# Alfonso Maria Del Re

### Quick Info

Calitri, Avellino, Kingdom of the Two Sicilies (now Italy)

Sorrento, Italy

**Alfonso Del Re**was an Italian mathematician who published works on geometry, statics and mathematical logic.

### Biography

**Alfonso Del Re**was the son of Raffaele Del Re and Rosa Margotta. He was born in the Kingdom of the Two Sicilies at a time when major changes were occurring due to the move towards the unification of Italy. In 1860 Avellino became part of the Kingdom of Sardinia and the following year it became part of the Kingdom of Italy. Alfonso's father, Raffaele Del Re, was a tailor. Alfonso began his education in his home town but, when he was fifteen years old, he went to Naples to complete his secondary school studies. After graduating from a private high school in Naples, he entered the University of Naples.

Del Re's first paper,

*Relazione tra due determinanti*Ⓣ, was published in the

*Giornale di Matematiche (Battaglini)*in 1881. Before completing his laurea he had a number of other papers published:

*La quadrica dei dodici punti e la quadrica dei dodici piani*Ⓣ (1884);

*Oblique e circoli osculatori alle coniche in relazione tra loro ed in relazione con altri elementi geometrici di cui sono casi particolari*Ⓣ (1884), and

*Sulle funzioni di forza*Ⓣ (1885). These were substantial pieces of work having 15 pages, 43 pages and 13 pages respectively.

For a list of Del Re's publications, see THIS LINK.

In 1885, still one year away from completing his laurea, he was appointed as an assistant to the Chair of Projective Geometry at Naples. He was awarded his laurea in 1886 and continued teaching at the University of Naples. In 1889 he moved to the university of Rome where he again worked as an assistant.

Del Re began to enter competitions for professorships. In 1891 he entered the competition for the extraordinary professorship in analytic and projective geometry at the University of Rome. A committee consisting of Eugenio Bertini, Enrico D'Ovidio and Giuseppe Veronese considered six candidates, ranking Guido Castelnuovo in first position with 49/50 points, Del Re second with 46/50 and in joint third place, Luigi Berzolari and Mario Pieri with 39/50. In November 1892, having won the contest to hold an extraordinary professorship in projective and analytic geometry at the University of Modena, he began teaching there. However, he continued to apply for professorships that became vacant over the following few years.

In 1893 Del Re entered the competition for the chair of projective geometry at the University of Naples. This was won by Domenico Montesano, who had previously held a chair in Bologna, with 45/50 points. Second was Luigi Berzolari with 44/50, third Del Re with 43/50 and fourth Mario Pieri with 41/50. The next competition was also in 1893 for the chair of projective and descriptive geometry at the University of Turin. This had become vacant when Giuseppe Bruno died in February 1893. The referees for this chair were Ferdinando Aschieri (1844-1907), Eugenio Bertini, Enrico D'Ovidio, Corrado Segre and Giuseppe Veronese. Luigi Berzolari was appointed, ranked first with 45/50 points, second equal were Del Re and Mario Pieri with 41/50 points.

When Domenico Montesano won the competition for the chair at Naples in 1893, he moved from the University of Bologna leaving vacant the extraordinary professorship in descriptive and projective geometry there. What followed was a drawn out battle for the position which is now known as the "Bologna Affair." Given the results of the two earlier competitions, Del Re and Pieri were considered the leading candidates. The faculty at Bologna, encouraged by Pincherle, decided that they wished to appoint Pieri without a competition. The minister of education, however, did not approve Pieri's appointment, telling the Faculty at Bologna that they had to hold a competition and make a temporary appointment while this was taking place. Federigo Enriques was appointed to the temporary post in January 1894. With no competition announced, Del Re made a request to the minister of education that he be transferred from the University of Modena to Bologna for family reasons. Since by this time Del Re held a full chair in Modena and was requesting a move to an extraordinary position at Bologna, this seemed a strong request. The Faculty at Bologna repeatedly requested the minister to hold a competition but no competition was held. The minister replied to the Faculty that he could not accept their request for a competition and saw no reason not to appoint Del Re and said he would appoint him immediately if the Faculty agreed. Enriques, keen to remain at Bologna, asked Castelnuovo to intervene and make sure the minister did not agree to Del Re's request. With no competition taking place, the Faculty at Bologna reappointed Enriques for another temporary year in January 1895. It then became clear that there were three candidates with strong cases, Enriques, Del Re and Pieri and the Faculty requested the minister to set a commission to decide between these three without opening a competition. The Faculty at Bologna now split with Arzelà favouring Del Re's transfer with Pincherle and others opposed. Enriques was appointed for yet another temporary year, the year 1896. Just before the Faculty meeting in November 1895 which made that decision, Enriques had written [3]:-

