Eugenio Giuseppe Togliatti

Quick Info

Born

3 November 1890
Orbassano, Turin, Piedmont, Italy

Died

5 October 1977
Genoa, Liguria, Italy

Summary

Eugenio Togliatti was an Italian mathematician who studied projective-differential geometry and is particularly remembered for discovering the fifth-degree surface with 31 nodes. He lived through difficult times during World War II.

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Biography

Eugenio Togliatti was the son of Antonio Togliatti and Teresa Viale. Antonio was a school teacher and also an accountant for the Administration of National Boarding Schools, while Teresa was also a teacher. Antonio had been born in 1852 in Coassolo, a municipality in the Lanzo Valley in the Metropolitan City of Turin. His family wanted him to become a priest in the Roman Catholic Church but Antonio, after studying in the seminary in Giaveno, decided against becoming a priest and studied in Turin to become a teacher. After graduating with a teaching qualification, he taught for a while before becoming an accountant. He married the elementary school teacher from Turin, Teresa Viale. She had to give up her teaching career to care for her children and became the central figure of the family. Antonio's work led to the family moving frequently between different cities.

Antonio and Teresa had four children: Eugenio Giuseppe Togliatti, the subject of this biography, born in Orbassano, Metropolitan City of Turin, Piedmont, on 3 November 1890; Maria Cristina Togliatti, born in Genoa, Liguria on 3 May 1892; Palmiro Michele Nicola Togliatti, born in Genoa, Liguria on 26 March 1893; and Enrico Togliatti, born in Turin in 1900. We will give a little more information about Eugenio's siblings below.

Although Antonio Togliatti had decided not to become a priest, he remained a staunch Roman Catholic and the whole family attended mass every Sunday. Eugenio Togliatti attended a number of different schools, for example in Genoa, Novara and Sondrio, but completed his secondary education at the Technical Institute in Sondrio in the alpine region of north Italy. He graduated with a physical-mathematical diploma from the Sondrio Technical Institute in 1908, the year when the other members of his family moved to Sassari. His brother Palmiro and his sister Maria Cristina both began to study at the high school Domenico Alberto Azuni in Sassari in 1908. Eugenio, however, began to study for his degree in mathematics at the University of Turin in that year. His studies were supported by a scholarship he was awarded from the Royal College Carlo Alberto, Moncalieri, Turin. He was fortunate in his mathematical studies to be taught by several outstanding mathematicians, in particular Corrado Segre, Guido Fubini, Gino Fano, Giuseppe Peano and Enrico D'Ovidio. He also became friends with some fellow students who were outstanding mathematicians such as Alessandro Terracini. These two, who shared research interests in differential projective geometry, became friends beginning in the summer of 1912.

The fortunes of the Togliatti family changed dramatically on 21 January 1911 when Antonio Togliatti died of cancer. Soon after the death of her husband, Teresa moved to Turin with her three younger children. Eugenio, who was already in Turin, being the oldest of the children, needed to help support his younger siblings. Although he was still an undergraduate, he was appointed as an extraordinary assistant of Analytic and Projective Geometry at the Polytechnic of Turin. In 1911 his brother Palmiro Togliatti began his university studies, enrolling in the Faculty of Law at the University of Turin. An exceptional student, he won scholarships and prizes to help fund his studies. Also in 1911 Maria Cristina Togliatti enrolled to study Modern Philology in the Faculty of Letters and Philosophy of the University of Turin. Eugenio did a remarkable job supporting his younger siblings. Palmiro graduated in November 1915 and began a career which led him to become the Secretariat of the Italian Communist Party. Maria Cristina graduated in December 1915 with a degree in literature and became a teacher in secondary schools. Enrico, who was ten year younger than Eugenio, obtained a degree in engineering, which led to him later working at the Southern Electricity Company in Naples.

Let us see how Eugenio Togliatti managed to support his siblings. He completed his studies at the University of Turin, graduating on 3 July 1912, while working as an assistant at the polytechnic during his final year of undergraduate studies. For his final examinations, advised by Corrado Segre, he wrote the thesis Contributo alla determinazione delle superficie algebriche del 5° ordine con una o più serie infinite di coniche Ⓣ

(Contribution to the determination of 5th order algebraic surfaces with one or more infinite series of conics.)

. After graduating, he was appointed as an assistant, at both the University of Turin and at the Polytechnic of Turin, to the chairs of Gino Fano, Enrico D'Ovidio and Guido Fubini.

His friend Alessandro Terracini wrote in an autobiography (see [10]):-

During his service as assistant, my friend E G Togliatti managed to accomplish a feat that has always seemed wonderful to me. With his dual post as assistant at the University and at the Polytechnic, he managed to scrape together two meagre salaries (it should be noted that at the time each assistant post usually brought in a salary of little more than a hundred lire per month), with which - added to a pension from his widowed mother - he performed the miracle of supporting his three siblings in their studies.

