# Luigi Berzolari

### Born: 1 May 1863 in Naples, Italy

Died: 10 December 1949 in Pavia, Italy

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**Luigi Berzolari**'s father was an infantry officer serving during a very difficult period. Italy was unified three years before Luigi was born and he grew up in a country that was coming to terms with this important event. The 1860 unification did not solve Italy's problems for Rome was not part of the newly created country. At the time when Luigi was born, Naples, the city of his birth, was the largest in Italy but it was a city of poverty and disease. The army was fully occupied in putting down peasant revolts and, after becoming involved in the 1866 war between Prussia and Austria, sought to bring Rome into the new Italy by force in the following year. Luigi's father was killed in the fighting round the major fortress at Gaeta so, from the age of four, he was brought up by his mother. Only in 1871 did Rome become the capital of Italy.

After the death of Luigi's father, his mother returned to her home town of Mortara, in Lombardy, where Luigi attended elementary school. He attended middle school in Pavia where one of his mathematics teachers was Salvatore Pincherle who taught for the three years 1874-77 at the liceo in Pavia. In 1880 Berzolari entered the University of Pavia and he lived in Ghislieri College, an ancient college founded by pope Pius V in 1567. At university, he studied mathematics with Eugenio Beltrami, Eugenio Bertini and Felice Casorati. He graduated with his laurea in 1884 and continued to work at Pavia as an assistant to Casorati, who held the chair of infinitesimal calculus. He published his first work, coming from his laurea thesis, in 1885, namely

*Sulla superficie del quarto ordine avente una conica doppia*Ⓣ. Then, remaining at Pavia, he became an assistant to Ferdinando Aschieri, who held the chair of projective and descriptive geometry. However, in addition to his work as an assistant at the university, he taught mathematics in middle schools in Pavia and Vigevano. He also spent a short time teaching in the military academy in Turin in 1888. In 1892 he received his 'libero docente', which is similar to the habilitation and gives the right to lecture in universities, and became a lecturer in analytic and projective geometry at Pavia having, by this time, published ten papers including the major work

*Ricerche sulle trasformazioni piane, univoche, involutorie, e loro applicazioni alla determinazione delle involuzioni di quinta classe*Ⓣ in 1889 and two papers with the title

*Intorno alla rappresentazione delle forme binarie cubiche e biquadratiche sulla cubica gobba*Ⓣ in 1891.

Berzolari entered the competition for the chair of analytic and projective geometry at the University of Rome in 1891. The referees were Eugenio Bertini, Enrico D'Ovidio and Giuseppe Veronese. Among the candidates who were eligible to enter the competition, in addition to Berzolari, there was Guido Castelnuovo, Alfonso Del Re, and Mario Pieri. Castelnuovo was a clear winner and appointed to the chair; Berzolari came third behind Del Re. Two years later, in 1893, Berzolari entered the competition for the chair of projective geometry at the University of Naples. The referees were Ferdinando Aschieri, Eugenio Bertini, Francesco Chizzoni, Vittorio Martinetti, and Giuseppe Veronese. In addition to Berzolari, Domenico Montesano, Del Re and Pieri were candidates. This proved a very close contest with Montesano just coming out ahead of Berzolari. Later in the same year of 1893 there was a second chair competition, this time for the chair of projective and descriptive geometry at the University of Turin. It came about through the death of Giuseppe Bruno in February of 1893. The referees were Ferdinando Aschieri, Eugenio Bertini, Enrico D'Ovidio, Corrado Segre, and Giuseppe Veronese. Berzolari was ranked first with Mario Pieri and Alfonso Del Re tied for second place. He was appointed and taught at the University of Turin for six years; there Pieri became his assistant and, from 1896, Beppo Levi was also his assistant for two years.

It certainly appeared that Berzolari would spend the rest of his career at Turin but, in 1899, he entered the competition for a chair at the University of Pavia. He was appointed and served as director of the mathematical institute at Pavia for the rest of his life. He did have a one-year break away from Pavia, spending the academic year 1924-1925 teaching at the University of Milan. His merits as a scientist and a teacher earned him many honours at Pavia: he was rector of the University twice, from 1909 to 1913 and from 1920 to 1922, and dean of the faculty of sciences in the periods 1907-1909, 1916-1920, and 1925-1929. Of course he held these important influential roles at a time, beginning around 1920, when Fascism gripped Italy. By 1922 Mussolini was in power in Italy and Fascist policies were imposed. Berzolari showed great courage in opposing fascism in the early days when he was rector but then ceased all attempts at resistance and accepted it as inevitable.

To give an idea of his contributions to geometry, we mention a few of his papers:

*Sugli invarianti differenziali proiettivi delle curve di un iperspazio*Ⓣ (1897),

*Sulle coniche appoggiate in più punti a date curve algebriche*Ⓣ (1900),

*Sul significato geometrico di alcune identità lineari fra quadrati di forme algebriche*Ⓣ (1918), and

*Sul complesso di covarianti di tre complessi lineari a due a due in involuzione*Ⓣ (1922). He published some popular books:

*Sulla teoria delle curve razionali*Ⓣ (1898), and the two-volume treatise

*Geometria analitica*Ⓣ (1911-1916), with later editions in 1920-22 and 1925-42. He wrote over 40 obituaries, including:

*Della vita e delle opere di Luigi Cremona*Ⓣ (1906),

*Commemorazione di Max Noether*Ⓣ (1921),

*Commemorazione di Corrado Segre*Ⓣ (1924),

*Commemorazione di Felix Klein*Ⓣ (1925),

*Cenni necrologici di C Neumann*Ⓣ (1925),

*Cenni necrologici di G Ricci Curbastro*Ⓣ (1925),

*Breve commemorazione di G Mittag-Leffler*Ⓣ (1927),

*Commemorazione di Eugenio Bertini*Ⓣ (1933),

*Commemorazione di Alexander von Brill*Ⓣ (1935), and

*Commemorazione di Salvatore Pincherle*Ⓣ (1936).

The Mathesis Association for Research into Instruction in Middle Schools was founded in 1895 and, although it only admitted schoolteachers at first, it opened up to university professors in 1908. In the following year a proposal was brought forward by Roberto Bonola for the society to produce a mathematics encyclopaedia and Berzolari was appointed to head the commission (which included Bonola). The editorial board was Berzolari together with Duilio Gigli and Giulio Vivanti. The aim of the encyclopaedia was:-

As well as heading the editorial board, Berzolari wrote a number of articles for theTo present to mathematics teachers and students in teachers' colleges a complete summary of elementary mathematics, not just to save time and effort for those who would desire precise and reliable reports on such elementary considerations, but also with the principal aim to diffuse the culture of mathematics among those who do not have the fortune to reside in a university centre, and cannot easily obtain materials to study... .

*Enciclopedia delle Matematiche Elementari*(1923-1950):

*Calcolo combinatorico*Ⓣ;

*Elementi della teoria dei gruppi*Ⓣ;

*Determinanti*Ⓣ; and

*Equazioni lineari*Ⓣ;

*Sostituzioni lineari, forme lineari, bilineari, quadratiche*Ⓣ.

Berzolari was honoured in many different ways. He was elected as president of the Mathesis Association and of the Italian Mathematical Union succeeding the founder of the Union Salvatore Pincherle in 1933. He was also president of the Lombard Institute of Science and Letters. He was elected to the Reale Accademia dei Lincei in 1919. He was also elected to the Academy of Sciences of Turin, the Academy of Science of the Institute of Bologna and the Academy Pontaniana of Naples.

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

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