How were Kurt Gödel's contributions revolutionary? What contribution did his incompleteness theorems make to our understanding of the foundations of mathematics? Why is his mathematical thinking so philosophical?

With
Jean-Paul Delahaye, mathematician, specialist in artificial intelligence
On September 7, 1930, in Königsberg, a young Austrian mathematician, Kurt Gödel, presented an unexpected result to an audience of logicians and philosophers: he demonstrated that no mathematical theory can ever tell us everything about the objects it deals with. Certain statements, known as “undecidables”, escape the theory in the sense that it cannot demonstrate whether they are true or false. Demonstrated with the utmost rigor, this result revolutionized logic, of course, but also the philosophy of mathematics, as it put an abrupt end to the dream of absolute coherence that mathematics could construct. It also has implications for computer science and artificial intelligence.