On the removal of infinities from divergent series

The consequences of adopting other definitions of the concepts of sum and convergence of a series are discussed in the light of historical and epistemological contexts. We show that some divergent series appearing in the context of renormalization methods cannot be assigned finite values while preserving a minimum of consistency with standard summation, without at the same time obtaining contradictions, thus destroying the mathematical building (the conditions are known as Hardy’s axioms). We finally discuss the epistemological costs of accepting these practices in the name of instrumentalism.Fil: Natiello, Mario A.. Lund University; SueciaFil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentin