# Emil Hilb

### Quick Info

Stuttgart, Germany

Würzburg, Germany

**Emil Hilb**was a German mathematician who did excellent work on special functions, differential equations and difference equations. His contributions to the

*Enzyklopädie der mathematischen Wissenschaften*are also important.

### Biography

**Emil Hilb**was the son of Adolf Hilb (1850-1894) and Klarchen Ulrich (1855-1926). Let us note at this point that there is some confusion as to whether his birthday was 24 April or 26 April. The 24 April date appears on all official documents Hilb completed early in his career, but later he gave his day of birth as 26 April which is the day given in the Stuttgart registry records. The date of birth of 24 April, however, is given on Hilb's gravestone, so we have followed that data.

We now give a paragraph with details of the Hilb family, mostly taken from [1]. Adolf Hilb was born 20 May 1850 into a Jewish family in Stuttgart, Baden-Württemberg, Germany, a son of Salomon Hilb (1815-1885) and Rosalie Kuhn (1819-1895). He became a merchant, working in Stuttgart all his life. Klarchen Ulrich, known as Clara, was born on 18 September 1855 in Harburg, a daughter of Jakob Ulrich and Sofie Schwab. She married Adolf Hilb in 1876 in Ulm, Baden-Württemberg. Adolf and Clara Hilb had four children, Elsa (born 1877), Max (born 1879), Emil (the subject of this biography, born 1882), and Julius (born 1885).

In 1890 Emil Hilb began his school education at the Eberhard Ludwig Gymnasium in Stuttgart. This school was founded in 1686 but it was only named the Eberhard Ludwig Gymnasium in 1881 when a second Gymnasium was opened in Stuttgart. After Emil's father died on 12 June 1894 at the age of 44, his mother Clara decided to move with her children to Augsburg to he closer to her hometown of Harburg in Donau-Ries, Bavaria. In Augsburg, Hilb entered the Realgymnasium where he studied from 1894 to 1899. The headmaster of the Realgymnasium was Georg Recknagel (1835-1920) and he had studied mathematics and physics in Munich and Würzburg before being awarded a doctorate in 1862 from the Ludwig Maximilian University of Munich. He taught in Kaiserslautern and Passau before being appointed to teach mathematics and physics at the Realgymnasium in Augsburg in 1891. He became the headmaster of the school in the following year but continued to teach mathematics and physics. Hilb later said how important Recknagel's mathematics teaching had been in inspiring him to become a mathematician.

Hilb was the youngest member of his class when he graduated from the school in 1899 and he entered the University and the Polytechnic in Munich in the winter semester of that year to study mathematics and physics. He took the standard introductory courses but also took two advanced classes by Alfred Pringsheim, Function Theory I in the first semester of 1899-1900 and Function Theory II in the second semester. It was typical of German students of this time to spend time at different universities and Hilb spent the two years 1900-1902 at the University of Berlin. He wrote in the CV attached to his habilitation thesis of 1907 (see for example [9]):-

In order to continue my education in function theory, I went to the University of Berlin for two years, where I attended Professor Fuchs' lectures on differential equations and higher function theory (automorphic functions, etc.). Through lectures with Professor H A Schwarz I was introduced to Weierstrass's ideas there; in the colloquia led by Schwarz, I learnt about his basic works on conformal mapping and boundary value problems, which are published in the second volume of Schwarz' collected works ['Gesammelte Mathematische Abhandlungen von H A Schwarz' Ⓣ (1890)].After two years in Berlin, Hilb returned to Munich in 1902 where his thesis advisor was Ferdinand von Lindemann. His 60-page thesis

*Beiträge zur Theorie der Laméschen Funktionen*Ⓣ earned him his doctorate in December 1903 'summa cum laude'. He had already passed the two stages, in 1901 and 1903, of the State Examinations which qualified him to teach mathematics and physics at Gymnasiums. Both parts were rated "very good". He then went to Göttingen to continue his studies and was immediately introduced to David Hilbert's current project on

*The Principles of a General Theory of Linear Integral Equations*. The other person at Göttingen who was a major influence on him was Felix Klein. Hilb wrote in the CV in his 1907 habilitation thesis:-

The suggestions that I received then and in later years through oral and written correspondence between Professor Hilbert and Professor Klein was of the greatest influence for my work published after the doctoral dissertation.Hilb always wanted to support his mother as much as possible so, after his time in Göttingen, he applied for a teaching position in the Realgymnasium in Augsburg where he himself had been taught. He was appointed and took up his position on 24 September 1904. He taught third year secondary school pupils, the syllabus being:-

