A new foundational crisis in mathematics, is it really happening?

The article reconsiders the position of the foundations of mathematics after the discovery of HoTT. Discussion that this discovery has generated in the community of mathematicians, philosophers and computer scientists might indicate a new crisis in the foundation of mathematics. By examining the mathematical facts behind HoTT and their relation with the existing foundations, we conclude that the present crisis is not one. We reiterate a pluralist vision of the foundations of mathematics. The article contains a short survey of the mathematical and historical background needed to understand the main tenets of the foundational issues.Comment: Final versio

The Common HOL Platform

The Common HOL project aims to facilitate porting source code and proofs between members of the HOL family of theorem provers. At the heart of the project is the Common HOL Platform, which defines a standard HOL theory and API that aims to be compatible with all HOL systems. So far, HOL Light and hol90 have been adapted for conformance, and HOL Zero was originally developed to conform. In this paper we provide motivation for a platform, give an overview of the Common HOL Platform's theory and API components, and show how to adapt legacy systems. We also report on the platform's successful application in the hand-translation of a few thousand lines of source code from HOL Light to HOL Zero.Comment: In Proceedings PxTP 2015, arXiv:1507.0837

Semantics, Algorithmics and Logic: Basic Research in Computer Science. BRICS Inaugural Talk

This is a transcript of a talk at the inauguration of BRICS, Basic Research in Computer Science, Centre of the Danish Research Foundation, on 2 February 1994 at the Steno museum, University of Aarhus, Denmark

The "Artificial Mathematician" Objection: Exploring the (Im)possibility of Automating Mathematical Understanding

Reuben Hersh confided to us that, about forty years ago, the late Paul Cohen predicted to him that at some unspecified point in the future, mathematicians would be replaced by computers. Rather than focus on computers replacing mathematicians, however, our aim is to consider the (im)possibility of human mathematicians being joined by “artificial mathematicians” in the proving practice—not just as a method of inquiry but as a fellow inquirer

Human-driven Machine-automation of Engineering Research

This paper presents a framework for efficiently producing engineering research in a global collaborative effort in a rigorous scientific manner. The proposed framework reduces subjective analysis, automates several mundane research tasks and provides a suitable formal structure for efficient information sharing and collaboration. The implementation of the framework involves multiple research groups setting up different web-servers that can perform the steps of the scientific method and automatically determine the quality and value of new research by directly communicating between servers via public and private Application Programming Interfaces (APIs) using a set of object-oriented protocols. The automation of many mundane research tasks (e.g. data manipulation), would allow researchers to focus more on the novel aspects of their research efforts. The increased clarity around the quality and value of research would allow the research efforts of individuals and available research funding to be better disbursed. The paper discusses the major aspects of the scientific method, object-orientated programming, the application of the proposed research framework for experimental/analytical/numerical engineering research, some of the potential benefits and drawbacks, as well as the current state of implementation