This little work was published about ten years ago as a chapter in Merriman andWoodward's Higher Mathematics. It was written before the numerous surveysof the development of science in the past hundred years, which appeared atthe close of the nineteenth century, and it therefore had more reason for beingthen than now, save as it can now call attention, to these later contributions.The conditions under which it was published limited it to such a small compassthat it could do no more than present a list of the most prominent names inconnection with a few important topics. Since it is necessary to use the sameplates in this edition, simply adding a few new pages, the body of the workremains substantially as it first appeared. The book therefore makes no claimto being history, but stands simply as an outline of the prominent movementsin mathematics, presenting a few of the leading names, and calling attention tosome of the bibliography of the subject.