# Octav Onicescu

### Quick Info

Botoșani, North Moldavia (now Romania)

Bucharest, Romania

**Octav Onicescu**was a Romanian mathematician with research interests that included many areas such as probability, Riemannian manifolds, absolute differential calculus, functional analysis, algebra, and the topological theory of functions. He is considered as the founder of the Romanian school of probability.

### Biography

**Octav Onicescu**was the son of Vlad Onicescu, from Stefanesti, Botoşani County, and Ana Schipor, from Bucovina, but of Macedonian origin. The Onicescu family were land owners and were involved in local government. Octav's primary education was at the Boys' Primary School in Botoşani and then he entered the "August Treboniu Laurian" High School, one of the best high schools in the country, which had been founded in 1858. In this High School he showed a special interest in mathematics and philosophy, and graduated with the highest possible average of 10. Although he excelled at mathematics, he also excelled at poetry which was another of his favourite subjects.

In 1911 Onicescu took the baccalaureate examinations, and then enrolled in the Faculty of Sciences of the University of Bucharest; he also attended courses in the Faculty of Philosophy. At the Faculty of Sciences he was taught mathematics by professors Gheorghe Țițeica, Dimitrie Pompeiu and Traian Lalescu (1882-1929). Țițeica and Pompeiu have biographies in this archive, while Lalescu was an expert on integral equations although he had broad mathematical interests including functional equations, trigonometric series, mathematical physics, geometry, mechanics, algebra, and the history of mathematics. Onicescu attended lectures in the Faculty of Philosophy by Constantin Radulescu-Motru (1868-1957) and Petre Paul Negulescu (1870-1951). These two eminent philosophers had very different political views, Radulescu-Motru being a socialist and Negulescu a Conservative who twice served as Education Minister during the 1920s.

At the University of Bucharest, Onicescu won the admiration of his teachers, especially Gheorghe Țițeica, the leading Romanian mathematician at that time. Onicescu and Țițeica became friends and had a long mathematical collaboration. In 1913 Onicescu graduated in Mathematics and Philosophy, completing his studies a year earlier than his fellow students. In 1914 he began his teaching career, becoming a mathematics teacher at the Military High School at the Dealu Monastery, 6 km north of Targoviste, where he worked until 1916. This Military High School had only been founded in 1912, two years before Onicescu began teaching there, by Nicolae Filipescu. It was a very important school for the Romanian army in the period between the Two World Wars, and it played a large role in the process of modernising the Romanian army.

In 1916 Onicescu married Luiza Zorio, who was born in Italy, the daughter of the hydraulic engineer Michele Zorio (1866-1931). Michele Zorio had brought the first water supply to the district of Botoşani. Octav

**and**

**Luiza Onicescu had two sons, Dan and Mircea. Mircea Onicescu (1925-2011) became a gynaecologist.**

World War I began in 1914 but for two years Romania was neutral. On 27 August 1916 Romania entered the war allied with Russia and Britain against the Central Powers of Germany, Austro-Hungary, the Ottoman Empire, and Bulgaria. Onicescu volunteered for military action and joined the Romanian army as an active fighter on the front. After the Russian Revolution in October 1917, Russia withdrew from the war and Romania's position become very difficult being totally surrounded by the Central Powers. They signed the Treaty of Bucharest with the Central Powers in May 1918 but the treaty was nullified after the war ended with the defeat of the Central Powers later that year. Onicescu ended his military service in 1918.

After leaving the army, he was awarded a state scholarship to undertake research for a doctorate in mathematical sciences at the University of Rome La Sapienza, with Tullio Levi-Civita as his thesis advisor. The topic of his doctoral thesis was one of great interest and topicality at that time, namely applying differential geometry to the general theory of relativity. We see how topical this was if we note that Albert Einstein had only published the general theory in late 1915, three years before Onicescu began to undertake research. Luigi Bianchi and Gregorio Ricci-Curbastro had both studied three-dimensional differential varieties that admitted groups of transformations, with major papers

*On the three-dimensional spaces which admit a continuous group of motions*(1897) and

*Méthodes de calcul différentiel absolu et leurs applications*Ⓣ (1900), respectively. In his thesis Onicescu took the 3-dimensional ideas of these papers and generalised them into the 4-dimensional analogues relevant to general relativity. While working on his doctorate, he published several papers in the field of differential geometry, which brought him great prestige, for example

*Campo newtoniano viciniore ad un campo vettoriale assegnato*Ⓣ (1920),

*Sulle varieth che ammettono una translazione infinitesima*Ⓣ (1920), and

*Spazi che ammettono una translazione infinitesima lungo le linee di lunghezza nulla*Ⓣ (1920). In June 1920 he defended his doctoral dissertation

