century. The fifth period, which might indeed be joined with the fourth, but which differs from it much as the nineteenth century of European mathematics differs from the eighteenth, extended from 1775 to 1868, the date of the opening of Japan to the Western World. This is the period of the culmination of native Japanese mathematics, as influenced more or Jess by the European learning that managed to find some entrance through the Dutch trading station at Nagasaki and through the first Christian missionaries. The sixth and final period begins with the opening of Japan to intercourse with other countries and extends to the present time, a period of marvelous change in government, in ideals, in art, in industry, in education, in mathematics and the sciences generally, and in all that makes a nation great. With these stupendous changes of the present, that have led Japan to assume her place among the powers of the world, there has necessarily come both loss and gain. Just as the world regrets the apparent submerging of the exquisite native art of Japan in the rising tide of commercialism, so the student of the history of mathematics must view with sorrow the necessary decay of the wasan and the reduction or the elevation of this noble science to the general cosmopolitan level. The mathematics of the present in Japan is a broader science than that of the past; but it is no longer Japanese mathematics,—it is the mathematics of the world.
It is now proposed to speak of the first period, extending from the most remote times to 552. From the nature of the case, however, little exact information can be expected of this period, It is like seeking for the early history of England from native sources, excluding all information transmitted through Roman writers. Egypt developed a literature in very remote times, and recorded it upon her monuments and upon papyrus rolls, and Babylon wrote her records upon both stone and clay; but Japan had no early literature, and if she possessed any ancient written records they have long since perished.
It was not until the fifteenth year of the Emperor Ōjin (284), so the story goes, that Chinese ideograms, making their way
