Enzo Martinelli around 1960
11 November 1911|
|Died||27 August 1999
|Institutions||Università degli Studi di Genova, Università di Roma|
|Alma mater||Università degli studi di Roma "La Sapienza"|
|Doctoral advisor||Francesco Severi|
|Other academic advisors||Enrico Bompiani|
|Doctoral students||Giovanni Battista Rizza
|Known for||Theory of functions of several complex variables, Bochner–Martinelli formula|
|Influenced||Several complex variables|
|Notable awards||prize of the Cotronei Foundation, prize of the Beltrami Foundation, Fubini prize, Torelli prize (jointly with Pietro Buzano), 1943 Prize for Mathematical Sciences of the Ministry of National Education|
Enzo Martinelli (11 November 1911 – 27 August 1999) was an Italian mathematician, working in the theory of functions of several complex variables: he is best known for his work on the theory of integral representations for holomorphic functions of several variables, notably for discovering the Bochner–Martinelli formula in 1938, and for his work in the theory of multi-dimensional residues.
He was born in Pescia on 11 November 1911, where his father was the Director of the local agricultural school. His family later went to Rome, where his father ended his working career as the Director-general of the Italian Ministry of Public Education. Enzo Martilnelli lived in Rome almost all of his life: the only exception was a period of nearly eight years, from 1947 to 1954, when he was in Genova, working at the local university. In 1946 he married in Rome Luigia Panella, also her a mathematician, who later become an associate professor at the faculty of Engineering of the Sapienza University of Rome, and who was his loving companion for the rest of his life. They had a son and a daughter, Roberto and Maria Renata (also her a mathematician), and four grandchildren.
In 1933 he earned his laurea from the Sapienza University of Rome: the title of his thesis was "Sulle funzioni poligene di una e di due variabili complesse", and his thesis supervisor was Francesco Severi. From 1934 to 1946 he worked as an assistant professor first to the chair of mathematical analysis held by Francesco Severi and then to the chair of geometry held by Enrico Bompiani. In 1939 he became "Libero Docente" (free professor) of Mathematical analysis: he taught also courses on analytic geometry, algebraic geometry and topology as associate professor. In 1946 he won a competitive examination by a judging commission for the chair of "Geometria analitica con elementi di Geometria Proiettiva e Geometria Descrittiva con Disegno", awarded by the University of Genova: the second place and the third place went respectively to Giovanni Dantoni and Guido Zappa. Martinelli held that chair from 1946 to 1954, teaching also mathematical analysis, function theory, differential geometry and algebraic analysis as associate professor. In 1954 He went back in Rome to the chair of Geometry at the university, holding that chair up to his retirement, in 1982: he also taught courses on topology, higher mathematics, higher geometry upon charge. In the years 1968–1969, during a very difficult period for the Sapienza University of Rome, he served the university as the director of the Guido Castelnuovo Institute of Mathematics.
He attended to various conferences and meetings. In 1943 and in 1946 he was invited in Zurich by Rudolf Fueter, in order to present his researches: later and during all his career he lectured in almost all Italian and foreign universities.
He was also a member of the UMI Scientific Commission (from 1967 to 1972), of the editorial boards of the Rendiconti di Matematica e delle Sue Applicazioni (from 1955 to 1992) and of the Annali di Matematica Pura ed Applicata (from 1965 to 1999).
According to Rizza (2002, p. 165), Enzo's talent for mathematics was already evident when he was only a lyceum student. While still attending the university, he won the Cotronei Foundation prize, and after earning his laurea, the Beltrami Foundation prize, the Fubini and Torelli prizes (this last one jointly with Pietro Buzano) and the Prize for Mathematical Sciences of the Ministry of National Education: this last one was awarded him in 1943, and the judging commission consisted of Francesco Severi (as the president of the commission), Ugo Amaldi and Antonio Signorini (as the supervisor of the commission). In 1948 he was elected Corresponding Member of the Accademia Ligure di Scienze e Lettere: in 1961 and in 1977 he was elected respectively Corresponding and Full Member of the Accademia dei Lincei, and from 1982 to 1985 he was "Professore Linceo". Finally, in 1980 he was elected Corresponding Member of the Accademia delle Scienze di Torino and then, in 1994, Full Member. Also, in 1986, the Sapienza University of Rome, to which Enzo Martinelli was particularly tied for all his life, awarded him the title of professor emeritus.
