# A History of Japanese Mathematics/Preface

Although for nearly a century the greatest mathematical classics of India have been known to western scholars, and several of the more important works of the Arabs for even longer, the mathematics of China and Japan has been closed to all European and American students until very recently. Even now we have not a single translation of a Chinese treatise upon the subject, and it is only within the last dozen years that the contributions of the native Japanese school have become known in the West even by name. At the second International Congress of Mathematicians, held at Paris in 1900, Professor Fujisawa of the Imperial University of Tokio gave a brief address upon Mathematics of the old Japanese School, and this may be taken as the first contribution to the history of mathematics made by a native of that country in a European language, The next effort of this kind showed itself in occasional articles by Baron Kikuchi, as in the Nieuw Archief voor Wiskunde, some of which were based upon his contributions in Japanese to one of the scientific journals of Tokio, But the only serious attempt made up to the present time to present a well-ordered history of the subject in a European language is to be found in the very commendable papers by T. Hayashi, of the Imperial University at Sendai. The most important of these have appeared in the Nieuw Archief voor Wiskunde, and to them the authors are much indebted.
Having made an extensive collection of mathematical manuscripts, early printed works, and early instruments, and having ​brought together most of the European literature upon the subject and embodied it in a series of lectures for my classes in the history of mathematics, I welcomed the suggestion of Dr. Carus that I join with Mr. Mikami in the preparation of the present work. Mr. Mikami has already made for himself an enviable reputation as an authority upon the wasan or native Japanese mathematics, and his contributions to the Bibliotheca Mathematica have attracted the attention of western scholars. He has also published, as a volume of the Abhandlungen zur Geschichte der Mathematik, a work entitled Mathematical Papers from the Far East. Moreover his labors with the learned T. Endō, the greatest of the historians of Japanese mathematics, and his consequent familiarity with the classics of his country, eminently fit him for a work of this nature.
Our labors have been divided in the manner that the circumstances would suggest. For the European literature, the general planning of the work, and the final writing of the text, the responsibility has naturally fallen to a considerable extent upon me. For the furnishing of the Japanese material, the initial translations, the scholarly search through the excellent library of the Academy of Sciences of Tokio, where Mr. Endô is librarian, and the further examination of the large amount of native secondary material, the responsibility has been Mr. Mikami's. To his scholarship and indefatigable labors I am indebted for more material than could be used in this work, and whatever praise our efforts may merit should be awarded in large measure to him.
The aim in writing this work has been to give a brief survey of the leading features in development of the wasan. It has not seemed best to enter very fully into the details of demonstration or into the methods of solution employed by the great writers whose works are described. This would not be done in a general history of European mathematics, and there is no reason why it should be done here, save in cases the where some peculiar feature is under discussion. Undoubtedly several names of importance have been omitted, and at least a score of names that might properly have had mention have ​been the subject of correspondence between the authors for the past year. But on the whole it may be said that most of those writers in whose works European scholars are likely to have much interest have been mentioned.
It is the hope of the authors that this brief history may serve to show to the West the nature of the mathematics that was indigenous to Japan, and to strengthen the bonds that unite the scholars of the world through an increase in knowledge of and respect for the scientific attainments of a people whose progress in the past four centuries has been one of the marvels of history.
It is only just to mention at this time the generous assistance rendered by Mr. Leslie Leland Locke, one of my graduate students in the history of mathematics, who made in my library the photographs for all of the illustrations used in this work. His intelligent and painstaking efforts to carry out the wishes of the authors have resulted in a series of illustrations that not merely elucidate the text, but give a visual idea of the genius of the Japanese mathematics that wards alone cannot give. To him I take pleasure in ascribing the credit for this arduous labor, and in expressing the thanks of the authors.
Teachers College, Columbia University,David Eugene Smith.
New York City, December 1, 1913.