Independence and the Development of the American Identity and Mathematics in the Ninteenth Century

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During the 1800s, we find the theme of independence, or freedom from outside constraints, in the development of two different frontiers. We find it in the American West through Manifest Destiny, freedom from caste, and in the chance that homesteaders had to acquire virtually free land. We find independence in math through in the building of stronger theoretical foundations, non-Euclidean geometries, and Cantor's infinities.

Independence involves breaking from the commonly accepted, traditional views in order to explore the new. It is not necessarily individual people working alone. We can see independence in a community of thought as well as in the work of a single person.

Independence is an important part of the Western culture as
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In the 1880s, Hulda Rocell and her daughter Mary emigrated from Sweden to the United States. Abe Lincoln had just been shot. Mr. Rocell had to stay in Sweden because of his tuberculosis. Nevertheless, Mr. Rocell said, "Go to the United States. It is strong enough that Lincoln's assassination will not plummet the nation into chaos." Although he did not place this optimism under the title of Manifest Destiny, the idea that the United States is strong, and will continue despite opposition, is a part of this concept.

Hulda married, and her family settled in a sod house in northern Minnesota. Her husband showed independence and determination for the family to survive by planting fruit trees on the farm. It was highly unusual to attempt to plant fruit trees that far north.

The family's independent spirit, and courage was a vital part of surviving in the harsh conditions they encountered. In 1881, there was a terrible blizzard. The snow was so high that it covered the fence posts. Father tied a rope around his waist and the porch post to tend the animals in a nearby shed, so that he would not get lost in the blizzard. However, many neighbors froze to death right outside their own front doors. During the storm, the wind blew the door of the sod house open. The younger children got in the trundle bed to keep warm, while the parents and older children shoveled snow out of the house for the rest of the day, so that they could shut the

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