Cakespy.com (http://www.cakespy.com/blog/2011/1/26/holey-grail-why-do-doughnuts-have-holes.html ) credits both theories to one seafarer:
“According to a 1938 article in The Tuscaloosa News, … an old New England Sea captain, one Hanson Gregory, from Camden, Maine, to introduce the hole in the doughnut, as we know it today. As an old man he liked to tell his story many times — how as a boy he had been watching his mother frying doughnuts and had noticed that the centers always remained partially uncooked and doughy. 'Mother', he said, "leave a hole in the center." Laughingly, she obliged him and never went back to the old way. Her method was widely copied.
“There is also an unlikely, but wholly (holey?) enjoyable, version of the story, also involving Gregory, which goes thusly (according to the Lewiston Evening Journal): "one legend is that he liked to munch fried cakes while steering his craft. One day, in 1847, the seas were rough and he needed both hands to control the rudder. So he slapped several cakes on the spoke of his wheel, making holes."
Cakespy also offers a third theory involving Gregory: “… Gregory purposefully poked a hole in the doughnut to lighten it up ‘because he had already lost six men overboard due to the heaviness of the doughnuts.’” That theory’s full of holes.
There’s little doubt, however, of his involvement in the shape of a doughnut, “In Rockport, Maine, you can find a plaque inscribed with the following: ‘In commemoration. This is the birthplace of Captain Hanson Gregory, who first invented the hole in the doughnut in 1847. Erected by his friends, Nov. 2, 1947.’” He apparently had really old friends.