Who introduced Western mathematicians to Latin squares?

Abstract

A Latin square is a grid or array containing the same number of rows and columns. The cell entries are a sequence of symbols inserted in such a way that each symbol occurs only once in each row and only once in each column. Since the beginning of the twentieth century, Latin squares have been studied in the field of combinatorics. This article is concerned with the issue of who, according to the published literature, introduced Western mathematicians to Latin squares. The first mathematician to provide a depiction of Latin squares seems to have been Jacques Ozanam (1640–1718), who demonstrated the use of Latin squares in a problem based on playing cards. However, he did not discuss the analytic properties or the potential applications of Latin squares. The first mathematician to provide an analytic description of Latin squares seems to have been Leonhard Euler (1707–1783).

Acknowledgements

I am grateful for the kind assistance of Michel Denis, Donald Knuth, and Annie Richardson. Figures 1 and 2 and some of the text of the present paper has been taken from the article cited as Richardson (2018).

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

John T. E. Richardson http://orcid.org/0000-0002-6267-0603