Two centuries-two crises in theoretical research

Resumen

paper, the chronologically first one has a logical nature and concerns the impossibility of demonstrating the internal coherence of mathematics. The second one has a sociological nature and is linked to the new features that distinguish pure contemporary research from pre-world war II research. These new features give strong scientific corporations the power to impose to society, as scientific truths, lines of research (paradigms) regardless of their actual scientific values. The danger of potential abuse of this power is illustrated with the case study of quantum computer. The last part of the paper is devoted to the analysis of the case of pure theoretical research, where this danger is stronger than in scientific fields more directly linked to external reality. The final part of the paper outlines some poposal to counter the risk of a decline in the general level of pure theoretical research and to re-establish its role as driving force of the development of science.