Giorgio Israel Bücher

Galileo and Newton’s work towards the mathematisation of the physical world; Leibniz’s universal logical calculus; the Enlightenment’s mathématique sociale. John von Neumann inherited all these aims and philosophical intuitions, together with an idea that grew up around the Vienna Circle of an ethics in the form of an exact science capable of guiding individuals to make correct decisions. With the help of his boundless mathematical capacity, von Neumann developed a conception of the world as a mathematical game, a world globally governed by a universal logic in which individual consciousness moved following different strategies: his vision guided him from set theory to quantum mechanics, to economics and to his theory of automata (anticipating artificial intelligence and cognitive science). This book provides the first comprehensive scientific and intellectual biography of John von Neumann, a man who perhaps more than any other is representative of twentieth century science.

The modern developments in mathematical biology, known as the "Golden Age of Theoretical Biology," occurred between 1920 and 1940, with Vito Volterra playing a crucial role. His interest in applying mathematics to non-physical sciences, particularly biology and economics, began around the turn of the century, highlighted in his inaugural address at the University of Rome in 1900/01. However, it wasn't until the mid-twenties, prompted by his son-in-law Umberto D'Ancona's inquiry about competition among animal species, that Volterra actively engaged in this field. From then until his death in 1940, he produced a substantial body of work. His aim was to adapt the models and concepts of classical mechanics to biology, creating a form of "rational mechanics" and "analytic mechanics" for biological associations. He sought to establish this new discipline on a solid experimental or empirical foundation, mirroring the approaches of mathematical physics. While few specific aspects of this reductionist program have endured, Volterra's contributions are now widely recognized as pivotal in inspiring further research in mathematical biology.

Che cosa sono gli oggetti della matematica, qual è la loro origine e la loro natura? L'intento di questo saggio è di mostrare che il difficile problema è stato reso oscuro e quasi insolubile dall'assunto che "il mondo è matematico". Questa tesi, che è indimostrabile in termini generali, è stata ammessa come un'ovvietà a partire da Galileo. Nella scienza contemporanea, con la sparizione del presupposto teologico presente nel pensiero galileiano, è divenuta un enigma, da cui tuttavia non ci si riesce a separare. Le analisi di questo saggio sono sviluppate in stretta relazione con quelle di Edmund Husserl di cui si dimostra la pertinenza, anche dal punto di vista della storia della scienza.