Decimal fractions; the 4 operations with decimal fractions; transformation of ordinary fractions into periodic decimal fractions and vice versa; simple and composite accounts, interest calculation. Exercises in mental arithmetic.Despite teaching elementary topics full time, Hilb was also undertaking research with the aim of entering university teaching. On 21 November 1904, he wrote to Hilbert explaining that he had successfully applied Hilbert's method of integral equations to a problem in potential theory and asked him whether his results were worth writing up and publishing. Hilbert encouraged him to write up the results and they appeared as Hilb's first paper

*Die Reihenentwicklungen der Potentialtheorie*Ⓣ published in

*Mathematische Annalen*in 1906. Albert Wangerin writes in a review of the paper:-

As is known, the most important systems of orthogonal functions used in potential theory can be seen as special cases of the system of confocal cyclids, and accordingly most of the series expansions occurring in that theory are contained in the series, by means of which the boundary value problem is solved for a body confined by six confocal cyclids. This general task is dealt with in detail in Bôcher's book "On the series expansions of potential theory"; however, there is no evidence of the existence and convergence of the expansions. The present work should fill the gap that still exists here. It is based on Hilbert's methods of the integral equation and shows that from the much more general Hilbert theorems the convergence of the series under consideration results almost without calculation.For a list of Hilb's papers, see THIS LINK.

Max Noether and Felix Klein were friends from their student days and it is likely that Max Noether was recommended the promising young mathematician Hilb through Klein. Certainly Max Noether offered Hilb an appointment as an assistant to the chair of mathematics at the University of Erlangen and he took up this appointment in September 1906. In April 1907 Paul Gordan, who had been at Erlangen for over 30 years, celebrated his 70th birthday and Felix Klein came to Erlangen and gave a lecture on his oscillation theorem to mark the occasion. This was particularly relevant to Hilb who had published

*Eine Erweiterung des Kleinschen Oszillationstheorems*Ⓣ (1907). When Klein was in Erlangen he suggested to Hilb that he might try to prove some conjectures he had made in a recent paper. Hilb succeeded and wrote the paper

*Über Kleinsche Theoreme in der Theorie der linearen Differentialgleichungen*Ⓣ (1908) where, after relating Klein's suggestions to him, he explains:-

I now found this proof to be extremely easy with elementary continuity considerations, which are quite analogous to those used in the teaching of the real roots of real algebraic equations. With the same ease, however, it is also possible to solve from the beginning all the problems that Mr Klein has proposed ...Hilb submitted his habilitation thesis

*Über Integraldarstellungen willkürlicher Funktionen*Ⓣ to the University of Erlangen in 1907 and Paul Gordan and Max Noether were asked to report on it. They wrote:-

The work contains very remarkable progress in a still fresh area. In the this work the author has taken up these developments with great energy, which are promising for the whole of functional theory and also for mathematical physics. It can be seen that he has mastered all functional theoretical techniques and is very sharp.In April 1908 Hilb became a docent at Erlangen but soon after this an extraordinary professorship became vacant at the University of Würzburg.

Friedrich Emil Fritz Prym (1841-1915) had studied for a doctorate at the University of Berlin advised by Ernst Kummer and had been on the faculty at the University of Würzburg since 1867. He held an ordinary professorship at Würzburg, retiring in 1909. Eduard Ritter von Weber (1870-1934) had studied at Munich, habilitated there in 1895 and became a professor at Munich in 1903. He had been appointed as an extraordinary professor at Würzburg in 1907. Another mathematician at Würzburg was Georg Rost (1870-1958) who had been a student of Friedrich Prym at Würzburg and then worked there on the staff for the rest of his career. When Prym retired, Eduard von Weber was promoted to ordinary professor on 3 July 1909 and Würzburg looked to appoint an extraordinary professor. The mathematicians at Würzburg knew of Hilb as a very promising young mathematician and Rost went to Erlangen to listen to one of Hilb's lectures. Hilb's recommendation included the following:-

He is a very excellent researcher, keen thinking, quick to understand, working both abstractly and with intuition, full of ideas ... Many brilliant achievements can still be expected from him while a young man. In Erlangen he gave exercises and lectures for beginners as well as for more mature students from different areas of mathematics with excellent success.The shortlist of candidates was drawn up ranking Ernst Zermelo as first, Hilb as second and Gerhard Hessenberg (1874-1925) in third place. In fact Zermelo had been a candidate for a extraordinary professorship at Würzburg in 1906 but Rost had been appointed then and again in 1909, despite being ranked first, he was not offered the position but the offer was made to Hilb. On 4 August 1909, Hilb wrote to Hilbert:-

