# ARTHUR SCHOENFLIES (1853 - 1928). *Krystallsysteme und Krystallstructur*. Leipzig: B.G. Teubner, 1891.

Arthur Schoenflies was born in Landsberg an der Warthe (modern Gorzów, Poland) and studied mathematics at the University of Berlin from 1870 to 1875. He obtained a doctorate in mathematical geometry 1877, and in 1878 he was a teacher at a school in Berlin. In 1880, he went to Colmar in the Alsace region of France to teach. He managed to continue research in this period along the lines begun in his thesis. The success of his work led to his becoming Privatdozent (Lecturer) in 1884 and later (1892) associate professor of applied mathematics in Göttingen. Schoenflies became professor of mathematics at the University in Königsberg in 1899 and accepted in 1911 a position at the 'Academy' in Frankfurt, which was about to obtain university status. He helped bring about this transformation and became, in 1914, the first Dean of the Science Faculty. In 1920/21, the year before he retired, he was Rector of the University.

In 1889, Schoenflies published an article *Über Gruppen von Transformationen des Raumes (On Groups of Spatial Transformations)*, in which he described 227 space groups, a result that was incorrect but close to the correct number. At the same time, nearly identical results had been developed quite independently in St. Petersburg by E. S. Fedorov. Over the next year, Fedorov and Schoenflies collaborated to resolve discrepancies in their lists and to complete the classification system, reaching consensus in 1890 that the correct number of space groups was 230. Schoenflies published his results in the book *Kristallsysteme und Kristallstructur (Crystal Systems and Crystal Structure*, Leipzig 1891), which instantly became a classic of crystallography. Fedorov also published his findings in his article *Simmetriia Pravil'nykh Sistem Figur (The Symmetry of Regular Systems of Figures*, St. Petersburg, 1890).

Schoenflies's book also features the first appearance of the Schoenflies notation, the system invented by the author to describe the symmetry of crystals.

P. P. Ewald, Ed., *Fifty Years of X-Ray Diffraction* Utrecht: International Union of Crystallography, 1962, p352.