Vladimir Voevodsky on the concept of mathematical structure in his letter exchange with Andrei Rodin

TL;DR

This paper explores Vladimir Voevodsky's conception of mathematical structure through his email exchange with Andrei Rodin, highlighting its historical, philosophical, and relevance to Homotopy Type theory.

Contribution

It provides a detailed analysis of Voevodsky's conception of structure, connecting historical examples to modern mathematical and philosophical contexts.

Findings

Voevodsky's conception of structure is linked to Euclidean commentary.

The paper clarifies Voevodsky's views in relation to current theories.

Historical and philosophical issues are discussed in depth.

Abstract

In 2016 Vladimir Voevodsky sent the author an email message where he explained his conception of mathematical structure using a historical example borrowed from the \emph{Commentary to the First Book of Euclid's Elements} by Proclus; this message was followed by a short exchange where Vladimir clarified his conception of structure. In this Chapter Voevodsky's historical example is explained in detail, and the relevance of Voevodsky's conception of mathematical structure in Homotopy Type theory is shown. The Chapter also discusses some related historical and philosophical issues risen by Vladimir Voevodsky in the same email exchange. This includes a comparison of Voevodsky's conception of mathematical structure and other conceptions of structure found in the current literature. The concluding part of this Chapter includes relevant fragments of the email exchange between Vladimir Voevodsky and the author.