Latin Squares

The first serious work on Latin squares was undertaken by Swiss mathematician Leohnard Euler, author of the Mechanica. For those who don’t know him, Euler was a badass.

A true polymath, Euler made significant contributions in areas such as infinitesimal calculus, graph theory, topology and analytic number theory. Much of our modern, mathematical notation derives from him, including the idea of mathematical functions. He also made contributions in mechanics, fluid dynamics, optics, astronomy, and music theory.

Euler is considered so great, they named the number e, a mathematical constant that is the base of the natural logarithm, for him. But he was such a badass, he has a second constant, γ, which bears his name.

Euler may have been attracted to Latin squares for the same reason [M]’s designer was—the combinatorial explosion that comes from it’s factorial nature. A 9×9 Latin sqauare has 5,524,751,496,156,892,842,531,225,600 possible combinations, and even when reduced for various symmetries, that number is still 377,597,570,964,258,816.

Even better, Latin squares are useful. Although the initial applications were restricted to simple scheduling, in the past decades research into Latin squares has yielded applications in a wider variety of fields, including cryptography and error-correcting codes. Applications for Latin squares will likely continue to expand as computing power and techniques for mathematical analysis advance.