Carl Hierholzer

Carl Hierholzer was a German mathematician, born on 2 October 1840 and died on 13 September 1871, when he was only thirty. He studied mathematics at the Polytechnic School in Karlsruhe and took his doctorate at Heidelberg in 1865, where his advisor was Ludwig Otto Hesse. In 1870 he wrote a habilitation on conic sections in space, Ueber Kegelschnitte im Raum, at Karlsruhe, where he later became a Privatdozent. He is remembered for proving that a connected graph has an Eulerian trail if and only if exactly zero or two of its vertices have odd degree, a result that Leonhard Euler had stated in 1736 without a proof of the converse. Hierholzer apparently presented the work to a circle of fellow mathematicians not long before his early death, and a colleague then arranged for it to be published after his death in a paper that appeared in 1873.