Freedom and truth in mathematics

The very essence of #mathematics is its freedom. (Georg #Cantor)

The way we deal with today's numbers in schools is essentially the same manner used by our ancestors Pythagoreans, who saw the numbers as concrete objects, of course, but in a way that prevented them from conceiving the infinity. The only ancient mathematician who approached the infinity was Archimedes, but in the history of mathematics can be considered a fairly unique case of lack of development mainly due to the isolation of the mathematicians at that time and of noticeable difference in quality between the Sicilian and colleagues. In order to return to touch the wall of infinity and use them in a profitable way the Earth had to wait the arrival of Georg Cantor.
The German mathematician actually faced numbers, revolutionizing mathematics, using essentially sets and logic, two tools that enabled him not only to approach, but even manipulate the infinite thanks to the transfinite numbers. Leading his steps was probably the following conviction:

The very essence of mathematics is its freedom.

According to Daniel Bonevac, this veritable mantra, written in 1883, is emblematic of the Cantor's libertarian approach to mathematics. With this milestone, Bonevac try to write a theory of mathematical truth, in order to explain some facts more or less established:

1) that the mathematical statements are either necessarily true or necessarily false;
2) that mathematical truth is derived primarily from logical truth;
3) that the existence in mathematics involves a kind of modality, which requires only the consistency or the constructability.