ABSTRACT
During World War II, American mathematician George D. Birkhoff contended that 'topology deserves to obtain a more prominent position in physical theories than it has yet obtained' [1943, 310]. Because of its impact on various parts of mathematics, topology undoubtedly was among the greatest successes of the twentieth century. But, prior to the early 1970s, and despite Birkhoffs wish, topology had generally retained the image of an abstruse pursuit that had found little concrete application elsewhere. Or to put it more accurately, very few leading topologists paid any attention to the concrete.^
By the early 1990s, a compelling alternative had emerged, and this image had become obsolete. For instance, British topologist E.C. Zeeman characterized the history of topology as a succession of hegemonic approaches branching off to establish new subspecialties. After the 1890s when it untangled itself from its 'applied origins,' topology was 'analytic' from 1900 to 1920, 'geometric' in the 1920s and 1930s, and then 'algebraic' But, the 1960s saw the resurgence of a 'geometric' standpoint, and the 1970s were labeled 'differential,' The wheel having turned a full circle, Zeeman saw in the 1980s the triumph of 'applications.'^ Now, 'applied topology' is hard to find as a standard classification in mathematics. In more than fifty years, the Mathematical Review has recorded only one single use of the expression in the title of an article.^ Clearly, the image of topology seems to have shifted recently,
Although part of larger mutations in the image of mathematics, this shift is best understood as resulting from the successful adaptation of notions and practices coming from topology to the modeling of certain
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