*Sopra gli einsteinieni a gruppo continuui di transformazione*Ⓣ at the University of Rome. He was examined by a committee consisting of eleven mathematicians, including Tullio Levi-Civita, as president, Vito Volterra and Guido Castelnuovo. His doctoral thesis was praised by the committee for its originality in applying differential geometry of the general theory of relativity. In addition to his main doctoral dissertation, he also presented three supplementary dissertations, one on the composition logarithm, one on the bases of geometry and one on hydrodynamics. On 20 June 1920, he graduated as Doctor of Mathematics from the University of Rome, with the distinction 'magna cum laude', and became the first Romanian to obtain the title of Doctor of Mathematics from La Sapienza in Rome. We should note here that while Onicescu was in Rome, he attended lectures on probability by Francesco Paolo Cantelli. These lectures, based on Guido Castelnuovo's book

*Calcolo della probabilità*Ⓣ (1919), created a strong impression and later in his career, Onicescu would do impressive work on probability and statistics.

After the award of his doctorate, Onicescu spent the year 1920-21 in Paris. He was a member of Jacques Hadamard's seminar at the Collège de France and also attended lectures by Émile Picard and Élie Cartan at the Sorbonne. Élie Cartan's lectures on integral invariants made a strong impression on Onicescu and gave him an interest in mechanics. In Paris he met up with the Romanian mathematicians Petre Sergescu and Alexandru Pantazi (1896-1948) who were both in Paris undertaking research for their doctorates. Another Romanian in Paris at that time was Serban Coculescu (1902-1959), known as Pius Servien, who was studying philology, mathematics, physics and philosophy at the Sorbonne. He was the son of the mathematician and astronomer Nicolae Coculescu (1866-1952). Onicescu organised a seminar in which all these Romanians took part. After his year in Paris, Onicescu returned to Romania where he continued as a teacher at the Military High School at the Dealu Monastery but was invited to lecture on general relativity at several institutions.

In 1922 Onicescu was appointed as a lecturer in the Faculty of Sciences of the University of Bucharest. He was appointed as an assistant professor in 1928 then, on 1 July 1929, he was appointed associate professor, and in 1931 he became a full professor. Over the following years he moved to head various departments in the University of Bucharest. His 1931 appointment was as Professor of Theoretical Mechanics in the Physics Section of the Faculty of Science, but in 1938 he became Professor of Algebra in the Mathematical Section of the Faculty of Science and in 1948, after the University of Bucharest was reorganised, he became Professor of Probability in the Faculty of Mathematics and Physics. It is perhaps surprising that he headed departments concerning very different areas of mathematics but we should emphasise that Onicescu's mathematical interests were indeed very broad. He taught courses on mechanics, absolute differential calculus related to Einstein's theory, continuous groups of transformations, probability calculus, statistical mechanics, statistics and insurance, and potential theory. His research interests included many areas such as: probability, Riemannian manifolds, absolute differential calculus, functional analysis, algebra, and the topological theory of functions. To quote from Onicescu [31], he considered himself:-

... a researcher of facts: human, social, economic, of natural phenomena, with mathematical means, preferable probabilistic or mechanical, a researcher who determined throughout his whole life to assimilate much more mathematical science in order to use it in his research activity.He gave a expanded version of this in a speech he made at the Romanian Academy at a meeting held to celebrate his 75th birthday [32]:-

I am not first of all a mathematician, by no means a probabilist as most agree, not even a mechanician as some do not want to consider me. I regard myself as a researcher of human actions, either social or economic, and natural phenomena, who used mathematical tools, preferably probabilistic or mechanical, who all his life strove to assimilate as much mathematics as he could for using it in his researches. I cultivated probability as a science of measurement of random events and processes. I cultivated mechanics as a support or a model of any science of natural motion. In this long and difficult way I met geometry, algebra, and analysis, sometimes topology, and I did not hesitate to take up the problems raised. It was my chance that at any important moments of my scientific or social enterprises I enjoyed ideas, and enthusiasm to materialise my projects that become common to all of us.In 1924 Onicescu gave a course on Probability, Statistics and Applications, the first university level course on this topic to be given in Romania. He approached the Central Institute of Statistics, arguing that statistics required a much greater input from mathematics and mathematicians than was happening at that time. He continued to teach probability theory until he retired in 1962. He was appointed as chair of the Romanian Census of 1930 but found it difficult to organise due to a lack of statisticians. In an attempt to remedy this situation, in 1930 he founded the School of Statistics, Actuarial Science and Computing in Bucharest, where he was director for several years. About ten years after it was founded, the School of Statistics changed its name to the Institute of Statistics, Actuarial Science and Computation of the University of Bucharest. For political reasons, the Institute was disbanded in 1947; we will say more later in this biography about Onicescu's involvement in politics.

