Group Theory and the theory of Semigroups of Operators serve as an important tool in Quantum Mechanics. Encryption algorithms that underly security of internet transactions are based on finding huge prime numbers. Orthogonal latin squares have been considered by Euler probably for their entertaining value. Besides having an exciting history latin squares developed into a very respectable branch of mathematics with various applications. The theory of designs depends on such abstract mathematical tools as finite fields and finite geometries.
Latin squares are good for scheduling round-robbin tournaments.
Algorithms for solving the Marriage Problem are also used in Linear Agebra to reduce matrices to block diagonal form. The Man-Made Universe , 3rd edition, Dover, 2000. Alexander Bogomolny 2411920 .