My advisor and I are currently crafting plans for a book focusing on Dedekind’s style of mathematics and the manner in which things like Galois theory and algebraic number theory evolved in his hands. Part of the book would consist of some translations (with commentary) of pieces by Dedekind.
I’ve just put a draft of [...]

In this post I gave a brief sketch of what I claim is a better approach to modelling the continuum. In this post I am going to develop the ideas a little bit more thoroughly and also explain why I this is a better approach than the usual set-theoretic definitions of the real numbers.
Here are [...]

I’ve recently finished a draft of the first chapter for my masters thesis, on the topic of mathematical structuralism. I argue that the philosophical discussion of mathematical structuralism has, by and large, misrepresented mathematical attitudes on the subject. This dialogue, beginning with Benacerraf’s classic What Numbers Could Not Be, has focused on the ontology of [...]

In a recent joint paper with Jeremy Avigad and John Mumma (forthcoming in the Review of Symbolic Logic, preprint available at the arXiv), we devise a formal system that is intended to faithfully capture the notion of Euclidean geometric proofs. Specifically, is meant to be a formal counterpart to Books I through [...]

For my first few blog posts here at unwanted capture, I’m going to talk about a subject that I will return to often: rethinking our mathematical foundations aesthetically. This time, I want to look at our definitions for the continuum; I think that a non-standard approach can give us a cleaner presentation which is closer [...]

To get the blog rolling, here’s something I came across in my recent reading.
My old advisor Peter Koellner, in a paper on pluralism in mathematics, raises the kind of interesting point (based on a simple observation) that I’m often disappointed didn’t occur to me already. The main issue Koellner is considering is the problem [...]