**Hildegard Ille**'s father was a doctor. She attended the Chamisso school in Berlin-Schöneberg, being awarded her Abitur (matriculation examination) in 1918. She entered the Friedrich-Wilhelm University of Berlin in the same year and there she studied mathematics, physics and philosophy. The ordinary professors of mathematics at the University were Friedrich Schottky and Erhard Schmidt, while Issai Schur was an extraordinary professor. In March 1923 she sat the State Examination to qualify as a secondary school teacher. She was already undertaking research for her doctorate, advised by Issai Schur, and she submitted her thesis

*Zur Irreduzibilität der Kugelfunktionen*Ⓣ to the University of Berlin. She was awarded a doctorate in 1924. Alexander Soifer writes that, after proving a Ramsey type conjecture [3]:-

From 1 April 1925, she held a one year scholarship at the Kaiser Wilhelm Institute of Physics, which was led at that time by Albert Einstein. Unlike some others who were awarded similar scholarships, for Ille the scholarship was her only means of support. Five other scientists received a grant from the Kaiser Wilhelm Institute of Physics in the academic year 1925-26. She was the only woman and, very unusually at this time, she received a higher scholarship than her male counterparts. This decision had been taken by Max von Laue (1879-1960) who, as a deputy of Albert Einstein, had been entrusted with the affairs of the Institute. It is also interesting to see that the physicists at the Kaiser Wilhelm Institute of Physics were looking to collaborate with a mathematician.... Van der Waerden walked away from Ramseyan prehistory. Issai Schur, on the other hand, continued to produce Ramseyan mathematics, and moreover directed and inspired his PhD students Richard Rado, Hildegard Ille and Alfred Brauer to do the same.

After holding the scholarship for a year, Ille began her teacher training as a student teacher at her former school, the Chamisso school in Berlin-Schöneberg. She taught there from 1926 until 1928 when she married Erich Rothe. Erich Rothe had studied at the University of Berlin at the same time as Ille. Although Rothe was four years older, he had served in the military in World War I so was older than normal when making his university studies. He took the State Examination to qualify as a secondary school teacher in March 1923, at the same examination diet as Ille. Rothe had worked at the Institute of Applied Mathematics at the University of Berlin in 1926-27 before being appointed to the Engineering School in Breslau in 1927 and habilitating there in 1928. In addition to his position at the Engineering School, he was appointed as a docent at the University of Breslau in 1931 after a second habilitation there. After Erich and Hildegard Rothe married in 1928, they had a son, Erhard William Rothe, who was born in Breslau on 15 April 1931.

Ille had submitted the paper *Einige Bemerkungen zu einem von G Pólya herrührenden Irreduzibilitätskriterium* Ⓣ on 15 May 1924 and it was published in 1926. After she married, she reviewed 40 papers which had been published between 1926 and 1928, under the name Hildegard Rothe, and reviewed 129 papers which had been published between 1930 and 1937, under the name Hildegard Rothe-Ille. Looking at these reviews, mostly of number theory papers, something struck me [EFR] as remarkable. The papers that Rothe-Ille reviewed were written in German, English, French, Italian, Russian and Japanese.

On 30 January 1933 Adolf Hitler came to power in Germany and on 7 April 1933 clause three of the Civil Service Law provided the means of removing Jewish teachers from the universities, and of course also to remove those of Jewish descent from other roles. All civil servants who were not of Aryan descent (having one grandparent of the Jewish religion made someone non-Aryan) were to be retired, with exemptions for participants in World War I and pre-war officials. Erich Rothe had served in World War I so was exempt but it quickly became clear that the exemption would be ignored. Because of his Jewish background, Erich Rothe was dismissed from his positions in 1935. Erich Rothe and his wife Rothe-Ille, together with their young son Erhard William, escaped from Nazi Germany and they went to Zürich. Wilfred Kaplan writes [2]:-

Later in 1937 Rothe-Ille, her husband and her son emigrated to the United States. Erich Rothe was appointed as an Instructor in Mathematics at William Penn College, Oskaloosa, Iowa in 1937. Rothe-Ille died from cancer in December 1942 at the age of forty-three.It was in the spring of1937that I first came to know Erich Rothe. I was spending a year in Zürich as a graduate student. I had come to Zürich mainly because of Heinz Hopf, and it was to his friend and former classmate Hopf that Erich Rothe had come as a refugee from Nazi Germany. With him were his wife and child, and all were warmly welcomed by the Hopfs.

Alexander Soifer, in [3], relates an interesting connection between Hildegard Rothe-Ille and Paul Erdős:-

In his first-ever open-ended problem paper, Paul Erdős indicates that before him and Turán, Issai Schur called on studying longest arithmetic-progression-free opening segments of positive integers. Erdős writes: "The problem itself seems to be much older(it seems likely that Schur gave it to Hildegard Ille, in the1920s)." Erdős returns to Issai Schur's contribution in his1961second open-problem paper... : "The problem may be older but I can not definitely trace it. Schur gave it to Hildegard Ille around1930." Paul told me[Alexander Soifer]that he "met Issai Schur once in mid1930s," more precisely in1936in Berlin ... Undoubtedly, they discussed prime numbers, but likely not arithmetic progressions. Erdős learned about Schur's interest in arithmetic progressions and early Ramsey-like conjectures and results from Hildegard Ille(1899-1942). Now this requires a bit of explanation, because they probably had never met! ... Erich Rothe was Paul Erdős's source of reliable information on problems and conjectures in number theory that Issai Schur shared with Rothe's wife Hildegard(Ille)Rothe. From Rothe, Erdős learned about Schur's authorship of the arithmetic progressions conjecture, proven by Van der Waerden. From Rothe, Erdős learned that Issai Schur yet again contributed to number theory and Ramsey theory when he asked his graduate student Hildegard to investigate arithmetic progression-free arrays of positive integers. ...[The]Erdős-Rothe conversations took place after Hildegard's passing in1942.

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

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