There are two distinct phases to Onicescu's work on probability. The first phase up to 1958 involved a very fruitful collaboration with Gheorghe Mihoc. Mihoc taught actuarial mathematics from 1930 to 1948 at the School of Statistics. He undertook research for a doctorate advised by Onicescu and, 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. They collaborated on many papers, four in 1936, three in 1937, one in 1938, and three in each of 1939 and 1940. This joint work laid down the basis of the Romanian school of probability theory. They were joint authors on five books, one of which was

*La Dépendance Statistique: Chaînes et Familles de Chaînes Discontinues*Ⓣ. This book was reviewed by Alex Aitken [2]; you can read an extract of Aitken's review at THIS LINK.

We noted above that there was a second phase in Onicescu's work on probability. This was after 1958 when he produced a new framework for probability theory, which replaced the classical event space concept with a Boolean σ-algebra. He wrote the book

*Probability Theory on Boolean Algebras of Events*(1976) in collaboration with Ion Cuculescu which was reviewed by Alan J Mayne [24], Demetrios A Kappos [22] and Sergiu Rudeanu [37]. You can read extracts from their reviews at THIS LINK.

Another of Onicescu's contributions was his work on mechanics. In this area he introduced 'invariant mechanics' which is [28]:-

... a science of motion in which the presence of the whole universe is to be found in each of its components, not by structural geometric ways, as in relativity, but by means of the analysis of the elementary processes of motion following the line of Newtonian thought, the Invariant Mechanics, without leaving the spatio-temporal frame of the old science, has found, together with gravity, a second inertial interaction, similar to an elastic repulsive force. Slightly sensitive to current distances, but very sensitive to intergalactic distances, this interaction is for a great part responsible for Hubble's expansion and at the same time for the stability of the universe, in its limits, necessarily finite.With this theory, it is tempting to think that Onicescu might be trying to solve the problem of 'dark energy' which, of course was not proposed until 1998!

The above quote is taken from the Preface to Onicescu's book

*Invariantive Mechanics*(1975). For a longer extract from this Preface and a short extract from the Introduction, see THIS LINK.

Onicescu's activities were so broad that it is impossible to give details of most of his contributions to the development of mathematics and statistics in Romania. Here are a few examples. From 1925 he taught mechanics applied to the human body at the Institute of Physical Education in Bucharest and served as rector of the Academy of Physical Education from 1929 to 1940. In 1932 he founded the Romanian Institute for the Study of the Economic Conjuncture and in the same year he founded the Romanian Society of Science. He was elected a corresponding member of the Romanian Academy in 1933 and was one of the founders of the "The Institute of Mathematical Sciences of the Romanian Academy" founded on 22 December 1945. A Probability Section of the Institute of Mathematical Sciences was created in 1949 with Onicescu as its head. He became president of the General Pension Establishment in the Ministry of Finance in 1941 and, in the same year, president of the Private Insurance Control Council in the Ministry of the Economy. In 1968 he was a cofounder of the International Centre for Mechanical Sciences in Udine, Italy.

Mihai Botez writes [3]:-

... in the 1930s, Onicescu was a 'public figure'; he was often invited to the Royal Palace for state dinners and other events, and the list of his personal friends included influential politicians from all political parties, leaders of spiritual life - like the controversial philosopher Nae Ionescu of the great composer George Enesco - and even people like philanthropist-industrialist N Malaxa (persuaded by the Professor to sponsor scientific events, including an international award for mathematicians).Although a 'public figure' in the 1930s, after the Communist takeover of Romania which followed the Soviet occupation of Romania after World War II, Onicescu concentrated on his scientific work and did not take part in other activities. He was not re-elected to the Romanian Academy, which had been renamed the 'Academy of the People's Republic of Romania'. He did, however, keep his professorship at the University of Bucharest. His already impressive output of papers increased further with, for example, 55 papers published in the ten years between 1954 and 1963. As Cezar Stanciu writes in [39]:-

... the 1960s was a good time for Romanians, as the Communist regime, aiming to affirm its autonomy in front of Moscow and pursue its national-communist project, seemed to lean closer and closer to the West. The cultural and ideological restrictions of the Stalinist era had slowly faded away and Romania appeared to be headed for a different version of Communism, one relying on liberalisation and openness to the West.A change in policy in 1971, however, changed the way that Onicescu behaved, leading to him becoming politically active. The change in policy is described in [39] as follows:-