He is unanimously remembered as a real gentleman, gifted by a caring attention, politeness, generosity and the rare ability to listen to colleagues and students alike: Gallarati (2000, p. 45) and Rizza (1984, p. 6) remember long conversations with him on various mathematical research topics, and his disposability to give help and advice to whoever asked for it. In particular Rizza (1984, p. 7) recalls the time when he was his doctoral student at the University of Genova: they meet every Sunday in the afternoon at Martinelli's home, since Martinelli was not able to meet him during the week. During one of their meetings, lasting a little more than two hours, Martinelli taught him Élie Cartan's theory of exterior differential forms, and Rizza used successfully this tool in his first research works. Another episode illustrating this aspect of Martinelli's personality is recalled by Gaetano Fichera. When he was back in Rome in 1945, at the end of the Second World War, he exposed to Martinelli a theory identical to the theory of differential form: he developed it while being prisoner of the nazists in Teramo during wartime. Martinelli, very tactfully, told him that the idea was already been developed by Élie Cartan and Georges de Rham.
An excellent teacher himself, capable to arose curiosity and enthusiasm by his lessons, he admired and respected much his own: however, this was quite common for the Italian scientists of the same and the preceding generations, who were advised in the early days of their scientific career by some of the best Italian scientists ever. His doctoral advisor was Francesco Severi: other great Italian mathematicians where among his teachers. Guido Castelnuovo, Federigo Enriques, Enrico Bompiani, Tullio Levi-Civita Mauro Picone and Antonio Signorini were all working at the Sapienza University of Rome when Enzo Martinelli was a student there, following their lessons: Zappa (1984) describes the activity of the institute of mathematics during that period as extremely stimulating.
Another central aspect of his personality was a deep sense of justice and legality: Martinelli was very careful in performing his citizen and university professor duties, and he was also ready to fight for his own rights and for the needs of higher education. Concerned by the growing interference of bureaucracy in university education, already in the 1950s he was heard by Rizza (1984, p. 6) complaining that: "In Italia mancano le menti semplificatrici". Martinelli was also free from every kind of authoritarianism to the point that when, during the protests of 1968 in Italy, many newspapers accused the Italian university scientific community of being so, all the assistant professors and students of Martinelli (and perhaps Martinelli himself) were perplexed. In the same period, while performing his duties as the director of the Guido Castelnuovo Institute of Mathematics at the Sapienza university of Rome, his rare intellectual honesty and rigorous rationality, according to Rizza, caused him troubles when dealing with many who "believed in everything except the cold light of reason".
Fin troppo meticoloso, scriveva più volte ogni suo lavoro, curandone fin nei minimi particolari sostanza e forma, fino a renderli di piacevole lettura. È difficile trovare nei suoi scritti un concetto che possa essere espresso in modo migliore.
He is the author of more than 50 research works, the first of which was published when Martinelli still was an undergraduate student: precisely, his research production consist of 47 papers and 30 between treatises, textbooks and various other publications. According to Rizza (1984, p. 2), his research personality can be described by two words: "enthusiasm" and "dissatisfaction": enthusiasm is meant as his steady interest in mathematics at all levels, while dissatisfaction is meant as the desire to going deeper into all mathematical problems investigated, without stopping at first success and expressing all the results in a simple, elegant and essential form.
The aspects of his personality described before and his deep professional commitment also made him a great teacher: at least fifteen textbooks on geometry, topology, complex analysis testify his didactic activity. Those books appear as models of clarity and mathematical rigour, and also offer insights on more complex theories and problems to the clever student: indeed, it was one of Martinelli's concerns to teach mathematics showing its lively development and its attractiveness in term of interesting difficult problems offered, in order that no gifted student would abandon the idea to do mathematical research.
- Martinelli, Enzo (1938), "Alcuni teoremi integrali per le funzioni analitiche di più variabili complesse", Atti della Reale Accademia d'Italia. Memorie della Classe di Scienze Fisiche, Matematiche e Naturali (in Italian) 9 (7): 269–283, JFM 64.0322.04, Zbl 0022.24002. "Some integral theorems for analytic functions of several complex variables" (English translation of the title) is the first paper where the now called Bochner-Martinelli formula is introduced and proved.
