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Answer by Mikhail Katz for Has philosophy ever clarified mathematics?

After Newton and Leibniz developed infinitesimal calculus, a number of critics emerged to criticize the new technique. These included Berkeley, Cantor, and others. One of the few schools to battle the negative attitude toward infinitesimals at the beginning of the 20th century was Hermann Cohen's school, also known as Marburg neo-Kantianism. Their efforts did not bear fruit immediately but they did influence one Adolf Fraenkel, who passed on his interest in infinitesimals to one Abraham Robinson. In his autobiographical work in the 1960s Fraenkel noted that "Robinson saved the honor of infinitesimals."

Thus Cohen's attempts to develop a respectable theoretical basis for a philosophy of infinitesimals eventually bore fruit in Robinson's framework for analysis with infinitesimals.


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