... lamenting the number of recommendation letters that Del Re had secured, and complaining that Del Re was always there lobbying and had gained so much ground that Pincherle feared a major coup. Del Re was arguing that he needed to relocate his family to Bologna. He had even approached Enriques himself asking for support and offering to help secure for Enriques the position he would vacate at Modena!The "Bologna Affair" ended in 1896 when the minister resigned after a crisis following the Battle of Adwa, and a new minister was appointed who immediately opened a competition. Enriques was appointed but Del Re does not appear to have entered the competition. In 1899 Del Re went back to the University of Naples when he was appointed to the Chair of Descriptive Geometry at the Institute of Mathematics. He held this chair until his death.

Let us now follow [7] in describing Del Re's mathematical contributions.

Because of his versatility and his in-depth studies in many fields of the exact sciences, he was able to obtain important results which he presented in one hundred and twenty five publications. His research developed in many directions. It comprised studies of pure and applied geometry as well as analytic and projective geometry (

*Lezioni di geometria proiettiva e analitica*Ⓣ, Modena 1894), studies of algebra (

*Sopra certe relazioni di identità fra determinant e matrici*Ⓣ, Naples 1916), of symbolic analysis of forms (

*Lezioni sulle forme fondamentali dello spazio rigato, sulla dottrina degli immaginari e sui metodi di rappresentazione nella geometria descrittiva*Ⓣ, ibid. 1906), works on statics, kinematics and dynamics, on the space of three and four dimensions (

*Sulla statica dello spazio a 4 dimensioni*Ⓣ, Roma 1908) as well as spaces of

*n*dimensions, for any

*n*and constant curvature (

*Le equazioni generali per la statica e dinamica dei sistemi materiali ad n dimensioni ed a curvature costante nell'analisi di Grassmann*Ⓣ, ibid. 1912;

*Le equazioni generali per la dinamica dei corpi rigidi ad n dimensioni ed a curvature costante nell'analisi di Grassmann*Ⓣ, Naples 1915), according to the most advanced position at the time and in close competition with research at the international level, oriented towards an algebraic and formal formulation and with an impetus from the geometry of J J Sylvester, K G von Staudt, W R Hamilton and even D Hilbert. In all of these fields he focused, with a modern spirit and according to a formal set-up, on explaining the results obtained from other authors, mostly foreign authors, rather than producing entirely new results himself.

Del Re also worked on the algebra of logic in the period of the great

*exploit*, taking place at the end of the last century; his lectures on the discipline (

*Lezioni di algebra della logica*Ⓣ, Napoli 1907), which he gave in Naples, were then published and obtained unanimous approval in Italy and abroad (cf. B A Bernstein,

*Postulati per la logica delle classi in termini della operazione "eccezione", e pruova dell'indipendenza dei postulate dovuti a Del Re*Ⓣ, Napoli 1918). They occupy a pre-eminent place within the publications in the field both for the originality of their content and for the way in which the treatment of the subject is carried out following an axiomatic approach. Furthermore, Del Re also took an interest in natural philosophy, which towards the end of the last century (the 19th century) was an object of many studies based on the dominant position of positivism. About this, we recall the address he gave in the November of 1896 at the inauguration of the academic year of the University of Modena, titled:

*Sulla struttura geometrica dello spazio in relazione al modo di percepire i fatti naturali*Ⓣ (Naples 1901). Here he anticipated the relativistic theory in general terms, tackling arguments which were then developed by Albert Einstein. In particular, he worked on the mathematical aspect of the theory of relativity, treating analytically a particular type of transformations of H A Lorentz (

*Sulle trasformazioni Voigt-Lorentz in elettrodinamica*Ⓣ, ibid. 1913).

Del Re was fellow of a number of academies, among which were the Academy of Sciences of Naples and the Pontiniana Academy.

