Minnesota’s little topknot was the result of an incorrect assumption made by the Congress when it was finalizing its border with Canada (then known as British North America). To the east the border was erratic and uneven, and it appealed to all involved to just declare a straight line and use it for the remainder of the border as it stretched west. The line they chose was the 49th parallel. One wonders why they didn’t pick a nice round number like 50, but placing the border at the 50th parallel would have cut Canada completely off from the Great Lakes.
They began the line at a western notch of Lake Superior and then had to work their way back up to the 49th parallel. They used a chain of lakes as their guide, which is how the northeast border of Minnesota got that series of zig zag lines. The problem was that the treaty had assumed that the Lake of the Woods topped out at the 49th parallel, and in the original wording of the charter they described the line through the chain of lakes ending at the northeast corner of the Lake of the Woods at which point it would continue straight west.
When the boots on the ground actually began the task of surveying the line, they discovered that Lake of the Woods actually extended further north than they thought. Given the choice of changing the charter and cutting Lake of the Woods in half, or just redrawing the line, the decision makers opted to just bend the line to encompass the lake, thus creating the bump at the top of Minnesota.