# Gheorghe Mihoc

### Born: 7 July 1906 in Brăila, Romania

Died: 25 December 1981 in Bucharest, Romania

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**Gheorghe Mihoc**'s parents were Ecaterina and Gheorghe Mihoc. The parents were born in Banat, an ethnically mixed region which, in 1920, was divided between Romania, Hungary and Yugoslavia. In order to improve their chances of making a living, they had moved from Banat to Brăila, a city on the river Danube and the second largest port in Romania. They were in that city when their son Gheorghe, the subject of this biography, was born but they did not remain there for very much longer. Again hoping to improve their circumstances, the family moved when Gheorghe was two years old, settling in Bucharest. It was in this city that Gheorghe spent the rest of his childhood, indeed he spent most of the rest of his life in Bucharest.

After attending elementary school in Bucharest, Mihoc's secondary education was at the Gheorghe Sincai Gymnasium. It was here that he developed a love of mathematics and it is interesting to quote his own thoughts on this [1]:-

Mihoc graduated from the Gheorghe Sincai Gymnasium in 1925 and, in the same year, entered the Faculty of Science of the University of Bucharest. However he could not concentrate fully on his university courses since he had to earn money to finance his studies. He would spend three undergraduate years working incredibly hard studying and earning money. At Bucharest University, he was taught geometry by Gheorghe Țițeica, the professor of Analytical Geometry. Țițeica had just published the monographI had some good teachers ... all of whom inspired my love for this science. But there was still another element that directed me at an early stage towards mathematics, namely the existence of the 'Mathematical Gazette'. ... In its pages the names of the young authors who solved and proposed mathematical problems were mentioned. the fact that students have the opportunity to publish problems which they have discovered is of great pedagogical importance. During lessons, as well as in their private work based on textbooks, they learn to solve problems, and this helps them to understand more deeply what they are taught.

*Géométrie différentielle projective des réseaux*Ⓣ (1923) and, when he taught Mihoc, was writing another important monograph

*The projective differential geometry of lattices.*Țițeica's geometry lectures gave the spirit of current research and inspired Mihoc. Sadly his other lecturers were much less good and, in particular, analysis courses were taught by lecturers who were not active in the research of the day nor had they kept pace with current developments. In his third and final undergraduate year, Mihoc attended a course on probability theory given by Octav Onicescu [1]:-

Octav Onicescu (1892-1983) had studied geometry under Tullio Levi-Civita in Rome before spending some time on a visit to Paris. He returned to his native Bucharest in 1922 and, two years later, taught the first college-level probability theory course in Romania.It was an inspiring course outlining the state of the field at that time. This was my first contact with the discipline that was later to become my speciality.

Graduating in 1928, Mihoc was unable to find employment as a teacher. However, his career was saved by Onicescu who was promoted to professor the year that Mihoc graduated. Onicescu not only found Mihoc a job in the Department of Statistics and Actuarial Studies of the Social Insurance Service, but even persuaded the Service that they should fund him to spend a year in Rome undertaking specialist actuarial training. He spent 1928-29 in the Faculty of Statistical and Actuarial Sciences of the University of Rome. There were many outstanding mathematicians in the Faculty including Francesco Cantelli, one of the most prominent Italian contributors to the mathematical theory of probability, and Guido Castelnuovo who, although a specialist in algebraic geometry, had written the probability text

*Calcolo della probabilità*Ⓣ (1919) and was teaching courses on probability. Castelnuovo wrote:-

Also teaching in the Faculty were the statisticians Corrado Gini (1884-1965), who set up the School of Statistics in Rome in 1928, and Franco Savorgnan (1879-1963), who went on to succeeded Gini as the head of Istituto Centrale di Statistica and Consiglio Superiore di Statistica in 1932. Mihoc was also taught by the economist Rodolfo Benini who had held the chair of statistics in Rome until 1928 when he was appointed to the chair of economics. Mihoc studied for the degree of Doctor of Statistical and Actuarial Sciences advised by Castelnuovo and defended his thesis on Markov chains in Rome in July 1930. In this thesis he applied results obtained by Sergei Bernstein in his 1926 paperProbability is a science of recent formation; hence in it, better than in other branches of mathematics, one can see the relationship between the empirical contribution and the one given by reasoning, and between the process of inductive and deductive logic used in it. The fact that it is a science in the making explains why it is appropriate to give frequent examples to show the applications of known methods or to introduce new ones.

*Sur l'extension du théorème limite du calcul des probabilités aux sommes de quantités dépendantes*Ⓣ to extend results obtained by A A Markov on Markov chains in his 1912 book.

