Francesco Paolo Cantelli (20 December 187521 July 1966) was an Italian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. He made contributions to

celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...

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 ...

, and actuarial science.

Biography

Cantelli was born in

Palermo Palermo ( , ; scn, Palermu , locally also or ) is a city in southern Italy, the capital (political), capital of both the autonomous area, autonomous region of Sicily and the Metropolitan City of Palermo, the city's surrounding metropolitan ...

. He received his doctorate in mathematics in 1899 from the

University of Palermo The University of Palermo ( it, Università degli Studi di Palermo) is a university located in Palermo, Italy, and founded in 1806. It is organized in 12 Faculties. History The University of Palermo was officially founded in 1806, although its ...

with a thesis on celestial mechanics and continued his interest in astronomy by working until 1903 at

Palermo Astronomical Observatory The Giuseppe S. Vaiana Astronomical Observatory is an astronomical observatory located in Palermo, Sicily, Italy, housed inside the Palazzo dei Normanni. It is one of the research facilities of the National Institute of Astrophysics. The observat ...

(''osservatorio astronomico cittadino''), which was under the direction of

Annibale Riccò Annibale Riccò (14 September 1844 – 23 September 1919) was an Italian astronomer. Biography He was born in Milan, Italy. In 1868 he was awarded a bachelor's degree from the '' Università di Modena'', then an engineering degree from the ' ...

. Cantelli's early papers were on problems in

astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...

and

. From 1903 to 1923 Cantelli worked at the ''Istituto di Previdenza della

Cassa Depositi e Prestiti Cassa Depositi e Prestiti S.p.A. (also kwown as CDP or CDP Group) is a prominent Italian investment bank founded on November 20, 1850, in Turin. Its main duty was to finance public works like roads and waterworks during the reign of Victor Emman ...

'' (Pension Fund for the Government Deposits and Loans Bank). During these years he did research on the mathematics of

finance theory Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of fin ...

and actuarial science, as well as the probability theory. Cantelli's later work was all on

. Borel–Cantelli lemma, Cantelli's inequality and the

Glivenko–Cantelli theorem In the theory of probability, the Glivenko–Cantelli theorem (sometimes referred to as the Fundamental Theorem of Statistics), named after Valery Ivanovich Glivenko and Francesco Paolo Cantelli, determines the asymptotic behaviour of the empir ...

are result of his work in this field. In 1916–1917 he made contributions to the theory of stochastic convergence. In 1923 he resigned his actuarial position when he was appointed professor of actuarial mathematics at the

University of Catania The University of Catania ( it, Università degli Studi di Catania) is a university located in Catania, Sicily. Founded in 1434, it is the oldest university in Sicily, the 13th oldest in Italy, and the 29th oldest university in the world. With a ...

. From there, he went to the

University of Naples The University of Naples Federico II ( it, Università degli Studi di Napoli Federico II) is a public university in Naples, Italy. Founded in 1224, it is the oldest public non-sectarian university in the world, and is now organized into 26 depar ...

, where he worked as a professor and then in 1931 to the

Sapienza University of Rome The Sapienza University of Rome ( it, Sapienza – Università di Roma), also called simply Sapienza or the University of Rome, and formally the Università degli Studi di Roma "La Sapienza", is a Public university, public research university l ...

where he remained until his retirement in 1951. He died in

Rome , established_title = Founded , established_date = 753 BC , founder = King Romulus (legendary) , image_map = Map of comune of Rome (metropolitan city of Capital Rome, region Lazio, Italy).svg , map_caption ...

. Cantelli made fundamental contributions to the foundations of probability theory and to the clarification of different types of probabilistic convergence. He also made seminal contributions to actuarial science. He was the founder of the ''Istituto Italiano degli Attuari'' for the applications of

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

and

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

economics Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and intera ...

. Cantelli was the editor of the ''Giornale dell'Istituto Italiano degli Attuari'' (GIIA) from 1930 to 1958.

Works

* ''Sull'adattamento delle curve ad una serie di misure o di osservazioni'', Palermo, 1905 * ''Genesi e costruzione delle tavole di mutualità'', 1914 * ''Sulla legge dei grandi numeri'', 1916 * ''La tendenza a un limite nel senso del calcolo delle probabilità'', 1916 * ''Sulla probabilità come limite della frequenza'' in "Rendiconti della Reale Accademia dei Lincei", 1917 * ''Una teoria astratta del calcolo delle probabilità'', GIIA, vol. 3, pp. 257–265, Roma, 1932 * ''Considerazioni sulla legge uniforme dei grandi numeri e sulla generalizzazione di un fondamentale teorema del Sig. Paul Levy'', 1933 * ''Sulla determinazione empirica delle leggi di probabilità'', 1933 * ''Su una teoria astratta del calcolo delle probabilità e sulla sua applicazione al teorema detto "delle probabilità zero e uno"'', 1939

References

External links

* {{DEFAULTSORT:Cantelli, Francesco Paolo 1875 births 1966 deaths 19th-century Italian mathematicians 20th-century Italian mathematicians Mathematicians from Sicily Italian statisticians University of Palermo alumni Academic staff of the University of Catania Academic staff of the University of Naples Federico II Academic staff of the Sapienza University of Rome People from Palermo Members of the Lincean Academy Italian actuaries Probability theorists Mathematical statisticians

Biography

Works

See also

References

External links