1. The Monte Carlo Hypothesis

The Prime Number Theorem says how the prime numbers are distributed but not why. On the other hand, an information-theoretic analysis of the Prime Number Theorem indicates that they are distributed in this way because prime encodings are algorithmically random and the prime numbers have a maximum entropy distribution.

It is not possible to prove that a particular object is incompressible within algorithmic information theory so the best we can do is perform rigorous experimental analysis using machine learning methods. Hence this challenge.

2. Koopman Open

The primary objective of this challenge in experimental mathematics is to query an information-theoretic lower-bound on the computational complexity of integer factorisation. Due to a natural correspondence between integer factorisation and unbounded Koopman operators, this problem is reducible to neural program synthesis for approximating the eigenfunctions of a suitable Koopman operator.