Abstract

This paper presents a technological approach for reducing the problem of believing a formal proof to the same psychological and philosophical issues as believing a conventional proof in a mathematics journal. The approach is not entirely successful philosophically as there seems to be a fundamental difference between machine checked mathematics, which depends on empirical knowledge about the physical world, and informal mathematics, which needs no such knowledge (see section 3.2.2). In the rest of this introduction I outline the approach and mention related work. In following sections I discuss what we expect from a proof, add details to the approach, pointing out problems that arise, and concentrate on what I believe is the primary technical problem: expressiveness and feasibility for checking of formal systems and representations of mathematical notions.

Citations