**Edgar Raymond Lorch**was known as

**Ray**but gave his name on papers as Edgar R Lorch or E R Lorch. His father, Henry John Lorch (1868-1957), was born in Brighton, Sussex, England, the son of a German father and English mother. Ray's mother, Myrtle A Racine, was born in 1876 in Switzerland to Swiss parents. Ray's older brother Arthur E Lorch was born in Frankfurt, Germany in 1904. Ray's older sister Madeline D Lorch was born in Frankfurt, Germany in 1905. Ray was born in Nyon, on Lake Geneva, in Switzerland in 1907. In 1916 Henry Lorch emigrated to the United States, leaving his family behind until he was settled. In the following year Myrtle, Arthur, Madeline, and Ray left Switzerland to join up with Henry Lorch who was working as a bank clerk in Bergen, New Jersey.

Lorch attended Columbia University in New York where he studied mathematics and was awarded a Bachelor's degree, summa cum laude, in 1928. In his final undergraduate year he was awarded the Albert Ascher Green prize. He continued to study at Columbia University for his Ph.D. advised by Joseph Ritt and submitted his thesis *Elementary Transformations* in 1932. In the same year he became an American citizen and he published a paper with results from his thesis in the *Annals of Mathematics*. This paper, with the same title as his thesis, begins as follows:-

He was awarded the degree of Ph.D. in 1933 which was the year in which the United States was suffering most severely from the Great Depression with over one quarter of the workforce unemployed. Obtaining a university position would have been almost impossible for Lorch but, fortunately for him, he was awarded a National Research Council Fellowship to finance a year of postdoctoral study at Harvard University working with Marshall Stone. Three others with a National Research Council Fellowship arrived in Harvard at this time, namely Magnus Hestenes (1906-1991), David Solomon Nathan (1903-1957) and Deane Montgomery. They formed a seminar to study topology lecturing to each other from Oswald Veblen'sIn a series of remarkable memoirs, Liouville demonstrated the impossibility of evaluating certain indefinite integrals, and of solving certain differential equations, in terms of elementary functions. The elementary functions are understood here to be those which are obtained in a finite number of steps by performing algebraic operations and taking exponentials and logarithms. ... A transformation on n variables is called an elementary transformation provided the n functions which define the transformation are each elementary. One of the problems arising in the study of elementary transformations is to determine under what conditions the inverse to such a transformation is itself elementary. For transformations operating on one variable, the problem has been completely solved by J F Ritt[in the paper "Elementary Functions and their Inverses," Trans. Amer. Math. Soc.27(1925)]. In this paper we analyse this problem for the case of elementary transformations of a special type operating on two variables.

*Analysis Situs.*Shortly after they began, they were joined by Norman Steenrod. Lorch explained in [4] that the National Research Council Fellowships:-

Stone advised Lorch to more deeply study Hilbert spaces and Banach spaces. Stone also said that the two mathematicians who would be of the greatest help to him would be John von Neumann and Frigyes Riesz [4]:-... had been severely cut, both in number and in stipend. Nevertheless, even with the reduced stipend of $1,600for twelve months, I managed to live in Boston like a Bohemian, dividing my activities between wooing the recalcitrant muse of mathematics and indulging in the follies of youth: drinking beer, going to symphony concerts, and jogging in the park. This extra year at Harvard was supposed to give us a "coat of varnish," as one of my friends put it. Whether it turned us into gentlemen or scholars is a moot question. It did provide a line in my curriculum vitae. Future employers were impressed.

With the Great Depression still causing great worries about future jobs, Lorch applied for an extension to his one-year National Research Council Fellowship to visit the Institute for Advanced Study at Princeton. He was delighted to be offered a position as John von Neumann's assistant and made a trip to Princeton to see what the duties of an assistant would be. Oswald Veblen, the director of the Institute, told him what was expected of von Neumann's assistant. Lorch did not feel that anyone could carry out all the tasks that were expected of the assistant but he said he'd think it over. Back at Harvard, he received a letter from Columbia University offering him a Cutting Traveling Fellowship. After a good deal of thought and taking advice from others, he decided to turn down the position at the Institute for Advanced Study, accept the Cutting Traveling Fellowship and visit Frigyes Riesz in Hungary. He wrote to Riesz and got back a positive reply.Stone had a special sense of humour. At one of our infrequent meetings I mentioned some problems as possible candidates for research topics. About the best one of my problems, Stone said, "Oh, I don't know. Somebody must have worked on that problem already." The following week, while browsing in Widener Library, I came upon an article containing the complete solution to the problem. The author: M H Stone.

Arriving in Szeged he found a sleepy market town with almost no cars and a great many horses. The University was of high quality with leading academics. He was given a room in the postgraduate college, Eötvös Kollégium. He had [4]:-

Lorch had a productive year with Frigyes Riesz.... an adequate room, with bed, table and hard chair. The room was kept in order by a hall boy, who would run errands for a tip. The entrance to the Kollégium was locked at11p.m. Access for latecomers was by ringing a bell to waken the concierge. After midnight you had to pay a fee. Poor students could not afford it, and were in their rooms by10p.m. The "rich" could spend their evenings drinking wine in the cafes and return at all hours. This was especially true during carnival, when merriment went on until the wee hours of the morning.

He had exceptionally good relations with Riesz [4]:-

His collaboration with Riesz led to a joint paper,The optimal relation between a mentor and his disciple is seldom achieved. The relation between Riesz and me was optimal. It was warm, intimate, continuous, without pressure, very calm, leaving each of us free to develop his own thoughts. My stay with him was a perfect amalgam of a healthy, pleasurable life and an uninterrupted communication of mathematical ideas. Access to mutual discussion was free, but never overused. Frigyes Riesz was indeed a perfect teacher and a warm companion.

