Some instructive mathematical errors

TL;DR

This paper examines notable mathematical errors from literature, including those by renowned mathematicians, and discusses how computational tools could help detect such errors earlier.

Contribution

It provides a detailed analysis of significant mathematical errors and explores methods to identify them using software like Maple or Sage.

Findings

Errors by esteemed mathematicians can remain undetected for years.

Computational tools can assist in early error detection.

Errors in published papers can propagate if not caught promptly.

Abstract

We describe various errors in the mathematical literature, and consider how some of them might have been avoided, or at least detected at an earlier stage, using tools such as Maple or Sage. Our examples are drawn from three broad categories of errors. First, we consider some significant errors made by highly-regarded mathematicians. In some cases these errors were not detected until many years after their publication. Second, we consider in some detail an error that was recently detected by the author. This error in a refereed journal led to further errors by at least one author who relied on the (incorrect) result. Finally, we mention some instructive errors that have been detected in the author's own published papers.