Automatically Discovering Euler’s Identity via Genetic Programming

Konstantine Arkoudas

We show that by using machine learning techniques (genetic programming, in particular), Euler’s famous identity (V - E + F = 2) can be automatically discovered from a limited amount of data indicating the values of V , E, and F for a small number of polyhedra — the five platonic solids. This result suggests that mechanized inductive techniques have an important role to play in the process of doing creative mathematics, and that large amounts of data are not necessary for the extraction of important regularities. Genetic programming was implemented from scratch in SML-NJ.

Submitted: Sep 10, 2008