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

- 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.
- 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 Ⓣ(Relationship between two determinants), 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 Ⓣ(The quadratic of the twelve points and the quadratic of the twelve planes) (1884); Oblique e circoli osculatori alle coniche in relazione tra loro ed in relazione con altri elementi geometrici di cui sono casi particolari Ⓣ(Oblique and osculating circles at conics in relation to each other and in relation to other particular cases of geometric elements) (1884), and Sulle funzioni di forza Ⓣ(On the functions of force) (1885).
- These were substantial pieces of work having 15 pages, 43 pages and 13 pages respectively.
- 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.
- 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 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.
- 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.
- 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.
- 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.
- 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 Ⓣ(Projective and analytical geometry lessons), Modena 1894), studies of algebra (Sopra certe relazioni di identità fra determinant e matrici Ⓣ(On some identity relations between determinants and matrices), 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 Ⓣ(Lectures on fundamental forms on ruled space, on the doctrine of the imaginaries and on the methods of representation in descriptive geometry), ibid.
- 1906), works on statics, kinematics and dynamics, on the space of three and four dimensions (Sulla statica dello spazio a 4 dimensioni Ⓣ(On the statics of space in 4 dimensions), 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 Ⓣ(The general equations for the statics and dynamics of material systems of n dimensions and constant curvature in the analysis of Grassmann), ibid.
- 1912; Le equazioni generali per la dinamica dei corpi rigidi ad n dimensioni ed a curvature costante nell'analisi di Grassmann Ⓣ(The general equations for the dynamics of rigid bodies of n dimensions and of constant curvature in the analysis of 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 Ⓣ(Lectures on the algebra of logic), 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 Ⓣ(Postulates for class logic in terms of the 'not-if' operation, and the independence of the postulates due to 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 Ⓣ(On the geometric structure of space in relation to the way of perceiving natural events) (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 Ⓣ(On the Voigt-Lorentz transformations in electrodynamics), ibid.
- 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.
- 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.
- 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.

Born 8 October 1859, Calitri, Avellino, Kingdom of the Two Sicilies (now Italy). Died 5 September 1921, Sorrento, Italy.

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Origin Italy

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