- Martinelli, Enzo (1941), "Studio di alcune questioni della teoria delle funzioni biarmoniche e delle funzioni analitiche di due variabili complesse coll’ausilio del calcolo differenziale assoluto", Atti della Reale Accademia d'Italia. Memorie della Classe di Scienze Fisiche, Matematiche e Naturali (in Italian) 12 (4): 143–167, JFM 67.0299.01, MR 0017810, Zbl 0025.40503. In "Study of some questions of the theory of biharmonic functions and of analytic functions of two complex variables by using the absolute differential calculus" (English translation of the title) Martinelli proves an earlier result of Luigi Amoroso on the boundary values of pluriharmonic function by using tensor calculus.
- Martinelli, Enzo (1942–1943), "Sopra una dimostrazione di R. Fueter per un teorema di Hartogs", Commentarii Mathematici Helvetici (in Italian) 15 (1): 340–349, doi:10.5169/seals-14896, MR 0010729, Zbl 0028.15201. Available at the SEALS Portal. In "On a proof of R. Fueter of a theorem of Hartogs" (English translation of the title), Martinelli gives a proof of Hartogs' extension theorem by using the Bochner-Martinelli formula.
- Martinelli, Enzo (1944–1945), "Sulla formula di Cauchy n–dimensionale e sopra un teorema di Hartogs nella teoria delle funzioni di n variabili complesse", Commentarii Mathematici Helvetici (in Italian) 17 (1): 201–208, doi:10.5169/seals-16336, MR 0013422, Zbl 0060.24404. Available at the SEALS Portal. (English translation of the title) "On the n–dimensional Cauchy formula and on a theorem of Hartogs in the theory of functions of n complex variables".
- Martinelli, Enzo (1945–1946), "Formula di Cauchy (n+1)–dimensionale per le funzioni analitiche di n variabili complesse", Commentarii Mathematici Helvetici (in Italian) 18 (1): 30–41, doi:10.5169/seals-16891, MR 0013423, Zbl 0060.24501, (in Italian). Available at the SEALS Portal. In "(n+1)–dimensional Cauchy formula for analytic functions of n complex variables" (English translation of the title), Martinelli goes further in its analysis of integral representations of holomorphic functions of n complex variables whose domain of integration is a set whose dimension (as a subset of the 2n–dimensional euclidean space) assumes all integer values between n and 2n-1.
- Martinelli, Enzo (1953), "Sulle estensioni della formula integrale di Cauchy alle funzioni analitiche di più variabili complesse", Annali di Matematica Pura e Applicata, IV Serie (in Italian) 34: 277–347, doi:10.1007/BF02415334, MR 0057989, Zbl 0104.30203 External link in
|journal=(help). "On the extensions of Cauchy's integral formula to analytic functions of several complex variables" (English translation of the title) is the concluding work of Martinelli on the theory of integral representations of holomorphic functions of complex variables.
- Martinelli, Enzo (1961), "Sulla determinazione di una funzione analitica di più variabili complesse in un campo, assegnatane la traccia sulla frontiera", Annali di Matematica Pura e Applicata, IV Serie (in Italian) 55: 191–202, doi:10.1007/BF02412084, MR 0170032, Zbl 0104.30203 External link in
|journal=(help). This paper contains Martinelli's improvement of the solution of the Dirichlet problem for holomorphic functions of several complex variables given by Fichera (1957) few years before: Martinelli relaxes the smoothness condition on the boundary of the given domain, requiring it to be only of class C1. However, the boundary value is required to be of the same class, far smoother than class H½ data allowed by Gaetano Fichera.
- Martinelli, Enzo (1975), "Sopra una formula di Andreotti–Norguet", Bollettino dell'Unione Matematica Italiana, IV Serie (in Italian) 11 (3, Supplemento): 455–457, MR 0390270, Zbl 0317.32006.
- Martinelli, Enzo (1984), Introduzione elementare alla teoria delle funzioni di variabili complesse con particolare riguardo alle rappresentazioni integrali, Contributi del Centro Linceo Interdisciplinare di Scienze Matematiche e Loro Applicazioni (in Italian) 67, Rome: Accademia Nazionale dei Lincei, pp. 236+II. "Elementary introduction to the theory of functions of complex variables with particular regard to integral representations" (English translation of the title) are the notes form a course, published by the Accademia Nazionale dei Lincei, held by Martinelli when he was "Professore Linceo".
