Using a long-standing conjecture from combinatorial group theory, we explore, from multiple perspectives, the challenges of finding rare instances carrying disproportionately high rewards. Based on lessons learned in the context defined by the Andrews--Curtis conjecture, we analyze how reinforcement learning agents handle problems of varying hardness. We also address many mathematical questions as a part of our study. Notably, we demonstrate the length reducibility of all but two presentations in the Akbulut--Kirby series (1981), and resolve various potential counterexamples in the Miller--Schupp series (1991), including three infinite subfamilies.

We introduce giotto-tda, a Python library that integrates high-performance topological data analysis with machine learning via a scikit-learn-compatible API and state-of-the-art C++ implementations. The library's ability to handle various types of data is rooted in a wide range of preprocessing techniques, and its strong focus on data exploration and interpretability is aided by an intuitive plotting API. Source code, binaries, examples, and documentation can be found at https://github.com/giotto-ai/giotto-tda.