"According to Guth, he had discovered the equations of De Sitter's cosmology (1917), written in the form introduced somewhat later by Georges Lemaitre (1925), as part of his MIT Thesis, before introducing inflation as the starting point of his new cosmology. After taking care, by means of inflation of the "monopole problem". ...Guth went one step further to solve the so called "flatness problem". ...Guth finally goes on to explain how his theory of inflation solves the "horizon problem". ...we will analyze in some detail to what extent the "monopole problem", the "flatness problem" and the "horizon problem" require, or not, cosmic inflation as a problem solving "paradigm"."