*The integral representation of unbounded self-adjoint transformations in Hilbert space*, which was published in the

*Transactions*of the American Mathematical Society in 1936. They discussed mathematics at the university in Szeged but also on other occasions. They spent free time together, at weekends, on vacation days, and they often went to Budapest where they stayed at the hotel "Gellért". The days in Budapest were spent visiting friends who were mathematicians but they especially loved the famous swimming pool at the hotel where mathematics was discussed while they swam slowly back and forward in the pool. The only unpleasant thing about the visit was the tension that was in the air due to the political situation where everyone was nervous at Hitler's rise to power.

This joint paper was not the only paper to come out of his visit to Szeged [4]:-

Returning to the United States in May 1935, Lorch was appointed as an Instructor in mathematics at Columbia University. He married the teacher Else Beylegaard Petersen, daughter of Lorentz Severin Petersen and C Ingrid Olsen, on 31 July 1937. Else had been born in 1915 in Bergen, Norway. They had three children, Edwin Duncan, Madeleine Louise and Ingrid Jacqueline. They were divorced in 1955.While I lived in Szeged, I published a paper on functions of self-adjoint transformations in which I replaced the previous definition by bilinear forms and Lebesgue-Stieltjes integration with a theory of measure determined by a resolution of the identity, where the measure of a set is a closed linear manifold. This measure has the virtues that the measure of the intersection and union of sets is the intersection and union of the measures, and the measure of a set essentially determines the set. Riesz was much interested in this paper, and made many useful suggestions while I was writing it.

In 1941 Lorch was promoted to assistant lecturer at Columbia University. In 1944 he became an associate professor but, at the same time, he spent the year 1944-45 doing war work as a research mathematician on the National Defense Research Committee. In 1948 he was appointed as Adrain professor mathematics, a position he held at Columbia until he retired. Also in 1948 he became Science advisor to the chief of staff of the United States Army. Lorch was enthusiastic about visiting European countries and able to deliver lectures in five different languages. For example during his career he lectured in France, Germany, Scandinavia, Switzerland, and Italy where, as well as collaborating with mathematicians he also worked with philosophers and psychologists. One of his trips to Italy was particularly important when he was Fulbright lecturer in Italy during the academic year 1953-1954. He gave a series of lectures in Italian at the University of Rome which he then rewrote in English to become his famous book *Spectral Theory* (1962) described by a reviewer as "a model of economy and clarity."

We noted above that Lorch was divorced from his first wife in 1955. On 25 March 1956 he married Maristella de Panizza Bové. Maristella had been born in Bolzano, Italy on 8 December 1919, studied at the Liceo Classico, Merano, before obtaining a doctorate from the University of Rome in 1941. She was a professor of Latin and Greek at the Liceo Virgilio in Rome, before emigrating to the United States in 1947. Like Lorch, she was divorced from her first husband, Claude Bové, in 1955. She had one daughter Claudia with her first husband. Ray and Maristella Lorch had two daughters Lavinia Edgarda Lorch and Donatella Livia Lorch. Maristella was on the Faculty of Barnard College and of Columbia University from 1951 until she retired in 1990.

Between 1958 and 1990, Ray and Maristella de Panizza Lorch worked to enhance links, particularly educational links, between Europe and the United States. For example they collaborated on developing the Lycée Français de New York, which integrates French and American education, with Ray serving as 'Conseiller Scientifique' and his wife a Senior Member of the Board. In 1986 they were co-founders, along with other members of Columbia University, of La Scuola New York, now called the Scuola d'Italia. This is a bilingual, bicultural school.

Lorch was Chairman of the Department of Mathematics at Barnard College from 1948 to 1963, and served as chairman of the committee on instruction in 1961. He was a Visiting professor at the Carnegie Institute of Technology in 1949, at the University of Rome in 1953-1954 and again in 1982, at the University of Florence in 1953-1954 and again in 1975, at the College de France in 1958, at Stanford University in 1963 and at the Middle East Technology University, Ankara in 1965. He was Fulbright lecturer in Colombia in 1977.

He was chairman of the mathematics department at Columbia University from 1968 to 1972 and, four years later in 1976, he retired from his Adrain professorship in mathematics and made professor emeritus. However he continued to lecture and retirement saw him become involved in a number of different projects [6]:-

Lorch played an active role in the American Mathematical Society. He served on the council from 1952 to 1955, was chairman of the committee on nominations in 1958, and was a member of the editorial board from 1945 to 1950. He was also an active member of the Mathematical Association of America. He was a member of the Accademia dei Lincei, the Societé Mathématique de France, the Oesterreichische Mathematische Gesellschaft, and the Unione Matematica Italiana.In1980Dr Lorch helped found the Center for International Scholarly Exchange at Barnard-Columbia. Since1982he had been chairman at Columbia of the University Seminar on 'Computers, Man and Society'.

It was music that was Lorch's greatest passion outside mathematics. He deeply loved music, as a composer, pianist and organist. It was fitting that Columbia University's Italian Academy for Advanced Studies, founded in 1991 by Maristella de Panizza Lorch, presented the first annual E R Lorch Memorial Recital on Wednesday, 1 May 2013 with a performance by Italian pianist Emanuele Torquati.

In May 1989 Ray and Maristella de Panizza Lorch visited Hungary to celebrate Ray's long connections with the country beginning with his doctoral studies there in 1934.

Lorch died on at St Luke's-Roosevelt Medical Center in Manhattan after a long illness. He had written two manuscripts for a proposed book on mathematics in Hungary. However, he never completed the project so, after his death, Reuben Hersh edited the two manuscripts to create the article [4]. In 1994 he received the posthumous award of the Lester R Ford award from the Mathematical Association of America for the article 'Szeged in 1934' published in the *American Mathematical Monthly*.

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