**Feodor Theilheimer**'s parents were Gustav Theilheimer (born on 25 March 1866 in Dittenheim, died on 8 March 1933) and Rosa Waldmann (born on 26 December 1869 in Dittenheim, died on 8 November 1929). We note that Dittenheim is a village about 5 km south of Gunzenhausen. Gustav, the son of Raphael Löw Theilheimer and Therese Bauer, and Rosa, the daughter of Veiss Nathan Waldmann and Regina Steiner, were married on 18 August 1898. Gustav Theilheimer was a cattle dealer and also bought hops. Gustav's parents had bought a house at 15 Brunnenstrasse in Gunzenhausen in 1885 and Gustav moved into it before his marriage in 1898. The family were Jewish which, of course, played a very significant part in their future after the Nazis came to power in 1933.

Gustav and Rosa Theilheimer had six children, all born in the house on Brunnenstrasse. These were Thekla (born 19 May 1899), Regina (born 26 May 1901 but died when one year old), Bella (born 3 November 1902), Hedwig (born 4 January 1904), Richard (born 30 March 1905), and Feodor (the subject of this biography, born 18 June 1909). Before we give a biography of Feodor, we give some details of what happened to his four siblings who survived to adulthood. As Jews they were all forced to leave Germany in the 1930s. Thekla married Bernhard Gutmann in 1926 and they emigrated to Argentina in early 1938 where they remained. Bella married Max Stoll in 1935 and they left Germany in 1939 making their way via England to Denver, Colorado in the United States. Hedwig emigrated to London, England in 1937 and remained there until the war ended when she emigrated to Denver, Colorado, United States where, in 1948, she married Berthold Maier. Richard emigrated to New York City in 1935 where he married Charlotte Strauss in 1937.

Feodor Theilheimer began his education in a one-room Jewish school in Gunzenhausen. There were about thirty children of different ages all being educated in the one room but they were divided into different classes. Feodor found the material taught to his class too trivial and preferred to listen to the lessons that were being taught to the older children. In 1919, after four years at this school, he entered the Realschule in Gunzenhausen studying there until 1925 when he was sixteen years old. This school was non-sectarian and had an entrance examination but this was not a challenge to Theilheimer. At this school Jews, Protestants and Catholics were all given separate religious instruction. Theilheimer was given religious instruction by Hauptlehrer Marx who had taught him in the Jewish school.

In order to attend a university a student had to spend three years studying at either a Gymnasium or at an Oberrealschule. However, Gunzenhausen did not have either of these schools so Theilheimer went to Nuremberg in 1925 to spend three years studying at the Oberrealschule there. Graduating from the Oberrealschule in 1928, he went to Lithuania to study at the Telshe Yeshiva in Telsiai. This rabbinical college was at that time under the leadership of Rabbi Yosef Leib Bloch. After three years in Telsiai, he returned to Germany in 1931 to attend the Hildesheimer Rabbiner Seminar in Berlin. This seminary, founded in 1873, trained rabbis in the tradition of Orthodox Judaism. Theilheimer only spent one year at this seminary before entering the Friedrich-Wilhelm University of Berlin in 1932 to study mathematics. In 1933 Theilheimer's father died, his mother having died five years earlier and, with his siblings Thekla, Bella, Hedwig, and Richard, he continued to treat half of the house at 15 Brunnenstrasse as his home.

Among the mathematicians at Berlin when Theilheimer was studying there were Ludwig Bieberbach, Alfred Brauer, Georg Feigl, Erhard Schmidt, Richard von Mises, and Issai Schur. Theilheimer entered the university before the Nazis came to power in January 1933 but once the Nazis took over the government things became exceptionally difficult both for Jewish professors and for Jewish students. On 1 April 1933, on 'Boycott Day', posters carried the message 'Germans defend yourselves against Jewish atrocity propaganda: buy only at German shops'. Jewish shops were boycotted and Jewish professors and lecturers were not allowed to enter the university. On 7 April 1933 the Nazis passed a law which, under clause three, ordered the retirement of civil servants who were not of Aryan descent, with exemptions for participants in World War I and pre-war officials. Despite Schur satisfying the exemption conditions, his lectures were cancelled and there was an outcry among the students and professors, for Schur was respected and very well liked.

