AN INESTIMABLE amount of specialization and self-criticism
characterizes current mathematical research. In the field of math-
ematics proper, a great number of mathematical books and pe-
riodicals 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-special-
ized topics presented ¹. 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 ². The same situation obtains in the literature, and at
the congresses dealing with applied mathematics. Even the non-
mathematician 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 investiga-
tions are concerned with the foundations of mathematics, with
theories on number, functions and structure. Numerous philosoph-
ical discussions deal with the applicability of mathematics to
physics, to chemistry and biology, and to psychological and eco-
nomic situations. The more extended problems covering the

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