Writings

 

My thesis Intuition Formalized:  Ancient and Modern Methods of Proof in Elementary Geometry

Proofs, pictures and Euclid’ Synthese, v. 175, no. 2, 2010.


A paper that gives a shorter exposition of the analysis I developed in the thesis.

Ensuring Generality in Euclid’s Diagrammatic Arguments

in G. Stapelton, John Howse, and John Lee (Eds.), Diagrammatic Representation and Inference, Springer, 2008.


‘Constructive Geometric Reasoning and Diagrams.’

Final version in Synthese, v. 186, no. 1, 2012.

A Formal System for Euclid’s Elements’ Review of Symbolic Logic, v. 2, no. 4, 2009.


A paper co-authored with Jeremy Avigad and Edward Dean that gives a different (but related) formal analysis of Euclid’s proofs.


‘The role of geometric content in Euclid’s diagrammatic reasoning’

A paper on the relation of formal systems Eu and E to Euclid’s

informal proof method.  It appears, translated, in the April 2011 issue of

Les Etudes Philosophiques (a special issue of the journal on the philosophy of math).

Technical notions of Eu


All the technical definitions of the proof system Eu from the thesis, with some additions and corrections.