I have just come from Würzburg, where I received confirmation of the fact that sounded to me almost fairytale-like that I had been appointed professor there ... I am almost ashamed of my luck, however, when I think of the many who would have earned the job much sooner thanks to their much greater merit; but I will now make double efforts to make myself worthy of the award.At Würzburg Hilb supervised the doctoral studies of eleven students: Otto Haupt (1911), Emil Goldschmidt (1912), Friedrich Betschler (1914), Siegfried Weikersheimer (1914), Gustav Löwenstein (1915), Richard Bär (1916), Axel Schur (1920), Walter Weidringer (1929), Joseph Roth (1930), Valentin Völker (1931) and Beda Thum (1932).

Otto Haupt writes about Hilb as a teacher [3]:-

For Hilb ... it was an innermost need to look around for young people interested in science and to try to draw them into the circle of his scientific work. He spared no effort to encourage the beginner. Then the lecture was continued on the way home or other scientific entertainment was given, since he was a young man himself, a good companion, in front of whom one could safely say stupid things. But in no way did he hold back with his criticism. I myself know how helpful his sarcastic judgment could be for the novice.On 18 May 1912, Hilb married Marianne Alice Wolff (1889-1943) in Würzburg. Marianne was the daughter of the Jewish textile manufacturer Oskar Wolff and his wife Gertrud Ostwald who were wealthy and had given Marianne a good education. She was musical and gifted in foreign languages. They made their home in Seelbergstrasse 5 and entertained friends, colleagues and students there. They had two daughters, Irene (1914-1943) and Anneliese (1918-2005). Hans-Joachim Vollrath writes [9]:-

Students were often invited to lunch on Sundays. Once a student didn't leave until midnight. They were happy that he had felt so comfortable. Students were also often invited to social events. They were popular as dancers. With the exception of Wagner, Hilb liked to listen to classical music. He enjoyed his wife's piano playing, but played no instrument himself. He deeply disappointed a music-loving doctoral student when he told him: "If you want to work scientifically, you have to give up your music!" Hilb was also interested in literature and theatre. He was involved in the "Society for Literature and Stage Art" and promoted artistic projects.Felix Klein was the driving force behind the

*Enzyklopädie der mathematischen Wissenschaften*Ⓣ, published between 1898 and 1933. Hilb was an enthusiastic contributor to the encyclopaedia, writing the articles

*Differentialgleichungen im komplexen Gebiet, Nichtlineare Differentialgleichungen*Ⓣ (1916), (with Marcel Riesz)

*Neuere Untersuchungen über trigonometrische Reihen*Ⓣ (1922) and (with Otto Szász)

*Allgemeine Reihenentwicklung*Ⓣ (1922). Hilb also founded his own series of textbooks "Mathematics and its applications in physics and technology" published by the Academic Publishing Company Geest & Portig in Leipzig.

Hilb had been appointed as an extraordinary professor at the young age of 27 but, ten years later, he had not found a position as an ordinary professor. Of course during these ten years, 1909-1919, half were years of World War I (1914-18) and this produced great difficulties in the German university system. In 1919 Max Noether retired as the ordinary professor at Erlangen and the university sought to fill the vacancy. Hilb had strong hopes that he might succeed in the competition to fill this position since he knew he was highly regarded by Max Noether and others at Erlangen. Ernst Fischer was a professor at Erlanger and he suggested to the appointing committee that Heinrich Tietze, Gustav Herglotz, Wilhelm Blaschke and Richard Von Mises as the strongest candidates. Max Noether felt that Ernst Fischer, who was an Austrian, was favouring Austrian candidates over Germans, particularly over Hilb. Max Noether wrote to Hilbert:-

I now consider this to be wrong for our Germans (especially Hilb), and I would like to ask you cordially to let me know your judgment that I should be able to present to the Committee.Max Noether put Hilbert's assessment to the appointing committee:-

Hilb is an authority in the vast field of oscillation theories and integral equations, and I have benefited from his ingenuity in this field until recently. He is also an excellent connoisseur of modern analysis in the broadest scope (real function theory, set theory, etc.), so that I would put him objectively in front of Hellinger and not behind Blaschke, Mises, Tietze. ... I propose the ranking Hilb, Tietze, Hellinger.Ernst Fischer's ideas prevailed, however, and Tietze was appointed. Hilb was very unhappy, particularly when he learnt of the objections against him put by the Erlangen appointing committee who were particularly critical of his teaching. He complained to the Ministry, asking them "to compensate for the injustice inflicted on him." Initially, following an uncomfortable correspondence, the Ministry refused but on 2 April 1923 they awarded him the title of ordinary professor, but not the academic rights of that position. The Faculty of Arts at Würzburg applied again for Hilb to be awarded full academic rights in December 1928 and these were granted on 16 January 1929. Very sadly he had little chance to enjoy these rights since he died in August of that year.

