Cassius Tocqueville Ionescu Tulcea ( ro, Casius Ionescu-Tulcea; October 14, 1923 – March 6, 2021) was a Romanian-American mathematician, specializing in

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...

statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

and

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

. Ionescu Tulcea was born in October 1923 in

Bucharest Bucharest ( , ; ro, București ) is the capital and largest city of Romania, as well as its cultural, industrial, and financial centre. It is located in the southeast of the country, on the banks of the Dâmbovița River, less than north of ...

. He received his diploma from the

University of Bucharest The University of Bucharest ( ro, Universitatea din București), commonly known after its abbreviation UB in Romania, is a public university founded in its current form on by a decree of Prince Alexandru Ioan Cuza to convert the former Princel ...

in 1946; there he was an assistant professor from 1946 to 1950, a lecturer from 1950 to 1951, and an associate professor from 1952 to 1957. Additionally, from 1949 to 1957 he was a researcher at the

Institute of Mathematics of the Romanian Academy The "Simion Stoilow" Institute of Mathematics of the Romanian Academy is a research institute in Bucharest, Romania. It is affiliated with the Romanian Academy, and it is named after Simion Stoilow, one of its founders. History On December 2 ...

. In 1957 he moved to the United States with his wife Alexandra Ionescu Tulcea (''née'' Bagdasar), who had been his student. From 1957 to 1961 he worked as a research associate and visiting lecturer at

Yale University Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the wo ...

. He received his doctorate from Yale in 1959 under the supervision of

Einar Hille Carl Einar Hille (28 June 1894 – 12 February 1980) was an American mathematics professor and scholar. Hille authored or coauthored twelve mathematical books and a number of mathematical papers. Early life and education Hille was born in New Y ...

with thesis ''Semi-groups of Operators''. Cassius Ionescu Tulcea was from 1959 to 1961 a visiting professor at

, from 1961 to 1964 an associate professor at the

University of Pennsylvania The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...

, and from 1964 to 1966 a full professor at the

University of Illinois at Urbana–Champaign The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Universit ...

. He became in 1966 a full professor at

Northwestern University Northwestern University is a private research university in Evanston, Illinois. Founded in 1851, Northwestern is the oldest chartered university in Illinois and is ranked among the most prestigious academic institutions in the world. Charte ...

and retired from there as professor emeritus. His marriage to Alexandra Ionescu Tulcea lasted from 1956 to 1969 when they divorced. During their marriage, the two mathematicians wrote a number of papers together, as well as a well-regarded research monograph on

lifting theory In mathematics, lifting theory was first introduced by John von Neumann in a pioneering paper from 1931, in which he answered a question raised by Alfréd Haar. The theory was further developed by Dorothy Maharam (1958) and by Alexandra Ionescu Tu ...

John von Neumann John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...

initiated lifting theory in functional analysis with applications in probability theory. The Ionescu-Tulcea theorem, an important existence theorem for time-discrete

stochastic process In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appea ...

es, is named after Cassius Ionescu Tulcea (1949). He also did research on mathematical game theory and mathematical economics. He co-authored a book on casino gambling and several textbooks on mathematics; he also wrote a 1981 book on casino dice games and gambling systems and a 1982 book on casino

blackjack Blackjack (formerly Black Jack and Vingt-Un) is a casino banking game. The most widely played casino banking game in the world, it uses decks of 52 cards and descends from a global family of casino banking games known as Twenty-One. This fami ...

. In 1957 he was awarded the Prize of the

Romanian Academy of Sciences The Romanian Academy of Sciences was an institution established in Romania by a group of 26 scientists, dissatisfied with the imperfect organization of the Scientific Section of the Romanian Academy, which was left in the background, with only 12 ...

. His doctoral students include George Maltese and

Robert Langlands Robert Phelan Langlands, (; born October 6, 1936) is a Canadian mathematician. He is best known as the founder of the Langlands program, a vast web of conjectures and results connecting representation theory and automorphic forms to the study o ...

. He turned 90 in October 2013 and died in

Chicago, Illinois (''City in a Garden''); I Will , image_map = , map_caption = Interactive Map of Chicago , coordinates = , coordinates_footnotes = , subdivision_type = Country , subdivision_name ...

in March 2021, at the age of 97.Forever Missed: Cassius Ionescu-Tulcea
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Selected publications

* A book on casino blackjack, Van Nostrand 1982 * with Virginia L. Graham: A book on casino gambling: written by a mathematician and a computer expert, 1976, 2nd edition, Van Nostrand 1978 * A book on casino craps, other dice games & gambling systems, Van Nostrand 1981 * with

Robert G. Bartle Robert Gardner Bartle (November 20, 1927 – September 18, 2003) was an American mathematician specializing in real analysis. He is known for writing the popular textbooks ''The Elements of Real Analysis'' (1964), ''The Elements of Integration'' ...

: Calculus, Scott Foresman 1968 * with Robert G. Bartle: An introduction to Calculus, Scott Foresman 1968 * with Robert G. Bartle: Honors Calculus, Scott Foresman 1970 * with William W. Fairchild: Topology, Philadelphia: Saunders 1971 * with William W. Fairchild: Sets, Saunders 1970 * with Alexandra Ionescu Tulcea: Topics in the Theory of Lifting, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 48, Springer-Verlag New York Inc., New York 1969, , .

References

{{DEFAULTSORT:Ionescu-Tulcea, Cassius 1923 births 2021 deaths 20th-century American mathematicians 20th-century Romanian mathematicians 21st-century American mathematicians 21st-century Romanian mathematicians Northwestern University faculty Probability theorists Romanian emigrants to the United States Scientists from Bucharest University of Bucharest alumni University of Illinois Urbana-Champaign faculty University of Pennsylvania faculty Yale University alumni