Mathematical problems related to the traveling salesman problem were treated
in the 1800s by the Irish mathematician Sir
William Rowan Hamilton and by the British mathematician Thomas
Penyngton Kirkman. The picture below is a photograph of Hamilton's
Icosian Game that requires players to complete tours through the 20 points
using only the specified connections. A nice discussion of the early
work of Hamilton and Kirkman can be found in the book *Graph
Theory 1736-1936* by N. L. Biggs, E. K. LLoyd, and R. J. Wilson,
Clarendon Press, Oxford, 1976.
The general form of the TSP appears to be have been first studied by
mathematicians starting in the 1930s by Karl
Menger in Vienna and Harvard. The problem was later promoted by Hassler
Whitney and Merrill
Flood at Princeton. A detailed treatment of the connection between
Menger and Whitney, and the growth of the TSP as a topic of study can be
found in Alexander Schrijver's paper
``On the history of combinatorial
optimization (till 1960)''.