Salvatore Cherubino


Born: 3 June 1885 in Naples, Italy
Died: 2 August 1970 in Pisa, Italy

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Salvatore Cherubino's parents were Alessandro Cherubino and Stella Europeo. The family was not well-off and could not afford to give their son Salvatore the solid education that his talents clearly deserved. He graduated from middle school in 1903, having shown considerable mathematical talents, and entered a technical school but, through lack of financial support, was forced to give up his studies shortly after he had enrolled. Having to earn a living, he began a clerical career taking a job in the Ministry of Posts and Telegraphs. He lived as cheaply as he possibly could while trying to save enough money to allow him to begin a university education.

In 1905, after a couple of years of sacrifices, he enrolled at the University of Naples to study mathematics. He graduated with a doctorate in pure mathematics in 1909. He had studied the theory of groups of substitutions for his thesis, publishing two papers on the topic in 1909, namely Sulle generatrici del gruppo alterno delle sostituzioni di n elementi and, related to Sylow's theorem, Alcune formule aritmetiche e loro applicazioni nella teoria dei gruppi di sostituzioni . Considered an exceptional student, he was appointed as an assistant to the professor of analytic geometry at the University of Naples for the year 1910-1911.

Ernesto Pascal had been appointed to the chair of Complementary Algebra and Higher Analysis at the University of Naples in 1907. Immediately after he graduated, Cherubino attended a course given by Pascal on classical binary forms. In this course Pascal described his own contributions to the topic as well as the work being published by Alfred Clebsch. This led to Cherubino publishing the paper Ampliamento di un sistema completo alle cui forme fondamentali si aggreghi una nuova forma di ordine n (1911) in Battaglini's Giornale di matematiche. He began teaching at secondary school level in 1911, winning three competitions for posts in that year. He was appointed to teach at the Women's Normal School at Siena in 1911, but in the following year, after winning another competition, he moved to Padua where again he taught in a secondary school. At Padua, however, he was able to become involved with the mathematics department at the university where there were three outstanding professors. These were Giuseppe Veronese, who held the Chair of Algebraic Geometry, Tullio Levi-Civita, who had been appointed to the Chair of Rational Mechanics in 1898, a post which he held for 20 years, and Francesco Severi, who had been appointed to the Chair of Projective and Descriptive Geometry in 1905. Cherubino was awarded a government scholarship for advanced study which allowed him to attend the courses of Levi-Civita and Veronese while, advised by Severi, he devoted himself to the study of algebraic geometry. This led to Cherubino publishing Sulle curve iperellittiche con trasformazioni birazionali singolari in sé e sui loro moduli algebrici (1913-14).

In 1913 Cherubino was appointed as an assistant to the Chair of Infinitesimal Calculus at the University of Naples but he continued to teach in secondary schools. However, his career was interrupted by the outbreak of World War I. In 1914, when Cherubino was teaching in Naples, World War I broke out but, shortly after hostilities began on 3 August, Italy declared that it would not commit troops to the fighting. This was despite having an alliance with Germany and Austria-Hungary. Italy revoked this alliance on 3 May 1915 and later that month declared war on Austria-Hungary. Cherubino was drafted into the military, first as a private soldier and then, at his request, as an officer in the Territorial Militia where he served as an telegraphic engineer. In 1918 he was sent in the 28th Telegraph Company of the XII Corps of the 6th Army to fight in the Altipiani campaign. The 6th Army fought in the Battle of the Piave in June 1918. This battle was the result of a final push by the Austro-Hungarian forces attempting to take the positions of the Allies (58 Italian Divisions alongside 3 British and 2 French Divisions) across the river Piave. Many died on both sides but the Austro-Hungarian forces were so depleted that they never able to mount another major offensive. Cherubino remained with his unit until the end of the war. When he was released from military duties, he was able to return to his two positions in Naples as a secondary school teacher and as an assistant at the university.