Theilheimer was able to continue to study at Berlin, mainly taking courses by Schur and Schmidt, and undertook research on invariant theory for his doctorate advised by Issai Schur. In 1935 Schur was dismissed from his chair in Berlin but he continued to work there suffering great hardship and difficulties. Despite this humiliating situation for Schur and his student, Theilheimer submitted his thesis* Ein Beitrag zur Theorie der charakteristischen Invarianten* Ⓣ and was awarded his doctorate in 1936. His diploma certificate contains the remark:-

He became Schur's last Ph.D. student. We note that the thesis was published inAdmitted as a non-Aryan within the percentage according to decree U I1331.

*Mathematische Zeitschrift*in 1936. In that paper Theilheimer writes:-

However, clearly for political reasons, he does not thank Schur or acknowledge his help in any way.This work was accepted by the Philosophy Faculty of the Friedrich-Wilhelm University of Berlin as a dissertation.

Theilheimer taught in a school in Berlin for a year after the award of his doctorate. The position of Jews in Nazi Germany had become quite impossible and his brother Richard Theilheimer had, as we mentioned above, emigrated to the United States in 1935 and was living in New York City. Richard had worked as a salesman in Germany before the anti-semitic laws forced him to stop work. In the United States he became involved in selling children's wear. It was Richard who made it possible for his brother Feodor to emigrate to the United States in November 1937 by signing an affidavit. However, after arriving in the United States was difficult for Theilheimer to find work suited to his academic attainments.

From 1937 to 1941 he was engaged in private tutoring of Jewish subjects in St Louis, where he had been sent by an organisation caring for Jewish refugees. Then, he made a move to applied mathematics through the summer school at the University of Chicago in 1941. He attended the forty-eighth Annual Meeting of the American Mathematical Society which was held at Lehigh University, Bethlehem, Pennsylvania, from Monday, 29 December to Wednesday, 31 December 1941. It was held in conjunction with meetings of the Mathematical Association of America, the Association for Symbolic Logic, and the National Council of Teachers of Mathematics. On Tuesday 30 December, Theilheimer was introduced by Richard von Mises and delivered the talk *The potential of curvilinear distributions* to the Applied Mathematics Section. During 1941-42, he took the 'Program of Advanced Research and Instruction in Mechanics' at Brown University. He published *Swept-back wings with arbitrary lift distribution* (1942) and *The influence of sweep on the spanwise lift distribution of wings* in the* Journal of Aeronautical Science* in 1943.

In September 1942 Theilheimer was appointed as an instructor in mathematics at Trinity College, Hartford, Connecticut. He was at Trinity College, when he joined the American Mathematical Society in 1943. On 16 February 1943, the *Trinity Tripod* carried the article *Trinity Math Instructor Contributes to Science. Feodor Theilheimer Carrying on Extensive Study in Special Field of Aerodynamics*:-

Three years later, in 1946, he was promoted to assistant professor at Trinity College. He was given leave so that he could visit the Institute for Advanced Study at Princeton from 1 January 1946 to 30 June 1946. In 1948 he joined the Naval Ordnance Research Laboratory [1]:-Dr Feodor Theilheimer, Trinity College Math instructor, who was one of the more brilliant scientists in Germany before his exile in1937, is now continuing his extensive study in the field of aerodynamics. He has just completed a paper dealing with aeronautics, which will soon appear in the "Journal of Aeronautical Sciences. Dr Theilheimer, German born and bred, received his degree from the University of Berlin. In1937he came to the United States and became a member of the faculty of Brown University, where he did his first important American work in the aerodynamics sphere. Dr Theilheimer resigned from the Brown faculty in1942to accept the post of instructor in mathematics at Trinity College in September of that year. In addition to all this research that he is conducting, Dr Theilheimer is instructing the Freshmen and other Math1majors in the principles of plane trigonometry and elementary calculus. He is also conducting extension courses in aerodynamics and advanced mathematics besides teaching Math2.

Also in 1948, Theilheimer married Henriette Rubel (4 February 1916 - 22 May 2013), known as Henny, originally from Hochspeyer in Germany, and they lived in Chevy Chase, Maryland. In fact the Theilheimer family lived at 2608 Spencer Road, Chevy Chase, Montgomery County, Maryland. They had one child, Rachel Theilheimer born 1950. His address in 1949 is given as Naval Ordnance Laboratory, White Oak, Maryland, 914 Flower Avenue, White Oak 12 and in 1951 as Naval Ordnance Laboratory, White Oak, Maryland, 2213 Washington Avenue, Silver Spring, Maryland. He spent 1952-3 as a lecturer in mathematics at the University of Maryland.After the war(1948-77), Theilheimer worked for the U.S. Department of Defense, contributing with his mathematical work to the theory of spline functions. The conditions of his emigration prevented him from returning to work as an academic teacher.

