“All teaching and all intellectual learning (mathesis) come about from already existing knowledge”. The beginning of Posterior Analytics was a topos in the sixteenth century. Aristotle synthesizes many things in these few words. Interpreted in early modern and modern terms, this statement contains the questions we are going to discuss in this section of the journal containing four articles. What matters for us is not so much what Aristotle meant by the sentence in the epigraph, but how sixteenth-century mathematicians and mathematical practitioners understood this text. Jacob Klein, in his two essays, developed a history of number and counting from the Pythagoreans to Wallis’ Mathesis Universalis (1657).