◀ ▲ ▶History / 19th-century / Person: Volterra, Samuel Giuseppe Vito

Person: Volterra, Samuel Giuseppe Vito

Vito Volterra published papers on partial differential equations, particularly the equation of cylindrical waves. His most famous work was done on integral equations.

Mathematical Profile (Excerpt):

• The name Volterra comes from the Tuscan town of Volterra where one of Vito's ancestor moved in the 15th century, having originally come from Bologna.
• They had lived in various different cities but from the 18th century there were Volterras living in Ancona.
• Vito, aged about three months, was in his cradle when a missile fell close by destroying the cradle yet, by good fortune, baby Vito survived.
• After elementary school, Vito studied at the lower secondary Dante Alighieri Technical School and later he spent three years at the Galileo Galilei Technical Institute in Florence.
• Alfonso put pressure on Vito to join Edoardo's firm but Edoardo kept delaying to allow Vito to continue his education.
• One of Vito's mathematics teachers at the Galileo Galilei Technical Institute was Cesare Arzelà and he quickly realised that Vito was an extremely talented mathematician.
• The physics teacher, Antonio Ròiti (1843-1921), became another important ally in Vito's bid to continue his education.
• Ròiti offered Vito a position teaching physics at the Istituto di Studi Superiori e di Perfezionamento in Florence in 1877, so managing to prevent him from being forced by Alfonso to take a job at the Banco d'Italia.
• Volterra was able to proceed to the University of Pisa in the autumn of 1878, enrolling in the faculty of Science.
• Volterra published three papers in 1881 before graduating, one on mathematical physics Sul potenziale di un' elissoide eterogenea sopra sè stessa Ⓣ(On the potential of a heterogeneous ellipsoid upon itself) and two on analysis, Alcune osservazioni sulle funzioni punteggiate discontinue Ⓣ(Some remarks on discontinued dotted functions), on pointwise discontinuous functions, and Sui principii del calcolo integrale Ⓣ(On principles of the integral calculus) which became important in the development of the history of integration.
• His thesis on hydrodynamics, Sopra alcuni problemi di idrodinami Ⓣ(On some problems in hydrodynamics), included some results of George Stokes, which Volterra had discovered later but independently.
• After graduating with his laurea, Volterra was appointed as Betti's assistant in December 1882.
• During these years while holding a chair at Pisa, Volterra had made a number of trips abroad.
• This proved an important event since it saw Volterra become a significant member of the international mathematical community.
• Pisa tried to entice him to stay, while Turin tried hard to persuade him to accept their offer which Volterra eventually did.
• The dispute did nothing to harm Volterra's reputation, if anything he came out of it rather well, and he continued to receive honours for his contributions.
• The next International Congress of Mathematicians was held in Paris in August 1900 and Volterra was invited to give one of the four plenary lectures; he gave the lecture Betti, Brioschi, Casorati - Trois analystes italiens et trois manières d'envisager les questions d'analyse Ⓣ(Betti, Brioschi, Casorati - Three Italian analysts and three ways of looking at questions of analysis).
• They spent their honeymoon in Switzerland visiting places that Volterra knew from his visit for the International Congress in 1897.
• Volterra took up the appointment in Rome in November 1900 and, in the following year, gave his inaugural lecture Sui tentativi di applicazione delle matematiche alle scienze biologiche e sociali Ⓣ(On attempts to apply mathematics to the biological and social sciences) which discussed applications of mathematics to the biological and social sciences.
• Volterra conceived the idea of a theory of functions which depend on a continuous set of values of another function in 1883.
• Hadamard was later to introduce the word 'functional' which replaced Volterra's original terminology.
• In 1890 Volterra showed by means of his functional calculus that the theory of Hamilton and Jacobi for the integration of the differential equations of dynamics could be extended to other problems of mathematical physics.
• During the years 1892 to 1894 Volterra published papers on partial differential equations, particularly the equation of cylindrical waves.
• He began this study in 1884 and in 1896 he published papers on what is now called 'an integral equation of Volterra type'.
• Actually the name "functional" was introduced later by Hadamard and has now replaced Volterra's original nomenclature.
• In developing this theory Volterra already followed a principle which guided him through many discoveries and which he called the passage from the discrete to the continuous.
• It was this principle which he applied to his celebrated researches on integral equations of Volterra's type.
• Volterra spoke out strongly against Italy honouring its treaty with the Central Powers.
• Volterra became a lieutenant in the corps of engineers and was sent to the Central Institute of Aeronautics.
• In other words he was interested in a mathematical theory of the "survival of the fittest." While there are today other methods of a stochastic nature, the work of Volterra still exerts a dominant influence on several modern and quite recent developments in mathematical biology.
• Volterra fought against the Fascists in the Italian Parliament but continued to be a leading figure being elected the first president of the Italian National Council for Research in 1923 and, in the same year, elected president of the Accademia dei Lincei.
• By 1926 the Fascists had abolished all opposition parties and Volterra felt he could not continue with these two roles, and resigned as president.
• When Volterra refused to take the oath of allegiance to the Fascist Government in 1931, which was required of all tenured and contracted professors, he was forced to leave the University of Rome.
• By this time, two of Volterra's sons held university positions and they were deprived of these by the racial laws.
• Volterra advised his sons to go abroad and try to start a new life there.
• Volterra was offered an honorary degree by the University of St Andrews in 1938 but, although he wished to come, his doctor did not allow him to travel to Scotland to receive it.

Born 3 May 1860, Ancona, Papal States (now Italy). Died 11 October 1940, Rome, Italy.

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References

Adapted from other CC BY-SA 4.0 Sources:

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