Terracini also writes that, in addition to supporting his siblings studies, Eugenio was able to offer his brothers a holiday in the Alpine village of Mompellato.

One might imagine that Eugenio, having two assistant positions, would not have much time for research. He realised, however, that if he was to become a full professor he had to have a strong publication record and indeed he was able to do this. For example, he published: Sul comportamento d'un sistema $∞^{1}$ di linee d'una superficie rispetto ad alcune operazioni eseguite su di esso Ⓣ

(On the behavior of a system ∞1 of lines of a surface with respect to some operations performed on it)

(1912); Sulle superficie algebriche, del 5° ordine, irriducibili, con un fascio ellittico di coniche Ⓣ

(On algebraic surfaces, of the 5th order, irreducible, with an elliptic bundle of conics)

(1912); Le superficie di sesto ordine con infinite coniche Ⓣ

(Surfaces of the 6th order with infinitely many conics)

(1914-1917); Sulle superficie algebriche contenenti infinite coniche Ⓣ (1915); and Sulle superficie di 6° ordine contenenti infinite coniche Ⓣ

(On surfaces of the 6th order containing infinitely many conics)

(1915).

At the public Leibniz session of the Royal Berlin Academy of Sciences held in Berlin on 30 June 1910 the academy proposed the following problem for the solution of which the Steiner prize of 7000 marks was to be awarded in 1914 [12]:-

To determine all those non-degenerate surfaces of order five on which one or more series of conies lie, and to investigate their properties. It is required to confirm the correctness and completeness of the solution by furnishing an analytic commentary on the results of the geometric investigation.

... competing memoirs should be written in German, French, Latin, English, or Italian, and be submitted to the secretary of the academy under the usual conditions on or before 31 December 1913.

Togliatti submitted his entry The determination of all non-degenerate surfaces of the fifth order on which lie one or more series of conics which was one of seven entries for the Steiner Prize to be awarded in 1914. The outbreak of World War I in July 1914 led to Germany entering the war on 1 August 1914 and the award of the Steiner Prize had to be delayed. In fact it was not until 1922 that Togliatti was declared the winner of the Steiner Prize and it was 1923 before the award could be made [13]:-

The Berlin Academy of Sciences has awarded its Steiner prize for a memoir on 'The determination of all non-degenerate surfaces of the fifth order on which lie one or more series of conics' to Dr E G Togliatti, of the University of Turin. This subject was announced in 1910, but the award was delayed by war conditions.

Now 7000 marks in 1914 was worth roughly the buying power of $55,000 today and would have been life changing to the young Togliatti in supporting his family. Sadly German hyperinflation in the 1920s meant that by the time Togliatti received the award it was practically worthless.

During World War I, Togliatti had been called up for military service but this only happened in July 1918 near the end of the war. He was, at that time, an assistant to Gino Fano who was very keen that he should be excused military service. Fano approached the Ministry of War and made a case for Togliatti to be discharged or at least be given extraordinary leave. These requests were ignored and Togliatti was enlisted in Ivrea, a town about 50 km north of Turin, and served as a private in the 54th infantry regiment.

Back in Turin for the start of the 1919-20 session, he began teaching the course in projective and descriptive geometry. He taught this course until 1924 and, in addition, he taught the course in complementary mathematics in the academic year 1923-24. Let us explain that complementary mathematics is an Italian academic discipline involving the history of mathematics, foundations of mathematics, and mathematical didactics.

In 1924 Togliatti left Turin and went to Switzerland when he was appointed as associate professor of Applied Mathematics at the Eidgenössische Technische Hochschule in Zürich. He remained in Zurich until 1926 when, having won the competition for the Genoa chair, he returned to Italy to take up the appointment of the chair of Analytical and Projective Geometry at the University of Genoa.

Togliatti's brother Palmiro had become highly involved in politics. Eugenio Togliatti said that during World War I, Palmiro was [2]:-

... hypercritical of the government's neutralist attitude and harshly anti-Giolitti (Giovanni Giolitti was the Italian Prime Minister).

Palmiro Togliatti had become a founding member of the Communist Party of Italy in 1921. Benito Mussolini's government made the Communist Party illegal in 1926 and many party members were arrested. Palmiro was in Russia at the time and avoided arrest but he was elected General-Secretary of the Communist Party of Italy in 1927 and had to remain in exile for many years. Although Eugenio Togliatti was strongly opposed to Mussolini's Fascist regime, he tried to keep out of politics and concentrate on his mathematical career. This must have been quite difficult given his brother's high profile.

