  Machine-learning methods are gradually being adopted in a great variety of
social, economic, and scientific contexts, yet they are notorious for
struggling with exact mathematics. A typical example is computer algebra, which
includes tasks like simplifying mathematical terms, calculating formal
derivatives, or finding exact solutions of algebraic equations. Traditional
software packages for these purposes are commonly based on a huge database of
rules for how a specific operation (e.g., differentiation) transforms a certain
term (e.g., sine function) into another one (e.g., cosine function). Thus far,
these rules have usually needed to be discovered and subsequently programmed by
humans. Focusing on the paradigmatic example of solving linear equations in
symbolic form, we demonstrate how the process of finding elementary
transformation rules and step-by-step solutions can be automated using
reinforcement learning with deep neural networks.
