5 Mathe matics as a Science

This chapter aims to consider mathematical knowledge not as the expression of some superior reality but as a huge collection of scientific facts whose shaping necessitated a fair amount of practical work. As we will see, by considering mathematical knowledge to be one specific product (among many others) of scientific activity, we may provide a reasonable explanation of its capacity to make important differences in other scientific domains (neurology, geography, gambling, computer science, etc.). Once this operationalization exercise is over, I will come back to the main goal of this part III: understanding when, how, and why mathematical knowledge takes active part in the constitution of algorithms (chapter 6).