We add a few more details. First we note the mathematical models described in [5]:-

Equipped with its own organic and very fine workmanship was the small collection developed by Alfonso Del Re in the Room of Descriptive Geometry attached to the corresponding chair of which he was the professor. Del Re also mentions this in 'The programme of the course and programme of the examination for the academic year 1906-1907', where the list of geometric models, constructed between 1901 and 1906 by the students of the School of Descriptive Geometry of the University of Naples, is presented. There are 36 models, of which thirty-one are in wood and wire, three in wood and brass, and two in wood, brass and horsehair. In this fine collection, the frames - generally called "castles" - which held the natural fibres of the striped surfaces represented, were made of artistically worked wood using a fretwork technique.Giovanni Acocella discusses Del Re's

*Corso di Algebra della Logica*Ⓣ in [4]:-

The 'Course of Algebra of Logic' published in Naples in 1907 by professor Alfonso M Del Re was the subject of extensive quotations, especially by some American scholars. I talked about this course, which took place regularly in the four years preceding its publication, at the previous Congress of the SISM in Alba. Del Re's course followed the path traced out by Ernst Schröder and took into account the complete set of independent postulates for class logic which were first set out by Edward Huntington in July 1904. With a later 1911 memoir, Alfonso Del Re illustrated a series of arguments on the independence of his series of postulates, in addition to those implicit in the reference to Huntington. B A Bernstein in a paper read before the American Mathematical Society (in San Francisco) on 25 October 1913, after quoting the contributions of Charles Peirce, Edward Huntington and H M Sheffer, proposed a series of postulates of completion in terms of the operation "exception". Bernstein himself deduced the sufficiency of these from the series of postulates indicated by A Del Re in his 'Logical Algebra', adding new evidence to those implicit in the reference to Huntington. In a postscript to an Italian translation of 1918, Dr Rosaria Giordano reports on the content of the letter that Bernstein himself sent to Del Re on 8 April 1917. In the same postscript he took note of a small necessary change, advising that all that remains is the integration of the reading of the text of 'Algebra della Logica' with the reading of the Memoir of Del Re of 1911.Finally we note that Abbagnano, a famous philosopher, married Del Re's daughter Rosa Del Re in 1924, three years after Del Re's death.

### References (show)

- B A Bernstein,
*A complete set of postulates for the logic of classes expressed in terms of the operation "exception," and a proof of the independence of a set of postulates due to Del Ré*(Berkeley, University of California Press, 1914). - B A Bernstein,
*Postulati per la logica delle classi in termini della operazione "eccezione" e pruova dell'indipendenza dei postulati dovuti a Del Re*(Tip. De Roberto, Naples, 1918). - E A Marchisotto and J T Smith,
*The Legacy of Mario Pieri in Geometry and Arithmetic*(Springer, 2007). - G Acocella, Le osservazioni di B. A. Bernstein ai postulati della logica di A Del Re, Quarto Congresso SISM - Padova - 9 (11.9.2004). http://www.sism.unito.it/node/congressi/IVcongresso/sunti.pdf
- La Costituzione Di Un Archivio Digitale Per I Modelli Di Superfici Dell'università "Federico Ii" Di Napoli,
*Università degli Studi di Palermo*. https://iris.unipa.it/retrieve/handle/10447/83713/92570/Art%20Nicla%20Palladino_04.pdf - E Huntington, Sets of independent postulates for the algebra of logic,
*Trans. Amer. Math. Soc.***5**(1904), 288-309. - A Mariani, Del Re, Alfonso: English translation of [6],
*University of St Andrews*(1 February 2018). - D Montesano, Alfonso Del Re (1859-1921),
*Rend. Acc. Scienze Napoli*(3)**28**(1922), 187-189. - N Palladino, La Costituzione Di Un Archivio Digitale Per I Modelli Di Superfici Dell'università "Federico Ii" Di Napoli,
*Università degli Studi di Palermo*. https://iris.unipa.it/retrieve/handle/10447/83713/92570/Art%20Nicla%20Palladino_04.pdf - F Rossi, Del Re, Alfonso,
*Dizionario biografico degli italiani***38**(Istituto dell'Enciclopedia Italiana, Rome, 1990). http://www.treccani.it/enciclopedia/alfonso-del-re_%28Dizionario-Biografico%29/

### Additional Resources (show)

Other pages about Alfonso Del Re:

Other websites about Alfonso Del Re:

Written by J J O'Connor and E F Robertson

Last Update May 2018

Last Update May 2018