Book Description

The historical proof of the development of mathematics as a firm and progressive science, rather than as a changing mental plaything or business calculating machine, is suggested at once in the table of contents. This short and philosophical summary furnishes to the teacher of mathematics, or to the general reader of history, the material from antiquity to modern times which enables him to place the subject where it belongs--among the old and reliable and constantly developing sciences. At practically every point which is taken up, quite full and satisfactory references are given, so that authorities on past and present historical material are placed before the reader. Those who are familiar with Professor Cajori's History of Mathematics, dated December 1893, will recognize with pleasure the reappearance of many of the well-preserved mathematical antiques which he then used to exhibit clearly and forcibly the contributions of the science during the ages. The authorship and the construction of many of these antiques are again shown to be insolvable problems, but the discussion of the possible originators forms an interesting and valuable part of the new book.Among racial contributions the book presents with great appreciation the work of the Hindus and the Arabs, and mentions the recently discovered numeral records of the Mayas of Central America as an early attempt on the part of American races to develop mathematics; but discussion of the possibility of more important discoveries and contributions by the Japanese and Chinese than have so far been credited to them is omitted. The index includes a fairly large number of names of early mathematicians and present-day writers, but those who desire to look up such a connection as that between logic and mathematics find no assistance in the index, though the subject is discussed on p. 289; and there is also no reference to the treatment on p. 300 of the introduction of graphic methods. All these items are of interest to the teacher of the present day and should be included in the index. One wishes also that the question that is quoted so often and in so many kinds of writing as a mathematical problem of the middle ages, "How many angels can stand on the point of a needle? ", had been traced to its source, in order to save the time of teachers and students in history, philosophy, literature or mathematics, who are anxious to know its origin.