The most illustrious among the few Polish mathematics whose accomplishments in the 19th century had an international impact was Franciszek (Franz) Mertens who worked in Krakow for some 20 years. After gaining a doctorate in Berlin, this is where he commenced his career which he was later to continue in Graz and Vienna.
Franciszek Karol Jozef Mertens was born on March 20, 1840 in Srodzie near Poznan. His grandfather on his mother’s side, Major de Malignon, was an officer in Napoleon's army. Quartered in 1812 in Wrzesnia, a town some 30 miles south east of Poznan, he married one of the daughters of the local Nahiring family. It was thus that Mertens mother spent her youth in France only to return to the with her sisters and her mother to her ancestral home after the death of her father in 1836. As a result Mertens grew up knowing French and it remained, with German and Polish, one of the three languages which he spoke fluently. The father of the future mathematician was a surgeon who practiced in Wagrowiec another town in the Poznan region. His family roots were from Bremen area. Much more however is known about Mertens mother and her family than his, which, based on information gained from the Mertens relatives, is noted by Auguste Dick, the author of his biography.
In the years 1853-1860, Franciszek Mertens was a student of the high school in Trzemszno, another town of the Poznan region and then in the 1860-1864 studied mathematics at the University of Berlin which in that era was one of the leading mathematical centers. There he listened to lectures Karl Weierstrass (1815-1897), Leopold Kronecker (1823-1891), Ernst Kummer (1810-1893) and Elwin Bruno Christoffel (1829-1900) among others. The areas his mentors were interested in surely had an influence on the later direction of his scientific work. He was particularly interested in number theory, algebra and many aspects of analysis, above all those related to number theory and algebra. He crowned his studies by gaining a doctorate in 1864 on the basis of a paper published in Journal fûr die reine und angewandte Mathematik, on the subject of the potentials of homogenous polyhedrons. His doctorate was awarded with the notation eximia cum laude. The records of doctorates in mathematics awarded by the University of Berlin in the years 1810 to 1933 reveal that this particular distinction was awarded of only 13 times during that period. It should be added that already in 1863, Mertens had been awarded the so called "Semesterprämie" of 10 talers and that in 1864 he received the "Prämie des Kultursministerium" of 50 talers. He was nominated for the latter by K and W. It is also worth noting that in 1867 his doctoral dissertation was published also in Polish, nor was this a unique event for Mertens published a dozen or more of his papers in both German and Polish.
In 1865, right after gaining his doctorate, Mertens received a professorial appointment at the Jagiellonian University in the extra-ordinary rank, and promoted to ordinary rank in 1869. He conducted classes in various mathematical topics, but particularly in those corresponding to his scholarly intersts, namely number theory, algebra and analysis as well as geometry. During 1873-74 he held the position of Dean of the Philosophy Department and, from its inception in 1868 till 1885 he was a member of the Commission for Teacher Rank Candidates.
In December 1872 he became a extra-ordinary member of the Polish Academy of Arts and Sciences which though located in Krakow, served as a learned and cultural society for the entire Polish nation. In October 1985 he gained the rank of active foreign member, foreign for in 1884 he had received an professorial appointment at the Technical Academy in Graz. Regarding his move to Graz, the Jagiellonian University Chronicle for the years 1884-1887 state "his scholarly contribution were of a high order and so enhanced his reputation that in 1882 he was offered a professorship at Hall University. The efforts of his collegues and the recognition he received from the High Council which appointed him as a Administrative Councilor, led him on that occasion, to remain in Krakow, thought two years later the University lost him with much regret." Likewise in another passage, the Chronicle for 1884, stated that the "University suffered a significant loss on account of the departure from the Philosophy Department of Dr. Mertens who moved to Graz."
In 1885, immediately upon taking on the position at the Technical Academy in Graz, he became the president of that institution, an indication of the high regard he enjoyed and the scholarly achievement gained in Krakow.
In the years 1892 to 1894 he was Dean of Engineering and in 1894 he was appointed professor of mathematics at the University of Vienna. As a representative of that institution he took part, in 1900, in the celebration of the 500th anniversary of the Renewal of the Jagiellonian University. He continued to lecture at the University of Vienna till 1911. In addition to his membership of various afore mention prestigious bodies, he was also a member of the Viennise Akademie der Wissenschaften, as well as of the Berlin Academy which had been founded in 1700 by one of the most renown mathematicians and philosophers, Gottfried Wilhelm Leibnitz (1646-1716). The Academy singled him out by honoring him with the Jakob Steiner award.
Franciszek Mertens died in Vienna on March 5, 1927.
An accounting of Merten's scholarly achievement, necessarily very general and concerning only selected aspects, will begin with an extensive exegesis from an article regarding 19th Century Krakowian mathematics penned by by Zdzislaw Opiala (1930-1974), a superb mathematician and an excellent historian of mathematics:
Mertens' first publication as well as his dissertation dealt with the theory of geometry and the then current questions in elementary geometry such as the famous Malfatti question (construction of three areas contiguous to each other and to a give triangle.) He published them in the, in those times, most selective mathematical German periodical 'Journal fur die reine und angewandte Mathematik' founded by Crelle. The breakthrough year for Mertens was 1874 when two papers of his on the analytical theory of numbers appeared in the afore mentioned journal and constituted, augmented by later published work on related topics, a significant advance in the field. What stupefies is that Mertens achieved these advances using elementary methods. His beautiful work have not lost their worth to this day and continue to be the subject of study and investigation of contemporary mathematicians.
Mertens' soujourn at the Jagiellonian University coincided with the repolonization of the university and that means that the matter about Auguste Dick wrote "Mertens sorach und schrieb Deutsch and Polnisch gleich gut" which equates his knowledge of Polish and German, had considerable importance. Indeed Mertens had an excellent command of the Polish language, as reference to documents written in his hand . Polish was for him simply his "own" language.
The above text is a partial translation by Peter K. Gessner of a Polish language article of the same title by Krzysztof Ciesielski, Andrzej Pelczar, and Zdzis³aw Pogoda