In Genoa, Togliatti met Giulietta Nacamuli. She had been born in Cairo, the daughter of the engineer Ruggero Nacamuli (born in Padua in 1876) and his wife Aurelia Camerino (born in Venice in 1875). She graduated with a mathematics degree from Genoa in 1925 and, following her graduation, was appointed as an assistant to Francesco Porro (1861-1937), professor of astronomy at the University of Genoa. After two years as an assistant at the Genoa Observatory, in 1927 she was appointed as assistant to Mario Bedarida (1890-1957), the professor of algebraic analysis at Genoa. Eugenio Togliatti married Giulietta Nacamuli and they had two children, Vittorio Togliatti and Giovanna Togliatti (1932-1990). Vittorio became a high school teacher but also worked for the Italian Communist Party. In August 1972, he was charged with stealing explosives and weapons, and plotting subversion with a group of wealthy professional people. He was released after a week and all charges were dropped. Giovanna graduated in mathematics, became a member of the Istituto di Topografia, Fotogrammerria e Geofisica, Politecnico di Milano and died on 13 November 1990.

For Togliatti's mathematical contribution during his career at Genoa, let us quote from [8]:-

In the field of projective-differential geometry, his research on three-dimensional varieties of five-dimensional space whose principal tangents present coincidences is noteworthy. He also studied hyperspatial surfaces that represent Laplace equations in the case in which such surfaces are algebraic or rational. In the field of algebraic geometry he constructed a fifth-degree surface with 31 nodes, known as the Togliatti surface, obtaining a significant partial result within the problem of determining the maximum number of nodes that an algebraic surface of order n of the ordinary projective space can possess. He was also interested in the teaching of mathematics in secondary schools, dedicating numerous popular articles to improving the scientific culture of teachers.

A picture of this surface is at THIS LINK.

We note that the fifth-degree surface with 31 nodes which Togliatti constructed in 1940 in his paper Una notevole superficie di 5° ordine con soli punti doppi isolati Ⓣ

(A remarkable surface of the 5th order with only isolated double points)

was the first example of such a surface. For 40 years it was an open problem to determine whether 31 was the maximum number of nodes possible for a fifth-degree surface. In 1980 Arnaud Beauville proved that no fifth-degree surface can have more that 31 nodes, so Togliatti example is optimal.

Togliatti attended the International Congress of Mathematicians held in Bologna in September 1928. His work was mentioned by two speakers at the conference, Alfred Rosenblatt and Charles H Sisam. At this Congress, delegates were welcomed by the Podestà of Bologna, Hon L Arpinati, who said:-

Fascist Bologna is proud to welcome you and to be able to show you what it has become under the vivifying impulse of Fascism.

We have to feel sorry for Togliatti when he heard these words, for he hated Fascism but refused to have any involvement in politics. Togliatti also attended the International Congress of Mathematicians held in Zurich in September 1932. Francesco Severi, the President of the Italian delegation, gave a speech at this Congress in which he said:-

I must also remember with particular satisfaction that one of ours, Professor Eugenio Togliatti, taught here in fraternal intimacy with his Swiss colleagues ...

Togliatti also attended the International Congress of Mathematicians held in Amsterdam in September 1954.

At the University of Genoa, Togliatti was Dean of the Faculty of Science from 1931 to 1963. He also served as Vice-President of the Opera Universitaria, which aimed to support students during their university career. From 1933 he was the director of the Mathematical Institute, continuing to hold this position until 1966. He also took a role in supporting mathematics on an Italian scale being a member of the Italian Mathematical Union from its foundation in 1922, and serving on its organising committee on several occasions. He served as national president of the "Mathesis" Society and also served on the Italian Commission for the Teaching of Mathematics.

As Fascist Italy moved towards World War II the Togliatti family had two major problems. Togliatti had a brother who was the leader of the Italian Communists and his wife was a Jew. The Racial Laws of November 1938 excluded Jews from public office and higher education, in addition to imposing many other restrictions. After Italy agreed an armistice with the Allies in September 1943, German troops took control of much of north Italy and Jews in that area were in danger of being put into concentration camps. On 16 December 1943, Giulietta's father Ruggero, her mother Aurelia, her sister Iside (born in Cairo in 1904) and her aunts Benvenuta and Eugenia Camerino (both born in Venice, in 1869 and 1872 respectively) were arrested by the Germans in Chiavari, about 40 km south of Genoa. On 6 February 1944 they all arrived in the Auschwitz concentration camp, and with the possible exception of Iside, were killed on the day they arrived. Iside probably died later some time later in Auschwitz. Giulietta had managed to avoid arrest by moving around Italy with her husband and two children. Later in 1944 Togliatti also became in danger (see [1]):-

Far from active politics, the fact of being Palmiro Togliatti's brother caused Eugenio Togliatti some serious problems in September 1944, during the period of the Italian Social Republic. In fact, an arrest warrant was issued by the Genoa police headquarters; the intention seemed to be to use him as a hostage in a prisoner exchange with the partisans. But a partisan courier made sure that the professor, who was living in Frabosa Soprana in the province of Cuneo at that time, was informed in time so that he could save himself together with his family.

