Jakob's education was not quite what one would have expected of someone who would go on to an academic career. This, basically, was because his parents did not envisage this future for their son, expecting him to follow his father's career. He attended the high school in Brody, then, in 1858 when he was sixteen years old, he went to Breslau where he became a clerk in a Mercantile house. Rosanes, however, wanted to attend university and between 1858 and 1860 he prepared himself to enter the University of Breslau. At first it was not mathematics that attracted him; rather his initial choice was to study chemistry which he did between 1860 and 1862. In this latter year he began to concentrate on mathematics and physics and, advised by Heinrich Schroeter, he undertook research and submitted his dissertation De polarium reciprocarum theoria observationes Ⓣ to the University of Breslau and was awarded his Ph.D. in 1865. In addition to Schroeter, Rosanes had been taught by some excellent lecturers at Breslau such as Ferdinand Joachimsthal, Rudolf Lipschitz, O E Meyer, and Paul Bachmann. He formed a close friendship with his fellow student Moritz Pasch, who also had Heinrich Schroeter as a thesis advisor and was awarded his doctorate in the same year as Rosanes. Burau writes :-
Rosanes' mathematical papers concerned the various questions of algebraic geometry and invariant theory that were current in the nineteenth century. One of his first papers, written with Moritz Pasch, discussed a problem on conics in closure-position.Following the award of his doctorate, Rosanes went to Berlin to continue his studies. He returned to Breslau where he submitted his Habilitation thesis and became a Privatdozent in 1870. Burau writes :-
In 1870 he provided a demonstration that each plane Cremona transformation can be factored as a product of quadratic transformations, a theorem that Max Noether also proved independently at about the same time.In fact there were gaps in both Rosanes' and Max Noether's proofs, and these were not filled until the first years of the 20th century by Guido Castelnuovo.
Rosanes taught at Breslau for the rest of his life. He became an extraordinary professor in 1873, a full professor in 1876, and was given the title 'Geheime Regierungsrat' in 1897. He was elected rector of the university during the years 1903-4. He married Emilie Rawitscher in 1876, the year in which he became a full professor.
Rosanes wrote on many aspects of algebraic geometry and invariant theory (particularly between 1870 and 1890) which were in fashion at that time. His papers include the joint paper with Pasch we mentioned above Das einem Kegelschnitt Umschriebene und einem Andern Eingeschriebene Polygon Ⓣ which was published in Crelle's Journal in 1865. We also mention Über Dreiecke in Perspectiver Lage Ⓣ (1870); Über Systeme von Kegelschnitten Ⓣ (1873); Über Ein Princip der Zuordnung Algebraischer Formen Ⓣ (1873); Über linear-abhängige Punktsysteme Ⓣ (1879); and (with Ferdinand Rudio) Zur Theorie der Flächen deren Krümmungsmittelpunktsflächen confocale Flächen zweiten Grades sind Ⓣ (1883). Let us mention a particularly important result, namely giving conditions for a form to be expressed as a power-sum of other forms. He also wrote a series of papers on linearly dependent point systems in a plane and in space. However, his research activity diminished as he grew older and he produced little of importance in the later part of his career.
Max Born attended Rosanes' course on linear algebra, which introduced him to matrix theory, in the first years of the 20th century. He later said these lectures were particularly important in his development as a mathematician and led him to one of his greatest ideas namely the realisation that Heisenberg's quantum mechanics was represented by matrices. Not everyone was an enthusiastic as Born, however, for Rosanes had a mixed reputation as a lecturer. He was considered a good teacher but seemed to lack some basic skills in lecturing techniques. Richard Courant, for example, described Rosanes' lecturing as follows:-
... he scribbled equations which his students never quite saw because as he wrote he hid them with his body and as he moved along he rubbed them out with his sponge.Rosanes' rectorial address, however, everyone agreed was inspirational. In this address he said that the estrangement of mathematics and physics, which had been going on for several decades, was past and an epoch of closer union had begun. The address was published in 1904. He also acted as thesis advisor to a number of outstanding students including Ernst Steinitz, who was awarded his doctorate in 1894, and Otto Toeplitz, who was awarded his doctorate in 1905.
Perhaps Rosanes' main interest outside mathematics was chess. He was able to beat even one of the leading players of his time Adolf Anderssen which he did in Breslau in 1862 (although he lost to him in the following year). He wrote an excellent chess book Theorie und Praxis des Schachspiels. He retired in 1911 but continued to live in Breslau for the rest of his life.
Article by: J J O'Connor and E F Robertson