Diagrammatic Reasoning in Mathematics

Document Type


Publication Date



"Diagrams are ubiquitous in mathematics. From the most elementary class to the most advanced seminar, in both introductory textbooks and professional journals, diagrams are present, to introduce concepts, increase understanding, and prove results. They thus fulfill a variety of important roles in mathematical practice. Long overlooked by philosophers focused on foundational and ontological issues, these roles have come to receive attention in the past two decades, a trend in line with the growing philosophical interest in actual mathematical practice. Seminal contributions include the historical/philosophical analysis of diagrams in Euclid’s geometry offered by Manders in his 1995 paper (2008),1 The date of publication of Manders’ paper is misleading. Though it was not published until 2008, it was written in 1995 and widely circulated, and became highly influential as a manuscript. the logical studies of diagrammatic reasoning contained in Gerard Allwein and Barwise’s compilation (1996), and Netz’s historical study on the place of diagrams in Greek geometry (1999)."


This article was originally published in Synthese, volume number 186, in 2012. https://doi.org/10.1007/s11229-011-9988-3

The Link to Full Text button above directs users to a free read-only version of the article.

Peer Reviewed