Publisher's Synopsis
In this book I will speak about unprovable truths within mathematics, namely truths that principles of mathematics cannot prove. I will focus my attention on G ¨odel's sentences and the Continuum Hypothesis. You have to pay attention to the fact that the Continuum Hypothesis was considered by David Hilbert as the fist mathematical problem to be solved. Unfortunately this problem does not have a solution as we will see. This book is constituted by two parts (e.g. two main chapters). In the first part, the i will address mathematical issues related to logic. In this part i will explain G ¨odel's theorems . This part must be considered as a sort of introduction to the part about the continuum hypothesis . This book might be considered a kind of travel where we can see how the phenomenon of incompleteness (e.g. unprovable truths) arises within mathematics. Many mathematicians, including Presburger, Skolem, Hilbert, Peano, Godel, Cohen and Woddin, during the last century were dreaming complete theories.