In July 1971, [Romania's leader Nicolae Ceausescu] made what appeared to many as a radical turn of his domestic policy: liberalisation of arts, culture, and social life were drastically limited and the Communist party engaged on a course which was strongly inspired by Stalinism.Mihai Botez, who knew Onicescu well at this time, writes [3]:-

His seminars were still tolerated by the authorities, but their content was almost subversive, prompting serious scientific approaches in a cynical milieu saturated by ideological dogmas. And his house became an island of intellectual freedom, where independent thinkers of different professions and ages were always welcomed. ... unlike the overwhelming majority of his colleagues in the Academy or University, he tried to use his immense prestige and position in order to help and even protect the dissidents, taking considerable risks for those days. It seems to me that such a courageous attitude should not be forgotten.Dan Carlea tells us in [5] that Onicescu was followed for years by agents of the State, listening devices were installed in his house, and his correspondence was censored. Only when he reached the age of 90 did these measures end.

Marius Iosifescu describes the end of Onicescu's life in [18]:-

Onicescu not only lived for a long time, but he also participated in many changes in the world and in his country. He was a man with a great deal of charm and wit, who enjoyed an exceptional family life. ... Onicescu was hard working up to the end. His physical and intellectual forces diminished only in his last two years. He found in his late work a remedy for the annoyances of the old age and the difficulties of everyday life. His last years were saddened by the fact that he missed his most beloved disciples who had settled far away. He rejoiced instead at the great affection extended to him by his family, friends and admirers throughout the world. I last saw Onicescu four days before his death. I had gone to his home to say good-bye before leaving for Warsaw to attend the International Congress of Mathematicians. Though already seriously ill he was still lucid. I expected to find him better on my return but, unfortunately, I was wrong. I was told he had just had the time to see his 90th birthday Festschrift so well deserved by him.Among the many honours given to Onicescu let us mention that he was elected a full member of the Romanian Academy in 1965, was elected as member of the Academy of Science in Torino in 1976 and became an honorary member of the International Statistical Institute in 1982. On the centenary of his birth in 1992 Romania issued a stamp in his honour. See THIS LINK.

The "Octav Onicescu" museum was founded in Botoşani in October 1995; it is the only museum in Romania for a mathematician.

### References (show)

- Acad. Prof. Octav Onicescu: 1892-1983,
*An. Univ. Bucuresti Mat.***33**(1984), 97. - A C Aitken, Review: La Dépendance Statistique: Chaînes et Familles de Chaînes Discontinues, by O Onicescu and G Mihoc,
*The Mathematical Gazette***22**(252) (1938), 518-519. - M Botez, Science and conscience: Octav Onicescu, as I have known him,
*Libertas Math.***12**(1992), 1-7. - I Bucur, G Ciucu, Gh Mihoc, C Iacob, Gh Galbura, C Petrescu, V Bulgaru, I Cuculescu and S Guiasu, Celebration in honour of academician Octav Onicescu (Romanian)
- D Carlea, The mathematician Onicescu and Rugul Aprins,
*LUMINA*(19 August 2017).

https://ziarullumina.ro/societate/timp-liber/matematicianul-onicescu-si-rugul-aprins-125390.html - H I Cohn, Review: Principles of probability theory (Romanian), by O Onicescu,
*Mathematical Reviews*MR0259963**(41 #4592)**. - I Cuculescu, Octav Onicescu (August 20, 1892 - August 19, 1983),
*Rev. Roumaine Math. Pures Appl.***29**(8) (1984), 639-640. - I Cuculescu, Academician Octav Onicescu (1892-1983) (Romanian),
*Gaz. Mat. (Bucharest)***88**(12) (1983), 433-434. - A Daia, S Stancu and C Ionescu-Tîrgoviste, Experimented Kinetic Energy as Features for Natural Language Classification,
*Proc. Rom. Acad., Series B***20**(3) (2018), 203-206. - A Daia, S Stancu, C Ionescu-Tirgoviste and I-M Stanciu, Octav Onicescu's Contribution to Informational Theory,
*Proc. Rom. Acad.*Series B**23**(1) (2021), 136-139. - M C Demetrescu and M Iosifescu (eds.),
*Papers in Honour of Octav Onicescu on his 90th Birthday*(Nagard, Rome, 1983). - J L Doob, Review: Nombres et systèmes aléatoires, by O Onicescu,
*Mathematical Reviews*MR0172314**(30 #2533)**. - J Douglas Jr., Review: Game theory, with applications to linear programming (Romanian), by O Onicescu,
*Mathematical Reviews*MR0180400**(31 #4635)**. - Editors, Review: The calculus of probability and its applications (Romanian), by O Onicescu, G Mihoc and C T Ionescu Tulcea,
*Mathematical Reviews*MR0085637**(19,69h)**. - H-O Georgii, Review: Mécanique statistique. Principes mathématiques, by Octav Onicescu and Silviu Guiasu,
*Mathematical Reviews*MR0418792**(54 #6828)**. - I J Good, Review: Nombres et Systèmes aléatoires, by Octav Onicescu,
*Journal of the Royal Statistical Society. Series A (General)***129**(2) (1966), 291. - History (Romanian),
*National College " Octav Onicescu"*.

