La matematica come occasione e stimolo per la formulazione di un giudizio critico

The thesis develops an analysis of the scientific knowledge construction based on a psychological description of the mental procedures which in our mind help to construct the mathematical thought. The analysis was carried on in the Part I of the thesis and was supported by a deep insight in the scientific research experience concerning mathematics. This research was the opportunity for the personal encounter with the mathematical discipline and gave also the possibility and ispiration to question the meaning of the mathematical thinking and the reliability of its cognitive procedures. In Part II the results of psychological and cognitive experience of the scientific research, discussed in Part I, have been described in details. The results of the scientific research, both in basic and applied fields of mathematics, has been described in different papers appeared in national and international journals and are collected in the thesis' appendix.