At Naples, Cherubino was influenced by Gaetano Scorza who taught at the University of Naples from 1920 to 1934. Of course, he was returning to the city where he had studied as an undergraduate and studied with Ernesto Pascal in the year following his graduation. Cherubino was again influenced by Pascal and he began to undertake research on a new topic, publishing Sulle varietà abeliane reali e sulle matrici di Riemann reali in 1922. However, Cherubino now studied Civil Engineering and was awarded his laurea in that topic in 1923 and began lecturing in mathematics at the industrial technical institute in Naples. In the following year he taught at the Art School attached to the Academy of Fine Arts in Naples. Continuing to work in that city, he taught analysis and descriptive, analytic and projective geometry at the Air Force Academy in 1926. He gave courses on infinitesimal calculus at the School of Architecture in the academic year 1927-28. He was the appointed as Deputy Director of the School of Architecture in Naples, a position he held from 1928 to 1933. Cherubino published several important memoirs on matrix theory around this time such as Le matrici riemanniane sottonormali (1927), Le matrici caratteristiche delle simmetrie sulle varietà abeliane reali (1928) and Una applicazione del calcolo delle matrici alla teoria delle forme quadratiche (1929). In 1933, approaching the age of fifty, Cherubino won the competition for the Chair of Analytical, Projective and Descriptive Geometry and Drawing at the University of Messina. He only held this chair for two years before moving to Pisa in 1935 to an ordinary professorship in geometry. He continued to hold this chair at Pisa until he retired in 1955. His lectures at Pisa were the basis for his textbook Lezioni di geometria analitica con elementi di proiettiva which he published in 1940. He also published the paper Identità birazionale di due curve algebriche in 1939 which also was based on his teaching. T R Hollcroft writes in a review:-

In the preface it is stated that this paper was originally intended for the use of the author's students in the University of Pisa. It is a compendium with numerous references to the work of several mathematicians. It deals chiefly with the conditions for the birational identity of two algebraic curves. In the last two sections, curves with the same Jacobian variety are treated. The work is often more detailed and in some places more precise than in the original papers.
After retiring, Cherubino published the monograph Calcolo dell Matrici (1957). C C MacDuffee writes in a review [2]:-
The reviewer read this book with a great deal of pleasure because it is different from most of the books on matrices which are currently appearing. While the concept of vector space is introduced, it is not used very much. The reduction to canonical form under similarity transformations is limited to the field of the characteristic roots. A paragraph entitled "the concepts of abstract algebra" consists essentially of the derivation of the first and second regular representations of a finite linear associative algebra. The concepts of ring and field are introduced, but most of the book is concerned with matrices with either real or complex elements. There is really a lot of factual material in this book, much of it not readily accessible in textbooks. The chapters dealing with the characteristic roots are especially complete, treating approximation to the dominant root, Hurwitz' stability theorem, maxima and minima of quadratic forms, Borchardt's theorem, bounds for the roots, etc. But the author's principal interest seems to be in the differentiation and integration of matrices whose elements are functions of one or more independent variables. Even the Cayley-Hamilton theorem is proved by a power series expansion.
We should also mention that Cherubino did some work on probability theory, for example he published a work on probability suggested by the theory of gases Una quistione di probabilità suggerita dalla teoria dei gas (1923). He also wrote a number of articles on economics and published the book Economia matematica . He was invited to give the talk Sui polinomi definiti o semidefiniti at the International Congress of Mathematicians at Bologna in 1928 and he published a paper of the same title in the Proceedings of the Congress.

Maria Passaquindici, who was a student of Cherubino's, gives this tribute in the obituary [3]:-

A man of vast culture, with which he combined a strict scientific training, he brought to everything the contribution of his competence and of his moral rectitude, and received due recognition with the gold medal high for quality teaching, culture and art which he received on the occasion of the inauguration of the Academic Year on 21 January 1961. He devoted much of his energies and his time to teaching and his loss is a great one for the world of culture and especially of research. ... His work was carried out quietly and modestly, without elaborate language and without exhibition, simply enjoying the satisfaction that he had given with the work he had done. He struck us with his generosity at being always available to students and all those who turned to him: how much patience he showed in reviewing our work which he undertook and how long he spent in valuable open conversation on all topics! His noble figure and his tireless scientific work deserve a better illustration. He was to me an advisor and teacher who cultivated attachment, gratitude and devotion which he reciprocated with love, understanding and kindness. The memory of Salvatore Cherubino remains deep in the hearts of all his students and we regret losing his counsel but we are committed to follow his example. He left a great legacy of love because he was very good, just and honest, he had a deep sense of humanity and a broad understanding towards his students, for whom he worked until the last days of his long and laborious life. I will always remember with gratitude and admiration the University of Pisa, which honoured him for his talent and his contribution. We students, mourning the loss of his friendship, give a heartfelt tribute to the Master, reverent homage to the scientist and devout thanksgiving for the man, as we work to continue, even though unworthily, with his interrupted work.
As well as the gold medal which Passaquindici mentions, Cherubino was honoured with election to the Accademia Pontaniana di Napoli in 1928 and to the Accademia Leonardo da Vinci di Napoli in 1932. In the same year he was elected to the Accademia Peloritana di Catania.

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

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School of Mathematics and Statistics
University of St Andrews, Scotland

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