**Emil Weyr**'s father, Frantisek Weyr (1820-1889), was born in Náchod to Jan Weyr (1791-1842) and Terezie Wanátková. Frantisek was a professor of mathematics at a realschule (secondary school) in Prague from 1855. He had married Marie Rumplová (1825-1889) in St Stephen's Church in the New Town of Prague on 10 June 1850 and they had ten children. Two of the children were born before their marriage. Before examining Emil's life in detail, let us briefly comment on all ten children. These were Karel Weyr (1844-1915), Emil Weyr, the subject of this biography, Marie (1850-1923), Eduard Weyr, who has a biography in this archive, Bedrich Weyr (1853-1908), Anna (1854-1884), Antonie (1856-1919), Emilie (1858-1934), Berta (1860-1927), and Helen (1867-1955). Karel, the eldest of the children, was rather different from his brothers and did not influence them greatly as they grew up. He became a financial controller and financial inspector. Bedrich, the one brother younger than the two mathematicians Emil and Eduard, studied chemistry at the Czech College of Technology (1871-1874) and at the University of Prague (1875-1878). He became an expert in sugar refining becoming director of sugar refineries. Of the girls, Marie married Albin Sieber, the director of a sugar refinery in Zdice. Anna married August Johann Friedrich Seydler (1849-1891), a distinguished theoretical physicist and astronomer who was a professor at the Charles University of Prague. Antonie married Rudolf Schuh (1848-1897). Emilie married the architect and builder Josef Roesel (1855-1922). Berta married the very wealthy wholesaler of sugar Leopold Brumlik (1849-1900). The youngest daughter, Helen, lived with her brother Emil in Vienna for many years. Eventually she married Colonel Ernst Grünfeld (1860-1938), the brother of the well-known pianist and composer Alfred Grünfeld (1852-1924). We note that the family were German speaking and only spoke Czech as a second language.

According to the parish records, Emil was born on 1 September 1848 and he was baptised in St Stephen's Church in the Upper New Town of Prague on 3 September. However, the Weyr family believed that Emil was born on 31 August and always celebrated his birthday on that day. He was four years older than his brother Eduard Weyr who also became a famous mathematician. He was brought up in a home where his father behaved like a philosopher. Frantisek displayed humour, perhaps somewhat tinged with melancholy, and looked at the deeper aspects of life rather than the day to day trivialities. He loved animals, especially dogs and birds, something which he passed on to his son Emil. The family dog, named Snapsl, was an important member of the large family. Frantisek's philosophical outlook on life meant that he tried not to show any emotions to his children. Emil entered the elementary school of Our Lady of the Snows in 1854 where he was taught by Frantisek Petter. From 1859, Emil attended the realschule in Mikulandska street in Prague where his father taught, but already at this time he was engaged in studying advanced mathematics guided by his father. Then he studied at the Prague Polytechnic from 1865 to 1868 where he was taught geometry by Otto Wilhelm Fiedler (1832-1911). Fiedler, who had obtained his doctorate from the University of Leipzig in 1858 advised by August Ferdinand Möbius, became professor of descriptive geometry at the Technical University of Prague in 1864 but left three years later to become a professor in Zürich.

Weyr was an excellent student and began publishing papers during his undergraduate studies. At the Technical University he studied engineering sciences but was less interested in the practical aspects of the courses. In September 1868, he became an assistant of Heinrich Durége (1821-1893). Durége had been born in Danzig and was professor at Zürich before being appointed as a professor at the University of Prague. He had published the books* Theorie der Funktionen elliptischen* (1861), *Elemente der Theorie der Functionen einer complexen veränderlichen Grösse* (1864), and *Die Ordnung Ebenen Curven dritter* (1871). He also wrote an important biography of Friedrich Wilhelm Bessel, namely* Bessel's Leben und Werken* (1861). Weyr volunteered to do one year's military service, from March 1869 to January 1870. During this time he received his doctorate from the University of Leipzig on 5 May 1869. The physicist and philosopher Ernst Mach (1838-1916), had been appointed as professor of Experimental Physics at the Charles-Ferdinand University in Prague in 1867 and he encouraged Weyr to habilitate at the Charles University. He became a Privatdozent at the Charles-Ferdinand University in Prague on 3 May 1870. He had an excellent publication record having published 31 items including the two books published in 1869 and 1870, *Theorie der mehrdeutigen geometrischen Elementargebilde und der algebraischen Curven und Flächen als deren Erzeugnisse* and *Geometrie der räumlichen Erzeugnisse ein-zwei-deutiger Gebilde, insbesondere der Regelflächen dritter Ordnung* .

In the summer of 1870, Weyr began preparing to go to Paris having been awarded a state scholarship to fund his visit. In Paris he planned to attend lectures by Charles Hermite, Joseph Alfred Serret, Michel Chasles, and other leading mathematicians. However, on 19 August France declared war on Prussia and the Franco-German war of 1870-71 began. Weyr quickly changed his plans and decided instead to visit Italy. On 7 November 1870 he set off on his travels to Milan. He travelled by train to Trieste, then he continued his journey to Venice where he spent several enjoyable days sightseeing. He arrived in Milan on 17 November but from the end of November until the middle of January he was back home in Bohemia. By early February he was again in Milan, and now he began to attend courses given by Luigi Cremona and Felice Casorati at the Polytechnic. He treated Cremona as his advisor at first but a friendship developed and the two exchanged letters as friends over the following twenty years. In February 1871 his brother Eduard Weyr visited him in Milan. The two brothers collaborated on the first volume of their three volume book on projective geometry entitled *Foundations of higher geometry* (Czech). The first two volumes had Emil as the main author while Eduard was the main contributor to the third volume. In April 1871 Emil Weyr set off on a sightseeing tour of Italy, visiting Padua, Bologna, Pisa, Florence, Rome, and Naples. While visiting Naples he climbed Mount Vesuvius. He took the opportunity to meet many Italian mathematicians on this trip and he continued to correspond with many of them after he returned from his Italian visit. The authors of [2] write about the importance of this visit for Weyr's mathematical development:-

