L’ombra del programa de Hilbert

Abstract

[en] The Hilbert’s program is one of the most important contributions of on the foundations of mathematics. Hilbert was looking with his program to formalize in a exact and precise way the foundations of mathematics. He did not get with the results but all of the questions that arose led to great math minds, like de Kurt Gödel o Alan Turing among other people, to get huge contributions in this field. Gödel’s incompleteness theorems changed the thinking of Hilbert and put an end to the Hilbert program, or at least to the approach that he and his disciples were chasing until then. Turing defined the notion of Computability in a clear and rigorous way with his machines later known around the world as Turing machines. Two very different characters,with different histories and theories, that had mu- tual intellectual admiration but never agreed physically or by correspondence. The passage of time has proved that there were many things in common in their teories. Currently, the Hilbert’s program continues to occupy an important place in the search for mathematical logic at the moment. The importance of having a solid foundation for the construction of our science is not just an issue that worries many mathematicians, but that is actually an essential topic for philosophical thought as the philosophy and logic go many times hand in hand in this path to the human mind.