"But perhaps most important, it wasn’t clear in Hamilton’s time just what the octonions would be good for. They are closely related to the geometry of 7 and 8 dimensions, and we can describe rotations in those dimensions using the multiplication of octonions. But for over a century that was a purely intellectual exercise. It would take the development of modern particle physics—and string theory in particular—to see how the octonions might be useful in the real world."