In the early 19th century we find diverse steps towards a generalization of geometric language to higher dimensions. But they were still of a tentative and often merely metaphorical character. The analytical description of dynamical systems in classical mechanics was a field in which, from hindsight, one would expect a drive towards and a growing awareness of the usefulness of higher dimensional geometrical language. Manifolds, the higher-dimensional analogues of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis,...
In the early 19th century we find diverse steps towards a generalization of geometric language to higher dimensions. But they were still of a tentativ...
