Ludwigstraße 23, 35390 Gießen, Germany
Alexander von Brill graduated from the University of Giessen in 1864 with a degree in architecture and passed his Habilitation in 1867.
Alexander von Brill was awarded the Cross of Honour of the Order of the Crown (Württemberg) in 1897.
Alexander Brill's school education was in Darmstadt where he attended elementary school and then a Gymnasium.
In 1860 Brill entered the Technische Hochschule in Karlsruhe where he studied architecture and engineering science. He was taught mathematics by his uncle Christian Wiener, attending his course on descriptive geometry, and by Alfred Clebsch who taught the course on mechanics. Clebsch had been appointed to Karlsruhe in 1858 but, in 1863, he moved from Karlsruhe to the University of Giessen. Brill also moved to Giessen and was again taught by Clebsch.
Brill graduated from the University of Giessen in 1864 with a degree in architecture and passed his Habilitation in 1867.
From then until 1869 he was a Dozent at Giessen; from 1869 to 1875, a professor at the Politechnikum in Darmstadt; and from 1875 to 1884, a professor at the Politechnikum in Munich, where he worked with Felix Klein and was influenced by him. From 1884 to 1918, when he retired, Brill was a professor at the University of Tübingen. He worked primarily on the theory of algebraic functions and algebraic geometry, characteristically using algebraic methods, striving to avoid transcendental methods and aiming at "Weierstrassian strictness" of exposition. The systematic study of those properties of algebraic functions which are invariant under birational transformations is contained in his fundamental work, written with Max Noether (1874). In it, many of the results obtained by Riemann and by Clebsch and Gordan, using transcendental means, are substantiated by algebraic-geometrical methods. Also noteworthy are his papers on three-dimensional algebraic curves (1907) and on pseudospherical three-dimensional space (1885), where the impossibility of putting such a space into Euclidean four-dimensional space and the possibility of its being placed in a Euclidean five-dimensional space are proved.
At the end of the last century, Brill published a series of articles on methodology of mathematics, participated - following Klein - in the movement to reform its teaching, and was an initiator of the use of models of geometrical figures in teaching; many such models were prepared under his guidance.
Brill also wrote on the theory of determinants, on the theory of elimination, on the theory of elliptic functions, on some special curves and surfaces, and on the singularities of planar and spatial algebraic curves. He was also concerned with theoretical mechanics. In Vorlesungen über allgemeine Mechanik (1928) and Vorlesungen über algebraische Kurven und algebraische Functionen (1925) Brill, who was then retired, summed up his scientific and pedagogical career.
Brill’s survey of the development of the theory of algebraic functions ("Die Entwicklung der Theorie der algebraischen Functionen in älterer und neurer Zeit," 1894), which was written with Noether, has significance for the history of mathematics. His last work, published when he was eighty-seven, dealt with Kepler’s New Astronomy.
Alexander von Brill was elected to the Reale Accademia dei Lincei, the Bavarian Academy of Sciences, the German Academy of Scientists Leopoldina, the Reale Istituto Lombardo di Scienze e Lettere, and the Göttingen Academy of Sciences.
On May 15, 1875, Alexander von Brill married Anna Johannette Christiane Schleiermacher, by whom he had three sons and one daughter.