Hermann Gunther Grassmam, a German mathematician, born in Stettin, Prussia, April 15, 1809. His father was professor of mathematics in the gymnasium of Stettin and the author of several mathematical text books. Hermann studied theology and mathematics, and from 1834 to 1852 was a teacher in the Otto-Schule in Stettin, when he succeeded his father as professor of mathematics in the gymnasium. In 1844 he published the first part of Die Wissenschaft der extensiven Grosse, eine neue rnathematische Disciplin. This part also bore the special title Die lineale Ausdehnungs-lehre, ein neuer Zweig der Mathematik, darge-stellt und durch Anwendungen avf die ubrigen Zweige der Mathematik, wie auch avf die Statik, Mechanik, die Lehre vom Magnetismus und die Krystallonomie erlautert. In the preface to this work he gave a short account of his discovery, and declared his intention to make its development and application the chief object of his life. He further developed his theory in Geometrische Analyse (1847), which obtained the prize offered by the Prince Jablo-nowski scientific society of Leipsic, and in articles in Crelle's mathematical journal treating the higher classes of curves.

In 1853 Cauchy published in the Comptes rendus of the French academy a method of resolving algebraical equations and other problems by means of certain symbolical quantities, which he called clefs alge-braiques. The method was identical with that employed by Grassmann, and the latter immediately addressed a "claim of priority " to the academy. A committee was appointed to examine the question, but it never made any report, and Cauchy abruptly broke off' the publication of his articles. In 1862 Grassmann completed the development of his theory by publishing Die Ausdehnungslehre vollstandig und in strenger Form bearbeitet. This work is in strict mathematical form, after the model of Euclid's Elements, consisting almost entirely of propositions and demonstrations. In it he develops the connection of his theory with every branch of mathematics, from arithmetic to the integral calculus, and discusses its application to geometry. The profoundly metaphysical character of his first work and the exceedingly abstract form of the last, together with the total absence of all geometrical figures and all simple illustrations, have very much retarded the progress of his doctrine among professed mathematicians, and have prevented its comprehension by any others.

It has many striking analogies to the quaternions of Sir William Rowan Hamilton. There can be little doubt that the theory of Grassmann, or one essentially the same, and only differing somewhat in form, will in time supersede the whole system of analytical geometry as founded by Descartes and so greatly developed by the labors of subsequent mathematicians. Grassmann has been a frequent contributor to the leading scientific journals of Germany, and has published text books on various branches of science. He has an extensive knowledge of languages, published in 1870 a work on the German names of plants, and is now (1874) engaged in publishing a Sanskrit-German dictionary to the Rig Veda.