In nineteenth-century, the studies leaded by German mathematicians about arithmetic were characterized by the pursuit of rigor, and of a strong support that served as a solid foundation upon which they could build the rest of mathematical knowledge. This project was developed not only because of the uncertain place on which mathematics of that time found themselves due to the emergence of new and unexpected results in geometry and analysis, but also because it was strengthened by the broader academic context, in which transformations in education and the German values of that period were shaping a particular conception of knowledge in which certain views on what and how should be studied were being privileged.
On the other hand, Mexico’s concerns about formality in demonstrations and about the search for a solid construction of mathematics emerged in the twentieth-century, in the decade of the forties, under the context of the establishment of the Faculty of Sciences and the professionalization of mathematics in the country. Because of this, the impact of studies such as those of Frege, Dedekind, Cantor, and Hilbert had a rather pedagogical orientation. An example of this, is “What is arithmetic?”, a book written by Francisco Zubieta Russi published in 1953. This book was the first to include the mathematical ideas of the above mentioned mathematicians on the principles that support arithmetic. The preface and the exposition of the notions of arithmetic throughout this book, give a clear idea of how mathematics and teaching of mathematics were conceived in this period.