Mathematics Based on Learning

Abstract

Learning theoretic aspects ofmathematics and logic have been studied by many authors. They study how mathematical and logical objects are algorithmically “learned” (inferred) from finite data. Although the subjects ofstudies are mathematical objects, the objective ofthe studies are learning. In this paper, a mathematics ofwhic h foundation itselfis learning theoretic will be introduced. It is called Limit-Computable Mathematics . It was originally introduced as a means for “ProofAnimation,” which is expected to make interactive formal proof development easier. Although the original objective was not learning theoretic at all, learning theory is indispensable for our research.