- Almost complex manifold
- Bochner–Martinelli formula
- Complex manifold
- Kähler manifold
- Pluriharmonic function
- Residue theorem
- Several complex variables
- Tomassini (2001, p. III) writes that his death year is 1998, unlike to Gallarati (2000, p. 43), and Rizza (2002, p. 163), but it is probably a typographical error.
- The contents of this section are mainly sourced from reference (Rizza 2002).
- See Gallarati 2000, p. 43, Rizza 1984, pp. 1–2 and Rizza 2002, pp. 163–165.
- According to Rizza (2002, p. 165), around 2002 she worked as a research fellow at the faculty of Engineering of the Sapienza University of Rome
- According to Rizza (2002, p. 165).
- An English translation reads as "Polygenic functions of one and of two complex variables".
- See reference Rizza 2002, p. 163.
- See references Rizza 1984, p. 1 and Rizza 2002, p. 163.
- According to references Gallarati 2000, p. 43 and Rizza 2002, p. 163. An English translation reads as "Analytic Geometry with elements of Projective Geometry and Descriptive Geometry with Drawing".
- As Zappa (1984, p. 14) himself remembers. See also the official communication in the Bollettino UMI 1947, p. 85, where all the winners of the chairs are listed, irrespectively of their placement.
- According to Gallarati (2000, p. 43): this topic is not the modern algebraic analysis founded by Mikio Sato, Masaki Kashiwara and collaborators, but an old standard Italian course topic in mathematics.
- It was the season of the protests of 1968: a few more detail about Martinelli's work during this season can be find in the section describing his personality.
- According to Rizza (2002, p. 165): Rizza also lists a few universities where Martinelli lectured.
- See Rizza 2002, pp. 165–166.
- Ugo was a noted Italian mathematician, a collaborator of Tullio Levi-Civita and Federigo Enriques, and the father of noted physicist Edoardo Amaldi.
- See the inventory of the Reale Accademia d'Italia by Cagiano De Azevedo & Gerardi (2005, p. 113): this reference lists and briefly describes the contents of the documents of fascicle 207 of box (Busta) 104 of section VII, titled "Premi di Incoraggiamento e Sussidi (Encouragement Prizes and Grants)".
- There is a discrepancy in the date of election reported by Gallarati (2000, p. 43) (1948) and Rizza (2002, p. 165) (1986): however, Dionisio Gallarati published his commemoration of Martinelli in the journal (Atti) of this Academy, and therefore his date is reasonably believed to be correct.
- See Rizza 2002, p. 165: the "Professore linceo" is a professor which is in charge to the Accademia dei Lincei as a distinguished lecturer.
- See Gallarati (2000, p. 45) and Tomassini (2001, p. IV): the exact Italian word they use to characterize him is signorilità, which is somewhat untranslatable in its exact meaning.
- See Rizza 2002, p. 166.
- They mean "mathematical research" in a broad sense: Rizza (1984, p. 2) precisely states that Martinelli was interested in all fields of mathematics, not only the ones within his personal research interest.
- See Rizza (1984, p. 7) and the entry about him for more details.
- Fichera sketches the episode in his "last lesson" (Fichera 1995, pp. 18–19): see also Colautti Fichera 2006, p. 21 and the entry about Gaetano Fichera for further information.
- According to Fichera (1995, pp. 18) himself.
- Some information on his teaching commitment can be found in the "Teaching activity" section of this entry.
- According to Rizza 1984, p. 7.
- See the entries about Italian mathematicians and physicists of that period, for example the entries about Renato Caccioppoli, Gaetano Fichera, Francesco Severi.
- See also the description sketched by Rizza 2002, p. 166.
- "Italy lacks of simplifying minds"An Italian translation.
- According to Rizza (1984, p. 6).
- According to Gallarati (2000, p. 45) and to Rizza (2002, p. 172).
- "... che in tutto credevano salvo nella fredda luce della ragione.", as precisely stated by Rizza (1984, p. 7).
