History of Mathematics



Starting from delate 19th century, Mathematics evolved significantly, reaching not only high-level risults but also an incredible level of generality and abstraction of topics and style. We could trace back to that period the origin of “modern” Algebra (which differentiated itself from the previous theory of equations), the birth of Functional Analysis which benefitted of the fundamental contribution of the Italian mathematician Vito Volterra, and it next reshuffling in algebraic and structural terms by the Bourbaki group in France since 1930s.

A focus on syntactic aspects was the essential precondition for the applications of Mathematics outside the traditional boudaries of Physics. The emergence of the first models, which derived from the application of Mathematics to the field of Economic Analysis, paved the way to the period between the two World Wars of the hight-theory on the existence, unicity, and stability of the economic equilibrium.

At the same time, however, the Italian school of Mathematics went through a dull period. The relationship between this decrease and the different political climate provides us good material for a case-study on the connection between text and context, and between the development of scientifc thinking and the surrounding social environment.