The Nature of Mathematical Knowledge based on the Centrality of Proof
Professor Kanamori is a mathematician who has conducted research mainly in set theory, particularly on strong axioms of infinity, combinatorics, and consistency results. In recent years, his work has focused on the history of set theory, and more broadly, the history and philosophy of mathematics. With the editing of the Handbook of Set Theory and of The Collected Works of Ernst Zermelo, the gains in knowledge and experience have stimulated several specific projects to be realized as papers on the historical beginnings of the axiomatics of set theory. These projects will be directly benefitted by proximity to colleagues and archives in Germany and Goettingen. These factors will be especially beneficial for broader projects in the investigation of the re-emergence of proof as central to mathematics in the mid-19th century, particularly in the pioneering work of Richard Dedekind and David Hilbert. The research here is to feed into a general articulation of the nature of mathematical knowledge based on the centrality of proof, especially in modern mathematics with all of its complexity, this eventually to lead to a monograph.