Machine learning leads mathematicians to unsolvable problem

The mathematicians, who were working on a machine-learning problem, show that the question of ‘learnability’ — whether an algorithm can extract a pattern from limited data — is linked to a paradox known as the continuum hypothesis. A 1940 result by Gödel (which was completed in the 1960s by US mathematician Paul Cohen) showed that the continuum hypothesis cannot be proved either true or false starting from the standard axioms — the statements taken to be true — of the theory of sets, which are commonly taken as the foundation for all of mathematics. Gödel and Cohen’s work on the continuum hypothesis implies that there can exist parallel mathematical universes that are both compatible with standard mathematics — one in which the continuum hypothesis is added to the standard axioms and therefore declared to be true, and another in which it is declared false.

Source: www.nature.com