**George Gunter Lorentz** was a Russian-born American mathematician who worked in approximation theory, interpolation theory of operators, and functional analysis.

- Rudolf Fedorovich was ethnically German while Milena Nikolaevna was ethnically Russian.
- We should say a few words about Lorentz's name.
- Following the Russian tradition his name was originally Georg Rudolfovich Lorentz.
- We shall explain later why he became known as George G Lorentz.
- However, in 1906, he refused to participate in the suppression of a strike on his railway near St Petersburg.
- This forced him to move to the Caucasus, where most railways belonged to private companies.
- This middle-sized town changed hands (from White to Red and back) three times during the civil war that followed the revolution.
- Next we moved to Tbilissi, the capital of Georgia.
- It was in Tbilissi that Lorentz attended secondary school.
- He entered a Russian school in 1923, moving to a German one a year later.
- In 1926, at the age of sixteen, Lorentz entered the Tbilissi Institute of Technology where he studied mathematics.
- His work was of such a high standard that his teachers advised him to transfer to Leningrad State University.
- St Petersburg, the city of his birth, had been renamed Petrograd in 1914 but had been renamed Leningrad four years before Lorentz entered the university there in 1928.
- At this time Leningrad was an excellent mathematical centre and Lorentz thrived there.
- Independent thinkers were being persecuted and the President of the Leningrad Mathematical Society, a man with a reputation for courage and independent thought, was in such danger that the Leningrad Mathematical Society was disbanded in 1930 in a successful attempt to save the life of the President and the lives of other mathematicians.
- Lorentz was awarded his diploma in 1931 but, with the government insisting that research be applied in nature, he could not register to study for a candidate's degree (equivalent to a Ph.D.).
- He was employed as a teaching assistant at the University and, after a while, he also lectured at the Herzen Pedagogical Institute.
- While carrying out a heavy teaching load, he also undertook research without the help of a thesis advisor.
- He published the results of his research during these years in several papers: Über lineare Summierungsverfahren (1932), Funktionale und Operationen in den Räumen der Zahlenfolgen (1935), Sur la convergence forte des polynômes de Stieltjes-Landau (1936) and Zur Theorie der Polynome von S Bernstein (1937).
- In September 1939, Russia, allied with Germany, invaded Poland from the east.
- This had little effect on life in Leningrad.
- However, in June 1941 the course of the war changed dramatically for those living in Russia since Germany invaded their country.
- By the following month Hitler had plans to take both Leningrad and Moscow.
- As the German armies rapidly advanced towards Leningrad, many people were evacuated from the city.
- The war was to bring the population of Leningrad horrible sufferings.
- During the severe winter of 1941-42, there was artillery fire into the city, but no air raids.
- For private use, there was no electric power, no water (the water piping was frozen), no public transportation.
- At the beginning of April 1942 we crossed the still frozen Lake Ladoga in trucks and joined a train.
- While in Kislovodsk he found Antoni Zygmund's Trigonometrical series in the library of a small nearby college - the book proved significant in his mathematical development.
- However, in August 1942 Kislovodsk was taken by the Germans and the library burned down so he could not return Zygmund's book.
- In 1943 he sent two papers with his latest results to Konrad Knopp, who held the chair of mathematics at Tübingen University, hoping that they might be published in Mathematische Zeitschrift.
- Kamke was writing a book on differential equations.
- Lorentz submitted his thesis Eine Fragen der Limitierungs theorie to Tübingen and was awarded a doctorate.
- the French authorities classified me as an undesirable foreigner, ...
- We mentioned at the beginning of this biography that Lorentz's name was originally Georg Rudolfovich Lorentz.
- In 1946 he began to use the name Georg Gunter Lorentz in an attempt to hide his Russian origins.
- 'Gunter' was made up and he only used it for a short while, afterwards using the name Georg G Lorentz.
- Offered a Lady Davis Foundation fellowship at the University of Toronto, Canada, he began work there as an Instructor in Mathematics in July 1949.
- Despite giving Lorentz low academic status, having already successfully supervised the doctorates of two students at Tübingen, he was immediately asked to supervise four doctoral students in Toronto - two of these being G M Petersen and P L Butzer.
- is a well-known expert in this field, and his careful up-to-date and easily readable account of problems and progress, the first in book form, should be welcome to a large class of advanced students of mathematical analysis.
- They were delivered with a command of English which made it difficult to believe he had not had much previous experience lecturing in this language.
- The organization of the material was very good and the content presented a titillating mixture of well-known theorems and personal research.
- We were always greeted with a smile and treated to an intelligent and pertinent discussion of our work.
- When we bogged down, he took a hand himself; when we succeeded, he praised us.
- He has always given of his knowledge freely and been very stimulating to students, even those in lines different from his own.
- By 1953 Lorentz, already an assistant professor at Toronto, was offered an associate professorship but chose not to accept that, rather preferring to accept a full professorship in the United States, at Wayne State University in Detroit.
- Real and functional analysis (18 articles on rearrangement of functions and Lorentz spaces); and 4.
- Approximation theory (38 articles on Bernstein polynomials, Korovkin theory, Bernstein and Markov inequalities, Kolmogorov's notion of entropy, width and the superposition of functions, best monotone approximation and incomplete polynomials).
- We looked briefly above at Lorentz's first book, namely Bernstein polynomials (1953).
- Here the author goes out of his way to keep the discussion elementary (not easy!).
- Chapters nine, ten, and eleven concern entropy and Kolmogorov's solution of Hilbert's thirteenth problem.
- Fascinating, but highly special, and not self-contained for non-specialists ...
- The book abounds with amusing and interesting insights.
- There are problems and notes which extend the results in the text and give their history.
- A special feature is the coverage of the Russian literature of this field.
- The book is aimed at the graduate or advanced undergraduate level, and includes a considerable number of problems (some of which are rather more challenging than others).
- As everyone familiar with the book knows, the author has been very successful at meeting his goals, and the book is indeed a very readable introduction to the subject and makes an excellent textbook.
- This second edition was hardly altered since Lorentz was working on a 15-year writing project with the idea of presenting a unified treatment of some of the many developments that have occurred in the subject since his 1966 textbook.
- The authors are top researchers in the field who had good taste and judgement in collecting the most important results of the constructive aspects of the theory.
- This monograph may well be the best book available on the subject, so it can be recommended to graduate students, mathematicians, physicists and engineers who have an interest in constructive approximation.
- The organization and presentation are extremely clear, and the book is suitable for graduate and even higher level undergraduate courses.
- Three years later, Lorentz published a companion volume to this text, in collaboration with Manfred von Golitschek and Yuly Makovoz, concentrating mainly on univariate approximation of real functions.
- While working on this volume he spent much time with Golitschek at the University of Würzburg.
- Lorentz received many honours for his outstanding mathematical contributions.
- He was awarded honorary doctorates from the University of Tübingen (1977) and the University of Würzburg (1996).
- Lorentz's hobby which we have not yet mentioned was stamp collecting.

Born 25 February 1910, St Petersburg, Russia. Died 1 January 2006, Chico, California, USA.

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Origin Russia

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive