ABSTRACT
The beginning of the 20th century was a foundation crisis for mathematics. Bertrand Russell had just published the paradox that bears his name. This devastating paradox shows the extreme difficulty to build mathematics upon solid foundations. In the absence of such foundations, mathematics looked like a sandcastle that could fall apart at the first wave. In 1963, the mathematician Andrey Kolmogorov answered by the affirmative. Kolmogorov built upon the theory of computation of Gödel, Church, and Turing, to define a measure of complexity for numerical sequences like 1, 2, 4, 8, 16, 32 and 1, 2, 4, 8, 16, 31. The language of probability then becomes essential. In particular, instead of making a deterministic guess - like saying that the next element of the sequence will be precisely 32 - it seems more reasonable to make a probabilistic prediction.
