Discovering Algebraic Shortcuts Using Monte Carlo Tree Search

Abstract

In mathematics, many formulas and rules are actually applications of bigger, more complex concepts. When learning math, we are often taught simpler adaptations so we can work up to the higher concepts incrementally. A common example in Calculus is the power rule, which is used when differentiating functions. Rather than using the formal definition: we have a simple algebraic shortcut for polynomials in the form of: These shortcuts save time and simplify complex problems. This project explores whether a computer can find algebraic shortcuts by using data and applying symbolic algebra moves and learning the most efficient paths from an input state to a goal state. Once a universal path is found, the program publishes the path in its symbolic form. If partial solutions (formulas that work for a subset of data) are found, these are also published along with their success rate and possible conditions for them to work. So far, we have used a MCTS, or Monte Carlo Tree Search algorithm which is commonly used in game engines to find solutions rather than brute force search. As a proof of concept, we have tested the model by using 500-1000 examples of single term polynomial data along with their derivatives to test if it could discover the power rule for differentiation and its integration equivalent and have had positive results.