Our Mathematical Universe?

TL;DR

This paper reviews Max Tegmark's 'Our Mathematical Universe', discussing its themes and philosophical implications, and includes additional material on symmetry breaking, Pythagoreanism, and properties, in an informal style.

Contribution

It provides a comprehensive, informal review of Tegmark's ideas, expanding on philosophical themes and defending quidditism about properties.

Findings

Discussion of symmetry breaking and Pythagoreanism in philosophy of mathematics

Defense of quidditism about properties

Integration of additional references and material

Abstract

This is a discussion of some themes in Max Tegmark's recent book, Our Mathematical Universe. It was written as a review for Plus Magazine, the online magazine of the UK's national mathematics education and outreach project, the Mathematics Millennium Project. Since some of the discussion (about symmetry breaking, and Pythagoreanism in the philosophy of mathematics) went beyond reviewing Tegmark's book, the material was divided into three online articles. This version combines those three articles, and adds some other material, in particular a brief defence of quidditism about properties. It also adds some references, to other Plus articles as well as academic articles. But it retains the informal style of Plus.