- An English translation reads as:-"Too much meticulous, he rewrote many times each of his works, curing every detail of their content and form, up to make them pleasant to read. It is difficult to find in his writing a concept that could be expressed in better way.".
- According to Rizza 1984, p. 2.
- For a complete list of his works, classified between research notes and memoirs or treatises, textbooks and various writings, see the paper Rizza 2002, pp. 172–176: a strictly shorter, chronologically ordered list appears also in the paper Rizza (1984, pp. 8–10).
- Precisely, Rizza (1984, p. 2) states the words "entusiasmo" e "insoddisfazione".
- See references Rizza 1984, p. 6 and Rizza 2002, p. 172.
- Gallarati (2000, p. 45) particularly praises this way the various geometry lecture notes redacted by Martinelli himself.
Biographical and general references
- Bollettino UMI (1947), "Notizie (Notices)", Bollettino dell'Unione Matematica Italiana, Serie III (in Italian) 2 (1): 81–92.
- Cagiano De Azevedo, Paola; Gerardi, Elvira, eds. (2005), Reale Accademia d’Italia. Inventario dell’archivio (Inventary of the Archive) (PDF), Pubblicazioni degli Archivi di Stato - Strumenti (in Italian), CLXVII, Roma: Ministero per i Beni Culturali e Ambientali - Dipartimento per i Beni Archivistici e Librari - Direzione Generale per gli Archivi, pp. lxxxiv+492, ISBN 88-7125-264-0 External link in
|publisher=(help), freely available from the Ministero per i Beni Culturali e Ambientali - Dipartimento per i Beni Archivistici e Librari - Direzione Generale per gli Archivi (a branch of the Italian Ministero per i Beni e le Attività Culturali). The complete inventary of the Reale Accademia d'Italia, which incorporated the Accademia Nazionale dei Lincei between 1939 and 1944.
- Colautti Fichera, Matelda (December 2006), ... ed è subito sera... La lunga, brevissima vita di Gaetano Fichera (in Italian), Roma: Self-published, p. 217. The story of the life of Gaetano Fichera written by his wife, Matelda Colautti Fichera. The first, untranslated phrase of the title is the last verse (and title) of a famous poem of Salvatore Quasimodo, and was the concluding phrase of the last lesson of Fichera, in the occasion of his retirement from university teaching in 1992, published in (Fichera 1995). An English translation of the second phrase reads as:"The long, extremely short life of Gaetano Fichera".
- Fichera, Gaetano (1995), "L'ultima lezione", Rendiconti della Accademia Nazionale delle Scienze detta dei XL, Memorie di Matematica e Applicazioni (in Italian) 19 (1): 1–24, MR 1387547, Zbl 0949.01011. The "Last Lesson" of the course of higher analysis by Gaetano Fichera, before his retirement from university teaching in 1992.
- Gallarati, Dionisio (2000), "Enzo Martinelli", Atti della Accademia Ligure di Scienze e Lettere, Serie VI (in Italian) II: 43–46, MR 1826907, Zbl 1159.01329.
- Rizza, Giovanni Battista (1984), "Enzo Martinelli: Scienziato e Maestro", Rivista di Matematica della Università di Parma, (4) (in Italian), 10*: 1–10, MR 0777308, Zbl 0557.01011. "Enzo Martinelli: Scientist and Master" (English translation of the title) is a celebratory article written by his first former doctoral student, published in the proceedings of the conference (Rizza & Succi 1984).
- Rizza, Giovanni Battista (October 1999), "Scomparsa di Enzo Martinelli", Notiziario dell'Unione Matematica Italiana (in Italian) XXVI (10): 36–37. The "Passing away of Enzo Martinelli" (English translation of the title) written by his first doctoral student.
- Rizza, Giovanni Battista (April 2002), "Commemorazione di Enzo Martinelli", Bollettino dell'Unione Matematica Italiana. Sezione A. La Matematica nella Società e nella Cultura, Serie VIII (in Italian) 5–A: 163–176, MR 1924344, Zbl 1194.01133. The "Commemoration of Enzo Martinelli" written by his first doctoral student.
