... so well received that he felt encouraged to continue his historical work.

It would be impossible to do justice to this monumental work within the brief limits of a book review, even if the task were not rendered supererogatory by the high standing of the work and the acknowledged authority of its author. Cantor's 'Lectures on the History of Mathematics' are the work of a man who has unswervingly devoted a life-time to this single task, who thirty-three years ago was well known for his important contributions to this subject, and who can now in the second edition of the first volume of his great work point with pride to the impulse and awakened interest which his endeavours have aroused in the historical studies of his science. He has had many predecessors, each of whom has distinguished himself in certain branches and by certain excellences ... Nevertheless, it may safely be said that profundity, accuracy, and extensiveness of treatment have never before in any history of mathematics been so thoroughly and intimately united as in the three volumes constituting these Lectures of Moritz Cantor.

It hardly requires to be stated that this history is certain to remain for many years the standard work on the subject with which it deals; in completeness, in accuracy, in clearness of arrangement, it stands unrivalled, and for the period which it covers is bound to be a permanent work of reference.

It is fifteen years since the second edition of the first volume of Cantor's 'Vorlesungen' made its appearance, and last year a third edition was called for. After the completion of Vol. III, which brought this monumental work up to 1758, the author felt that the time had come when the claims of advancing years were strong enough to force him to leave the completion of his magnum opus to others. He must have felt that he had not lived in vain and that an historical school worthy of German traditions had grown up around him, when, inspired by his example and enthusiasm, men were found able and eager to continue his great work under his direction. We are unfortunate in that the health of the aged savant has prevented him from giving that full personal supervision which is so essential in securing a general unity of treatment when the mathematical labours of half a century are divided among so many hands, however individually competent they may be. And when we say that no less than nine monographs by nine men constitute this fourth volume, it is not surprising to find, that although there is less diversity of treatment than might be expected, yet the volume is not what it would have been had Cantor been able to continue his colossal task. As it is, he had intended to append to this portion of the work a general treatment of the progress of mathematics during the latter part of the eighteenth century. We are, however, disappointed at the absence of what would of course have been a masterly survey of the development of ideas in that period, and greatly regret that the plan had to be abandoned. The greatest mathematical historiographer found himself compelled to be content with a chronological index. Even so, it is one of the most useful features in the book. His 'Überblick' gives a mass of information in a couple of dozen pages, fortified with ample cross references to the sections of this volume.

I feel that I may be allowed to mention my personal impressions of Professor Cantor, gained from an acquaintance of about thirty years. It began with a visit to his home when I was planning to spend a year in his course at Heidelberg. I shall never forget his kindliness of manner when I stated that I wished to devote time to the early stages of the calculus. He asked me where I thought it best to begin and I said with Kepler or Cavalieri. The pleasant way in which he approved, with the suggestion that it might be better to start with Archimedes, impressed the young American of thirty, but now he would begin somewhat earlier still. Circumstances have a way of changing one's life rather suddenly, and the plan was never carried out in Heidelberg University, but it did not interfere with the making of several visits from time to time in his home. The last of these was made about 1910, I believe. He was then nearly blind. As I entered his study he rose from a chair near the window, held out his hands, and advanced towards me. I took them and led him back to his chair and we talked over the years since we had first met. ... When I was leaving he rose, motioned with his hand to his bookcase (not a large collection) and said, "these are my books, but I cannot see them." Then he walked with me to the door and I said the conventional "Auf Wiedersehen", knowing that it would never come.

... a hewer of timber who with a big axe and with powerful strokes roughly cut the timber to proper form and dimension, but left it for those who follow him to dress, polish and finish.

Almost complete blindness had compelled him to stop research. He said he could see the general outline of a person's body, but could not make out the features. He could move about in his house without assistance. His hearing was still good and his mind fairly clear. Neither of us touched upon war issues, except that he once referred to me as coming from a nominally neutral country. Later in the day I met his son and daughter, who were free in expressing to me the hope that the United States would soon come to observe real neutrality. Cantor made inquiries about certain American and English mathematicians and spoke of special historical researches then in progress in Germany. ... After a dinner which was served in the garden in the open, the writer, having been told that it was Cantor's habit to lie down after the mid-day meal, departed.