He returned to Prague in late May 1871 where he continued to teach. He deputised for an extraordinary professor at Prague Polytechnic on 15 October 1871 and in December of that year his appointment as extraordinary professor was confirmed. He also taught at the University of Prague as a privatdocent. In 1872 he was elected to be Head of the Union of Czech Mathematicians and Physicists, an organisation of which he had been a co-founder two years earlier. Weyr returned to Italy for another visit in April 1873. His main task on this trip was to have further discussions with Luigi Cremona since Weyr was translating Cremona's books. He made up for having had to cancel an earlier trip to Paris when he went there for a holiday in 1874. On this occasion he took the opportunity to have discussions with Chasles and, before leaving France, he went to Bordeaux to talk with Jules Hoüel. He was appointed permanent secretary of the Union of Czech Mathematicians and Physicists in 1874 and, in July of that year, he was appointed as editor of the new JournalWeyr's stay in Italy was immensely important and inspirational for his further scientific work. He acquainted himself with the latest achievements in projective and synthetic geometry and wrote several treatises that helped him to gain the attention of European geometers. In a reaction to his stay in Italy, Emil Weyr wrote22works in1871(13German,8Italian,1Czech),11works in1872(6German,3Czech,2Italian)and11works in1873(5German,4Czech,2Italian). Italian papers were published in journals 'Rendiconti di Real Istituto Lombardo' and 'Analli di matematica pura ed applicata'(thanks to the cooperation of L Cremona)and in 'Giornali di Matematiche'(thanks to the cooperation of G Battaglini).

*Archive of mathematics and physics*that the Union had just founded. On 23 September 1875 he was appointed as professor of mathematics at the University of Vienna. He, together with his brother Eduard Weyr, were the main members of the Austrian geometric school. They were interested in descriptive geometry, then in projective geometry and their interests turned towards algebraic and synthetic methods in geometry. Among many works Emil Weyr published were

*Die Elemente der projectivischen Geometrie*and

*Über die Geometrie der alten Aegypter*.

In 1877 Emil Weyr married Marie Waniek von Domyslowa (1860-1934) in Vienna. Emil and Marie Weyr had three children: Frantisek (1879-1951) became a lawyer and was professor at Masaryk University in Brno; Jindrich (1880-1957); and Marie (1883- ?). The 1st Congress of Czech Physicians and Naturalists was held in Prague in the spring of 1880. Both Emil Weyr and his brother Eduard Weyr were invited to lecture at the Congress. The 2^{nd} Congress was held two years later and again both brothers were invited to lecture. In August 1889, both Weyr's parents died, his father suffering a stroke thirteen days after the death of his mother; they were buried in the Olsanské Cemetery in Prague

Emil Weyr led the geometry school in Vienna throughout the 1880's up until his death. His approach to synthetic geometry was in the style of Chasles and Cremona while the other geometric approach at the time, namely that of Karl von Staudt and Theodor Reye, had little influence on him. He introduced a method to derive from some well-known property of a geometric structure, a new property through an algebraic correspondence. Weyr, with great skill and ingenuity, became a great master of this method and produced many results using his approach. He also made an important contribution to the theory of involutions, studying first the cubic before moving on to mapping of rational curves on each other. In his own time, Emil Weyr was considered to have made more significant contributions than his younger brother Eduard Weyr but, now that we can see how the contributions of the two brothers influenced later research, it is possible to suggest that Eduard Weyr made some of the the more lasting contributions.

Together with the Austrian mathematician Gustav Ritter von Escherich (1849-1935), Emil Weyr founded the important mathematical journal *Monatshefte für Mathematik und Physik* in 1890. The first volumes of the journal contain papers written by his brother Eduard Weyr. In 1891 Emil Weyr became one of the first 19 founder members of the Royal Czech Academy of Sciences. He was also a full member of the Austrian Academy of Sciences in Vienna and shortly before his death he received an appointment as Councillor. He died after a long illness in the prime of his life. Gustav Kohn [6] remarks that he was an exceptionally hard worker, producing over 150 publications in his short life, and he worked tirelessly almost as if he knew his lifespan was to be short. We end this biography with the following tribute by Gustav Kohn [6]:-

His lectures at the University of Vienna were plain and unadorned but still of exemplary clarity, so that even the less gifted could follow them easily. If among Austrian middle school teachers geometric knowledge and understanding of the methods of geometry are widely used, that is mostly due to Weyr. He is in many cases also to be thanked for the fact that, during his time in Vienna, Austria has experienced a very significant increase in effective scientific mathematical production, which can be clearly seen in the respective volumes of the proceedings of the Vienna Academy of Sciences, where mathematical work occupies a large part and constitutes mainly geometric investigations on the subject. The greater part of these studies is due to him and his students, among whom the only one preceding him in death, Adolf Ameseder(1858-1891), may be mentioned here by name.

**Article by:** *J J O'Connor* and *E F Robertson*