*THE FUTURE OF MATHEMATICS*

THE FUTURE OF MATHEMATICS |

UNIVERSITY OF ILLINOIS

PROFESSOR A. VOSS, of the University of Munich, recently made the following statement: "Our entire present civilization, as far as it depends upon the intellectual penetration and utilization of nature, has its real foundation in the mathematical sciences."^{[1]} He adds that this truth finds expression in the ever-increasing appreciation of the educational value of mathematics, notwithstanding the fact that it is the most unpopular of all the sciences. This unpopularity is natural since "unpopularity is an essential feature of a real science," because such a science can be comprehended only through tireless and continued efforts.

An intelligent expression as regards the future of mathematics must be based not only upon the past and present state of this science, but also upon its real essence. One of those elements which mathematics has in common with some of the other sciences, but which are more prominent in mathematics than in any of the others, is the tendency to use thought in the most economical manner. When one considers the extent to which efforts to simplify methods, theorems and formulas direct mathematical endeavor, one must admit that the statement "Mathematics is the science of saving thought" expresses a great truth, even if it is too sweeping to serve as a definition.

That mathematics is the science which is preeminently devoted to the discovery and mapping of routes along which thought may ascend securely and with the greatest ease, is supported by the fact that it has the oldest and the most extensive symbolical language. In the introduction to his classic history of mathematics, Moritz Cantor asks, "Why has mathematics, since the remotest times, found support, simplification and advancement by means of word symbols, whether these are number symbols or other mathematical symbols?" Although the oldest of these word symbols are probably relics of a very ancient picture language, yet it is of great interest that in mathematics the picture language was retained and used side by side with an alphabetic and syllabic language, while the latter displaced the former elsewhere. Even those who have mastered only the elements of algebra and the

- ↑ Voss, "Ueber das Wesen der Mathematik." Rede gehalten om 11. Marz, 1008, in der oeffentlicben Sitzung der k. bayerischen Akademie der Wissenscnaften; Teubner, 1908, p. 4.