Mathematics underfoot: The formulas that came to Wuerzburg from New Haven

Two formulas are set in floor-tiles in the foyer of the Wuerzburg building that houses the laboratory in which Wilhelm Roentgen discovered X-rays in 1895. But what do they mean, and what have they got to do with Roentgen or his work? The answers involve two distinguished professors and their PhD students, working on opposite sides of the Atlantic in the 19th Century.