In April 1945 with the Allies in control of almost all of Italy, the Togliatti family returned to Genoa. He continued to hold his position in the University of Genoa until he retired in 1967 and was made professor emeritus.

Togliatti received several honours: he was elected a corresponding member of the Accademia dei Lincei in 1957 and a full member in 1968; he was elected a corresponding member of the Academy of Sciences of Turin; he also a member of the Ligurian Academy of Sciences and Letters, and served a term as president of its class of physical, mathematical and natural sciences.

Although Togliatti had spent his life avoiding politics, he decided in 1960 that he could not continue to keep his views to himself. The neo-Fascist Italian Social Movement proposed holding their Congress in Genoa on 3 July 1960. Togliatti said:-

I have never been involved in politics but I feel that in these moments one cannot stay outside.

Although shy and very reserved, Togliatti made his political statement by leading a procession of anti-fascist students and teachers.

He died in Genoa at the age of 87. A report of his death reads (see [1]):-

Eugenio Togliatti, the elder brother of comrade Palmiro Togliatti and a distinguished mathematician, died yesterday morning in Genoa at the age of 87. Eugenio Togliatti was struck down by an attack of bronchopneumonia after his body had been weakened in recent months by an operation for a cerebral haemorrhage, the same illness that caused Palmiro's death. If one element of his biography should be highlighted, it is his intellectual rigour. A rigour directed mainly towards the deepening of a scientific activity that made Eugenio Togliatti one of the most notable personalities in the mathematical field.

The head of the Communist Party of Italy sent a telegram to Togliatti's wife and children following his death [1]:-

The most sincere and profound condolences of the party leadership and my personal ones for the painful passing of Professor Eugenio Togliatti. The communists and the men of culture and the Italian school will always remember him as a clear figure of a democrat and as an anti-fascist and above all as an exemplary teacher in whose humane and rigorous classes generations of scholars were educated and formed.

Other Mathematicians born in Italy
A Poster of Eugenio Togliatti

References (show)

R Balestrieri, Giulietta Nacamuli, Astronomia versus Astrofisica (2015).
http://uranialigustica.altervista.org/nacamuli/index.htm
G Bocca, Palmiro Togliatti (Mondadori, Milan, 2005).
D C Demaria, Eugenio Giuseppe Togliatti (3-XI-1890–5-X-1977), Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 112 (5-6) (1978), 367-370.
Eugenio Giuseppe Togliatti, geni.com (2024).
https://www.geni.com/people/Eugenio-Giuseppe-Togliatti/6000000068364535907
Eugenio Giuseppe Togliatti (1890-1977), Matematica Italiana (2024).
https://matematicaitaliana.sns.it/autori/1270/
D Gallarati, Eugenio Giuseppe Togliatti, Atti Accad. Ligure Sci. Lett. 35 (1978), 72-78.
D Gallarati, Eugenio Giuseppe Togliatti, Boll. Un. Mat. Ital. A (5) 15 (2) (1978), 490-493.
L Giacardi, Eugenio Giuseppe Togliatti (1890-1977), Corrado Segre e la Scuola italiana di Geometria Algebrica (2024).
https://www.corradosegre.unito.it/togliatti.html
E Luciano, Togliatti, Eugenio Giuseppe, Dizionario Biografico degli Italiani 95 (2019).
https://www.treccani.it/enciclopedia/eugenio-giuseppe-togliatti_(Dizionario-Biografico)/
E Marchionna, Eugenio Giuseppe Togliatti. Memorial speech read at the session of 21 April 1979, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 66 (4) (1979), 309-319.
Maria Cristina Togliatti, Archivio storico dell'Università degli Studi di Torino (2024).
https://www.asut.unito.it/studenti/web/index.php?r=studenti%2Fview&id=1673
Notes, Bulletin of the American Mathematical Society 17 (1) (1910), 48.
Notes, Bulletin of the American Mathematical Society 29 (3) (1923), 141.
Palmiro Togliatti, Archivio storico dell'Università degli Studi di Torino (2024).
https://www.asut.unito.it/studenti/web/index.php?r=studenti%2Fview&id=1945
M T Rivolo Eugenio Togliatti, in C Silvia Roero (ed.), La Facoltà di Scienze Matematiche Fisiche Naturali di Torino, 1848-1998 (Subalpine Deputation of National History, Turin, 1999), 585-588.

Additional Resources (show)

Other pages about Eugenio Togliatti:

Gino Loria by Eugenio Togliatti

Other websites about Eugenio Togliatti:

Honours (show)

Honours awarded to Eugenio Togliatti

Steiner Prize 1922

Cross-references (show)

Other: Recent Changes — up to March 2025

Written by J J O'Connor and E F Robertson
Last Update March 2025