Euler's lute and Edwards' oud

TL;DR

This paper emphasizes the importance of studying historically significant mathematical texts directly, without interpretive biases, to fully appreciate their style and substance, using Euler's Institutiones as a case study.

Contribution

It highlights how reading Euler's Institutiones without modern interpretive lenses reveals more of its original style and content, contrasting with Edwards' constructivist approach.

Findings

Reading Euler's work without modern biases uncovers more of its original style.

Constructivist interpretation can obscure the historical and stylistic aspects of classical texts.

Direct engagement with historical texts enriches understanding of their true content.

Abstract

In a piece published in 1981, H. M. Edwards touts the benefits of reading the masters. A quarter-century later, Edwards takes seriously his own advice by publishing an encomium on Euler's Institutiones (1755). While we agree with Edwards that we shall all do well by studying the masters, we argue that to derive the full benefit, one must read historically important texts without interposing a lens formed by one's own mathematical accomplishments. We show, in particular, that Edwards misses much of the style and substance of Euler's Institutiones by reading the text through a constructivist lens.