After returning to Bucharest, Mihoc continued with his actuarial work and was appointed as an assistant at the School of Statistics, Actuarial Studies, and Calculation which had been founded in that year. At this School, which was later named an Institute, Mihoc taught actuarial mathematics from 1930 to 1948. At the same time, he undertook research for a doctorate advised by Octav Onicescu. In 1934 he submitted his thesis

*On the general properties of dependent statistical variables*(Romanian) to the University of Bucharest and was awarded a doctorate in mathematics on 28 April of that year. His thesis was published in two parts in 1935 and 1936. By this time Mihoc was collaborating with his former professor, Octav Onicescu, and they published

*Sur les chaines de variables statistiques*Ⓣ in 1935. In this paper they gave sufficient conditions for ergodicity of a Markov chain. Their collaboration was very fruitful with four joint papers being published in 1936, three in 1937, one in 1938, and three in each of 1939 and 1940. In 1937 Mihoc was appointed as an assistant at the University of Bucharest and was promoted first to lecturer, then to professor. He worked at the University of Bucharest until 1973.

We give a few more details of his career at the University of Bucharest after first looking at other aspects of Mihoc's contributions. One of these is the remarkable collection of books he authored or co-authored. After looking at these we give some details of the many positions he held, both academic and non-academic, which were highly influential in the development of statistics in Romania. To see a selection of the many books that he wrote, some followed by reviewers comments, the reader should consult THIS LINK.

Let us mention here that the list, which is not complete, contains 26 items spanning 44 years. The last book in the list was published in 1981, the year in which Mihoc died at the age of 75. Most are Romanian texts that were never translated into English. A few were written in French. Five are co-authored with Octav Onicescu including:

*La dépendance statistique. Chaînes et familles de chaînes discontinues*Ⓣ (1937) and

*Lectures on mathematical statistics*(Romanian) (1957). Only two of the 26 are singled authored:

*Treatise on actuarial mathematics*(Romanian) (1943) and

*An Introduction to the calculus of probability*(Romanian) (1954). We should also single out for special mention the four volume

*Treatise on mathematical statistics*(Romanian) he wrote with Virgil Craiu. The four volumes are subtitled:

*Sampling and estimation*(1976);

*Testing statistical hypotheses*(1977);

*Sequential analysis*(1979); and

*Correlation and linear regression*(1981). We note that, several years before this collaboration, Mihoc supervised Craiu's doctoral studies; he was awarded his doctorate in 1968.

Despite this outstanding publication record consisting of the impressive list of books already mentioned together with 70 research papers, Mihoc also spent much of his career in administration. However, he writes in [1]:-

We have already given a few details of Mihoc's career, but we now give a few more. Between 1942 and 1946 he was a lecturer at the University of Bucharest, and then between 1946-1948 professor for financial mathematics at the Academy of Commerce. After educational reforms in 1948, he was appointed professor in the Faculty of Mathematics and Physics of the University of Bucharest, where he went on to become head of Applied Mathematics. He continued to hold this chair until his retirement. Meanwhile he was Director General of the Central Directorate of Statistics (1948-1951), dean of the Faculty of Mathematics (1951-1960) and vice-rector of Bucharest University between 1960 and 1963, after which he became rector for a period of five years until 1968. He was elected a corresponding member of Romanian Academy of Sciences in 1955. Elected a full member on 20 March 1963, he became President of the Academy in March 1980, holding this position until his death. On 1 April 1964 Mihoc founded, as a research institute of the Romanian Academy, the Centre for Mathematical Statistics where most of the Romanian specialists in probability theory, theoretical statistics and applied statistical sciences meet:-After a life devoted to science, I still feel I should have done more. This would have been possible if I could have spent less time in administrative and organisational work. On the other hand, I think that my involvement in such activities put me in a position where I was able to facilitate the access of deserving young people to research and teaching. Thus, at least in part, I do not regard these administrative duties as pure waste.

He was director of the Centre until 1976 and, in 1997 was given the honour that the Centre was named for him.Mihoc's motivation was a visionary understanding of the part that probability and statistics would play in the not very distant future, rather than the considerable expansion of these fields at the time.

In addition he organised many conferences in Romania. We mention in particular the series of conferences on probability in 1955, 1962, 1968, 1971, 1974 and 1979. He also organised the Anglo-Romanian Conference on Mathematics and Archaeological and Historical Sciences in 1970 and, four years later, the Eighth International Conference on Biometry. He died suddenly on Christmas day in 1981 having suffered a coronary thrombosis.

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

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**List of References** (8 books/articles)

**Mathematicians born in the same country**

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