- Roghi, G. (December 2005), "Materiale per una storia dell'Istituto Nazionale di Alta Matematica dal 1939 to 2003.", Bollettino dell'Unione Matematica Italiana, Sezione A, La Matematica nella Società e nella Cultura, Serie VIII (in Italian) 8–A (3, parte 2): x+301, MR 2225078, Zbl 1089.01500. This is a monographic fascicle published on the "Bollettino dell'Unione Matematica Italiana", describing the history of the Istituto Nazionale di Alta Matematica Francesco Severi from its foundation in 1939 to 2003: an English translation of the title reads as:-"Materials toward a history of the Istituto Nazionale di Alta Matematica from 1939 to 2003". It was written by Gino Roghi and includes a presentation by Salvatore Coen and a preface by Corrado De Concini. It is almost exclusively based on sources from the institute archives: the wealth and variety of materials included, jointly with its appendices and indexes, make this monograph a useful reference not only for the history of the institute itself, but also for the history of many mathematicians who taught or followed the institute courses or simply worked there.
- Tomassini, Giuseppe (December 2001), "Ricordo di Enzo Martinelli", Annali di Matematica Pura ed Applicata, Serie 4 (in Italian) 179 (1): III–IV, doi:10.1007/BF02505944, Zbl 1128.01309. "Recollections of Enzo Martinelli": personal reminiscences about his geometry teacher Enzo Martinelli, by Giuseppe Tomassini.
- Zappa, Guido (1984), "La scuola matematica di Francesco Severi intorno al 1940", Rivista di Matematica della Università di Parma, (4) (in Italian), 10*: 11–14, MR 0777309, Zbl 0562.01015. The English translation of the title of this work is:-"The mathematical school of Francesco Severi around 1940". It describes the research activity at the Sapienza University of Rome and at the (at that time newly created) "Istituto Nazionale di Alta Matematica Francesco Severi" from the end of the 1930s to the early 1940s.
- Fichera, Gaetano (1957), "Caratterizzazione della traccia, sulla frontiera di un campo, di una funzione analitica di più variabili complesse", Rendiconti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, 8 (in Italian) 22 (6): 706–715, MR 0093597, Zbl 0106.05202. An epoch-making paper in the theory of CR-functions, where the Dirichlet problem for analytic functions of several complex variables is solved for general data. An English translation of the title reads as:-"Characterization of the trace, on the boundary of a domain, of an analytic function of several complex variables".
- Severi, Francesco (1958), Lezioni sulle funzioni analitiche di più variabili complesse – Tenute nel 1956–57 all'Istituto Nazionale di Alta Matematica in Roma (in Italian), Padova: CEDAM – Casa Editrice Dott. Antonio Milani, pp. XIV+255, Zbl 0094.28002, (in Italian). Notes from a course held by Francesco Severi at the Istituto Nazionale di Alta Matematica (which at present bears his name), containing appendices of Enzo Martinelli, Giovanni Battista Rizza and Mario Benedicty. An English translation of the title reads as:-"Lectures on analytic functions of several complex variables – Lectured in 1956–57 at the Istituto Nazionale di Alta Matematica in Rome".
- Marchiafava, S.; Piccinni, P.; Pontecorvo, M., eds. (1999), Proceedings of the Second Meeting on Quaternionic Structures in Mathematics and Physics. Dedicated to the Memory of André Lichnerowicz and Enzo Martinelli (Roma, Italy September 6–10, 1999), European Mathematical Society, Zbl 0958.00032, retrieved 1 January 2011. The electronic proceedings of a conference on topics belonging to or related to André Lichnerowicz and Enzo Martinelli fields of research.
- "Martinèlli, Enzo", Enciclopedia Treccani (in Italian), 2008, retrieved April 13, 2011. The biographical entry about Enzo Martinelli the Enciclopedia Treccani.
- Rizza, G.B.; Succi, F., eds. (1984), "Convegno Internazionale in onore di ENZO MARTINELLI – Roma, 30 MAGGIO - 1 GIUGNO 1983", Rivista di Matematica della Università di Parma, (4), 10* External link in
|journal=(help). The proceedings of the "International Meeting in honour of ENZO MARTINELLI – Rome, 30 May – 1 June 1983", an international conference in his honour organized by M. Bruni, G. Fichera, S. Marchiafava, G. B. Rizza e F. Succi, published in the "Rivista di Matematica della Università di Parma" journal: the papers (Rizza 1984) and (Zappa 1984) are taken from them.