Some instructive mathematical errors

• Published in 2021
• Added on 2021-08-29

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.

Links

• http://arxiv.org/abs/2106.07269v2
• http://arxiv.org/pdf/2106.07269v2

Other information

BibTeX entry

@article{Someinstructivemathematicalerrors,
	key = {Someinstructivemathematicalerrors},
	type = {article},
	title = {Some instructive mathematical errors},
	author = {Richard P. Brent},
	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.},
	comment = {},
	date_added = {2021-08-29},
	date_published = {2021-10-09},
	urls = {http://arxiv.org/abs/2106.07269v2,http://arxiv.org/pdf/2106.07269v2},
	collections = {history,the-act-of-doing-maths},
	url = {http://arxiv.org/abs/2106.07269v2 http://arxiv.org/pdf/2106.07269v2},
	year = 2021,
	urldate = {2021-08-29},
	archivePrefix = {arXiv},
	eprint = {2106.07269},
	primaryClass = {math.NT}
}