The American Mathematical Society reported:-

In fact he went to the Applied Mathematics Laboratory at the David Taylor Model Basin. Ray Mejia writes:-In1954Dr Feodor Theilheimer, who has been at the Naval Ordnance Laboratory, Silver Spring, Maryland, has a position with David Taylor Model Basin, Carderock, Maryland.

[Theilheimer was much involved with the Mathematical Association of America. He attended the Association meeting at Yale University, New Haven, Connecticut on 1-2 September 1947. He also attended the Association meeting at Columbia University, New York City, on 30 December 1949, and the meeting at Johns Hopkins University, Baltimore, Maryland on 31 December 1953. He attended the Maryland District Section of the Mathematical Association of America meeting on many occasions, for example at the American University, Washington D.C. on 10 December 1949, at the Catholic University, Washington D.C. on 9 December 1950, at Howard University, Washington D.C. on 6 December 1952, at The George Washington University, Washington D.C. on 5 December 1953, and at Georgetown University, Washington D.C. on 4 December 1954. The references [9] to [17] below describe these meetings of the Mathematical Association of America.I]become interested in numerical analysis, and[that]resulted in several years of work at a Navy research laboratory, the David Taylor Model Basin(now the Naval Ship Warfare Center in Carderock, MD). At the same time I began graduate work at the University of Maryland ...The years at the Model Basin were great fun, working with many dedicated mathematicians and scientists in several disciplines, including ... Feodor Theilheimer ...

In 1961, in collaboration with William Starkweather, he published the paper *The fairing of ship lines on a high-speed computer*. This paper gives a good indication of the type of work Theilheimer was carrying out at the Model Basin. The authors write in the Introduction to the paper:-

In 1961, Theilheimer and Pao C Pien were awarded the David W Taylor Award for Scientific Achievement. TheBefore the actual construction of a ship can begin, considerable time and effort has to be spent in the drawing of the ship lines. The purely graphical methods of determining ship lines are very tedious and time-consuming. Therefore, the problem of implementing the graphical methods by analytic procedures has been studied for a considerable time. ... The analytical approach to the ship line problem has become particularly attractive since high-speed computers became available. This offers an opportunity to eliminate much of the drudgery inherent in the graphical method. When ship lines are found by an analytic method, they may possess unwanted fluctuations. It is, therefore, desirable to have an analytic criterion which permits us to determine whether or not a line is free of unwanted fluctuations. This paper furnishes such a criterion and gives a method of finding lines without such fluctuations.

*David Taylor Model Basin Bulletin*described the award [3]:-

In 1969 Theilheimer published the paperDuring a ceremony held on13July1961in the presence of the Management Council, Captain J A Obermeyer, Commanding Officerand Director, announced that Drs Pao Pien and Feodor Theilheimer have been selected as the first recipients of the David W Taylor Award for Scientific Achievement. Dr Theilheimer was present to receive the award letter and citation. ...

Dr Feodor Theilheimer. By developing a mathematical technique for calculating ship profiles with the use of a high speed calculator, you have made it practical for the first time to calculate ship profiles automatically. Your methods have been tested on several Navy vessels and the results obtained have proved their feasibility. They will have a profound impact on the design of ships in the future, making possible a systematic approach to the study of more complex ship design problems as a function of specific mathematical parameters. For this outstanding accomplishment you richly deserve the David W Taylor Award for Scientific Achievement.

*Matrix Version of the Fast Fourier Transform*in the

*IEEE Transactions on Audio and Electroacoustics*. He writes:-

He received further honours for his outstanding work:-The fast Fourier transform is considered to owe its speed to the fact that a certain matrix, none of whose elements is zero, can be factored into matrices with very many zeros. This paper describes and discusses a procedure for explicitly carrying out such a factorization. This paper is not intended to give a new, improved, or speedier version of the fast Fourier transform. It only attempts to formulate an answer to a question which is often posed by colleagues who have heard about the fast Fourier transform. They ask: What makes the fast Fourier transform so fast?

He was a member of the American Mathematical Society, the Mathematical Association of America, the Society for Industrial and Applied Mathematics, and the Association for Computing Machinery.Feodor Theilheimer, Naval Ship R&D Center Bethesda, MD was elected to full membership of the Sigma Xi, The Scientific Research Society in1975.

After retiring in 1977 Theilheimer taught mathematics courses at the University of Maryland until 1983. Theilheimer and his wife continued to live in Chevy Chase after he retired and, in December 2000, he died there. Henny Theilheimer, his wife, moved to New York after the death of her husband and died there on Wednesday, 22 May 2013.

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

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