is provided, and it is shown that to examine them, we must integrate resources and concepts from mathematics philosophy and technology philosophy. Finally, the argument is made that the philosophically and historically uncharted territories of the technology-mathematics connection hold much greater promise for future developments.