Mathematik#

Mathematics: A translator of mathematical and astronomical texts, Hermann von Kaernten became the first outstanding Austrian mathematician during the first half of the 12th century. The science of mathematics began to flourish in Austria in the 15th century, when the first School of Mathematicians was founded at Vienna University. Its main representatives were Johannes von Gmunden, Georg von Peuerbach and Regiomontanus (J. Mueller). They made mathematics an ancillary science of astronomy (methods of calculation, trigonometry, revision of astronomical tables). During the 16th century the second Vienna School of Mathematicians began to form, the main representatives of which were J. Stabius, S. Rosinus, G. Tannstetter, J. Voegelin, H. Schreiber and C. Rudolff. These remarkable men made major contributions to arithmetic and algebra (most of them were members of an association of mathematicians teaching basic mathematics to traders and merchants in the 15th and 16th centuries), to cartography, geometry and the calculation of cubic capacity. The first university professors of mathematics were appointed by Emperor Maximilian I at Vienna University. G. J. v. Lauchen (also called Rheticus), born at Feldkirch, Vorarlberg, wrote the mathematical introduction to the work of Copernicus. J Kepler lectured at the Universities of Graz (from 1594), Prague and Linz (from 1612). He used conic sections for astronomical calculations (Kepler´s laws), calculated tables concerning the motion of planets (Tabulae Rudolphinae) and worked out tables of logarithms (in cooperation with Jost Buergi; proved their correctness by means of algebraic calculations). Together with W. Schickhart, he invented the first mechanical calculating machine. His approach to the problem of calculating cubic capacity ("Nova Stereometria doliorum vinariorum") made him one of the pioneers in the field of infinitesimal calculus. The eminent mathematicians of the 16th and 17th centuries were to be found among Jesuit monks, e.g. P. Gudin, who intensely occupied himself with the calculation of cubic capacity and lectured at the Universities of Vienna and Graz; C. Grienberger, born at Hall in Tirol, who lectured at Graz before he was offered a chair at Rome University. Other outstanding mathematicians among the Jesuits worked as missionaries (e.g. J. Grueber).

In the 19th century J. Petzval lectured at Vienna University. He managed to work out the Laplace transform with which differential equations could be solved. Because of a conflict with S. Spitzer, however, the transform was named after the French mathematician Laplace. Petzval developed high-speed lenses, cooperated with the famous Austrian optician, Voigtlaender, and invented a special lens for portrait photography. He also made important contributions to mathematical optics, ballistics and music theory. A general reform of the universities enforced in 1852 led to mathematics reaching another zenith in the second half of the 19th century. As well as Petzval, E. Weyr and G. v. Escherich, the founders of the leading publication on mathematics in Austria (Monatshefte fuer Mathematik und Physik), worked at Vienna University. Other remarkable mathematicians of that time were L. Koenigsberger, F. Mertens and L. Gegenbauer (introduced a course on actuarial theory at Vienna University).

A. v. Burg and J. Salomon lectured at the Vienna University of Technology, which had been founded in 1815. The latter wrote textbooks which became extremely popular with students of mathematics. He also worked out the algorithm of subtraction, which since that time has been referred to as "Austrian method". K. Zsigmondy studied number theory. W. Czuber concerned himself with statistics, probability calculus and actuarial theory. O. Stolz (responsible for the dissemination of modern differential and integral calculus) and K. Zindler (expert in geometry; later professor at Graz) taught at Innsbruck University. R. Sterneck (number theory, tidology) and J. Frischauf (spherical functions, geodesy and cartography) lectured at Graz University.

During the 20th century numerous outstanding Austrian mathematicians appeared on the scene. Some of them held a chair at Vienna University, e.g. W. Wirtinger (function theory, third mathematician to be awarded the Cayley Award after Cantor and Poincare), H. Hahn (one of the originators of functional analysis, Hahn-Banach´s theorem), P. Furtwaengler (one of the co-originators of the Vienna School of Number Theory), J. Radon (theory of measure and content, integral theory), N. Hofreiter (geometry of numbers, algebra), E. Hlawka (number theory, managed to verify a hypothesis by Minkowski), K. Goedel (basic mathematics) and K. Menger (topology, dimension theory). Another well-known mathematician, A. Tauber (Tauber´s theorems) belonged to the teaching staff of both the Vienna University of Technology and Vienna University. Other notable professors of Vienna University were H. Tietze, E. Helly, L. Vietoris (one of the originators of general topology) and O. Schreier (algebra). It should also be mentioned that E. Mueller, J. Krames and W. Wunderlich founded a centre of descriptive geometry at the Vienna University of Technology.

Literature#