Can an A.I. win a medal in the mathematical olympiad?-Benchmarking mechanized mathematics on pre-university problems ¹

This paper introduces a benchmark problem library for mechanized mathematics including computer algebra and automated theorem proving. The library consists of pre-university mathematical problems taken from exercise problem books, university entrance examinations, and the International Mathematical Olympiads. The subject areas include real algebra, geometry, number theory, pre-calculus, calculus, and combinatorics. It thus includes problems in various areas of pre-university mathematics and with a variety of difficulty. Unlike other existing benchmark libraries, this one contains problems that are formalized so that they are obtainable as the result of mechanical translation of the original problems expressed in natural language. In other words, the library is designed to support the integration of the technologies of mechanized mathematics and natural language processing towards the goal of end-To-end automatic mathematical problem solving. The paper also presents preliminary experimental results of our prototype reasoning component of an end-To-end system on the library. The library is publicly available through the Internet.