Hilb died at the age of 47 after his last years were marred by ill health. He had spells when he suffered from a kidney disease but his death was due to a stroke. He died in Würzburg but he was buried in the Pragfriedhof Jewish Cemetery in Stuttgart where both his parents were buried.

Otto Haupt, Hilb's first doctoral student, gave a memorial speech in which he said [3]:-

Anyone who knew Emil Hilb, even those who may have only met him briefly, is remembered as one of the most important things about him, his amiable and cheerful temperament. How much more difficult life would have been for him if his temperament had not helped him again and again over his worries, not least about the premonition of the illness that threatened him, which seems to have struck him more than once in his last years. And this cheerfulness of mind corresponded to a fundamentally benevolent being, who, even outside the family, always allowed him to take the warmest part in the state of health of his acquaintances and friends. We know how he was always ready with advice and action, how he made others' concerns his own concerns and did nothing better than give pleasure to others. We all also know what beautiful, intimate family life Hilb led, to which kind fate had given him a wife who was the most understanding companion.Finally we should say a few words about Hilb's wife Marianne and his daughters. In March 1933, three and a half years after Hilb's death, Hitler came to power and began enacting his anti-Semitic legislation. In 1937, with increasing difficulties for those of Jewish descent, the family moved from Seelbergstrasse 5 to a smaller flat in Würzburg where they lived with Gertrud Wolff, Marianne's mother. In November 1938 around 1000 SA paramilitary men raided Jewish houses and shops in Würzburg, robbing and destroying the contents. They devastated the Hilb's flat and Marianne filed a complaint for theft of valuables but, of course, this was simply a waste of time for the authorities were supporting the raids. Hilb's daughter Anneliese escaped to England in 1939 while in 1940 Marianne and her mother Gertrud moved to Frankfurt am Main where Irene was working as a secretary. On 20 May 1942, Marianne and Irene were deported ending up in the Treblinka concentration camp in German occupied Poland. They died there in 1943. Gertrud Wolff was also deported but she was sent to the Theresienstadt concentration camp in German occupied Czechoslovakia. She died there on 23 August 1942.

### References (show)

- R Strätz,
*Biographisches Handbuch Würzburger Juden 1900-1945*(Würzburg, 1989). - R Flade, Emil Hilb,
*Juden in Würzburg, 1918-1933*(Freunde Mainfränkischer Kunst und Geschichte, 1985), 47; 434. - O Haupt, Emil Hilb,
*Jahresbericht der Deutschen Mathematiker Vereinigung***42**(1933), 183-198. - O Haupt, Hilb, Emil, in
*Neue Deutsche Biographie***II**(Duncker & Humblot, Berlin, 1972), 115. - T Kramer, Emil Hilb, in
*Quellen und Forschungen zur Geschichte des Bistums und Hochstifts Würzburg*(Kommissionsverlag F Schöningh., 2002), 105-106. - J C Poggendorff, Hilb, Emil, in
*Poggendorff's biographisch-literarisches Handwörterbuch für Mathematik, Astronomie, Physik, Chemie und verwandte Wissensgebiete***V**(Leipzig-Berlin, 1926), 536. - J C Poggendorff, Hilb, Emil, in
*Poggendorff's biographisch-literarisches Handwörterbuch für Mathematik, Astronomie, Physik, Chemie und verwandte Wissensgebiete***VI**(Leipzig-Berlin, 1937), 1117. - M Reindl, Hilb, Emil, in
*Lehre und Forschung in Mathematik und Naturwissenschaften, insbesondere Astronomie, an der Universität Würzburg von der Gründung bis zum Beginn des 20. Jahrhunderts*(Degener & Co, Neustadt an der Aisch, 1966), 79-80. - H-J Vollrath, Emil Hilb (1882-1929), in
*P Baumgart (ed.), Lebensbilder bedeutender Würzburger Professoren*(Degener & Co, Neustadt an der Aisch, 1995), 320-338.

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Last Update September 2020