https://onicescu.ro/istoric/ - M Iosifescu, Obituary notice: Octav Onicescu, 1892-1983,
*Internat. Statist. Rev.***54**(1) (1986), 97-108. - M Iosifescu, Octav Onicescu (20 August 1892-19 August 1984), in C C Heyde, E Seneta, P Crépel, S E Fienberg and
*J Gani (eds.), Statisticians of the Centuries*(Springer Science Business Media, New York, 2001) - M Iosifescu and S Grigorescu,
*Dependence with Complete Connections and Its Applications*(Cambridge University Press, Cambridge, 1990). - C Jacob, L'académicien Octav Onicescu à 90 ans,
*Proceedings of the seventh conference on probability theory*(Brasov, 1982), 11-14. - D A Kappos, Review: Probability theory on Boolean algebras of events, by O Onicescu and I Cuculescu,
*Mathematical Reviews*MR0448469**(56 #6775)**. - L'académicien Octav Onicescu (à l'occasion de son 85e anniversaire),
*Rev. Roumaine Math. Pures Appl.***22**(10) (1977), 1357-1358. - A J Mayne, Review: Probability Theory on Boolean Algebras of Events, by O Onicescu and I Cuculescu,
*Operational Research Quarterly (1970-1977)***28**(4, 2) (1977), 1030. - G Mihoc, A life for probability, in
*J Gani (ed.) The Making of Statisticians*(Springer-Verlag, New York, 1982), 22-37. - I Negura, Le séminaire concernant l'application des méthodes statistiques et mathématiques à l'économie dirigé par l'académicien Octav Onicescu, in
*Studies in probability and related topics*(Nagard, Rome, 1983), 361-367. - Octav Onicescu (1892-1983), Mari matematicieni români,
*Mate.info.ro*.

https://mate.info.ro/resursa-mari_matematicieni_romani.html - O Onicescu,
*Invariantive Mechanics*(Springer-Verlag, Vienna-New York, 1975). - O Onicescu,
*Principes de logique et de philosophie mathématique*(Éditions de l'Académie de la République Socialiste de Roumanie, Bucharest, 1971). - O Onicescu,
*Memoirs*(Romanian). Volumes 1 and 2 (Scientific and Encyclopedic Publishing House, Bucharest, 1982-84). - O Onicescu,
*On the life's pathways*(Romanian) (Scientific and Encyclopedic Publishing House, Bucharest, 1981). - Onicescu, Octav,
*Encyclopedia of Mathematics*.

https://encyclopediaofmath.org/wiki/Onicescu,_Octav - Onicescu, Octav,
*OMNIA*.

https://www.omnia.ie/index.php?navigation_function=2&navigation_item=%2F2020801%2Fdmglib_handler_biogr_17198004&repid=1 - M Oprea, An Overview on the Contributions of the Academician Octav Onicescu to the Informational Statistics and Further Developments, in
*Proceedings of the 12th International Conference On Virtual Learning*(University of Bucharest, 2017), 54-62. - A Precupanu, Review: Almost periodic random functions in probability (Romanian), by O Onicescu, Gh Cenusa and I Sacuiu,
*Mathematical Reviews*MR0725331**(86a:60080)**. - V Preda and S Dedu,
*Octav Onicescu - The man and his work: Contributions to the development of economic research: Informational entropy in economics*(Romanian) (National Institute of Economic Research, Romanian Academy, Bucharest, 2015). - S Rudeanu, Review: Probability theory on Boolean Algebras of Events, by O Onicescu and I Cuculescu,
*Bulletin mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie, Nouvelle Série***21**(69) (1/2) (1977), 220-222. - S Rudeanu, Review: Probability theory on Boolean Algebras of Events, by O Onicescu and I Cuculescu,
*Bulletin mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie, Nouvelle Série***21**(69) (1/2) (1977), 220-222. - C Stanciu, The end of Liberalization in Communist Romania,
*The Historical Journal***56**(4) (2013), 1063-1085.

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Written by J J O'Connor and E F Robertson

Last Update March 2022

Last Update March 2022