The Philosophy of Mathematics

The Philosophy of Mathematics

The Philosophy of Mathematics

The Philosophy of Mathematics

Excerpt

An inestimable amount of specialization and self-criticism characterizes current mathematical research. In the field of mathematics proper, a great number of mathematical books and periodicals are being issued, containing countless new theorems, restatements and new, original solutions of old problems, and new methods of proof. It has been said that though the delegates to mathematical congresses may be quite competent mathematicians themselves, they cannot possibly comprehend all the over-specialized topics presented . According to the historian Cajori, if the history of mathematics in the nineteenth century alone were written with some detail, fourteen or fifteen large volumes would be required . The same situation obtains in the literature, and at the congresses dealing with applied mathematics. Even the nonmathematician feels the impact of mathematics on general culture through the increasing number of books and articles endeavoring to present mathematics in a simplified and popularized form.

Contemporary research in mathematics itself is nearly rivaled by an equal productivity in philosophical inquiries on mathematics. Questions of mathematical method and symbolism are being examined under the title of Symbolic Logic, while other investigations are concerned with the foundations of mathematics, with theories on number, functions and structure. Numerous philosophical discussions deal with the applicability of mathematics to physics, to chemistry and biology, and to psychological and economic situations. The more extended problems covering the . . .

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