Machine learning and information theory concepts towards an AI Mathematician

The paper argues that current AI excels at intuitive, system‑1 tasks but falls short on system‑2 reasoning needed for mathematics. It proposes using information theory to define what makes a mathematical statement interesting, aiming to guide the creation of an AI mathematician that can generate novel conjectures rather than merely prove existing theorems. The central hypothesis is that a concise, descriptive set of theorems can efficiently capture the space of all provable statements by minimizing description length while remaining close to many derivable results.

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