Oscar Chisini

Born: 14 March 1889 in Bergamo, Italy
Died: 10 April 1967 in Milan, Italy

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Oscar Chisini was the third son of a noble Venetian family. His father, who held a degree in law, was a professional soldier and as his family accompanied him along the path of his career. The young Oscar received a classical education, first in Ravenna and then in Bologna. This was to leave its mark on him, as we know from Carlo Felice Manara [1] that Professor Chisini enjoyed quoting long passages from Dante's Divina Commedia.

Later, enrolled as an engineering student at the University of Bologna, Oscar Chisini met Federigo Enriques in a meeting that was to change his life. Indeed, Enriques immediately recognised his talent, led him to obtain a degree in mathematics in 1912, and engaged him as assistant and coauthor in the writing of the treatise Lezioni sulla teoria geometrica delle equazioni e delle funzioni algebriche . The four volumes of this monograph, started in 1915 and finished in 1934, were conceived in what Chisini called a peripatetic way, that is walking under the porches of Bologna with Enriques possibly stopping to write on the flooring with the tip of his umbrella. This could be related with the origin of Chisini's idea that:-

Geometry teaches you how to carry out the correct reasoning on the wrong picture.
The four volumes appeared in 1915, 1918, 1924 and 1934 and were reprinted as two books, of two volumes each, in 1985. Du Val, reviewing Chisini's 1960 paper Singolarità delle curve algebriche piane: Schemi rappresentativi e questioni connesse , writes:-
This is a sort of mature meditation on the theory of the singularities of a plane curve, classically laid down by Enriques and [Chisini], over half a century ago.
The Great War marked a break in Chisini's academic career, as he volunteered in the alpine artillery. On the other hand, it gave him an opportunity to display his versatility by applying mathematics to solve technical military problems. In particular, he invented a telemeter that was patented. After the war, he first became a professor in Cagliari in 1923, then in 1925 he moved to Milan where he remained until he retired in 1959. At the time of his death, he was professor emeritus and also a member of the Accademia dei Lincei.

According to Eugenio Giuseppe Togliatti [2], the activity of Oscar Chisini in the mathematical sciences was threefold: scientific research in the field of algebraic geometry, high level original reconstruction of mathematical theories, and active involvement in the teaching of mathematics at secondary school level. It was the latter that led him to reflect on the notion of mean, eventually giving an original definition that was first appreciated by Bruno de Finetti and then became a point of reference in statistics. Also as part of his work on mathematical education he was associated over a period of 46 years with the journal Periodico di Matematiche and wrote many articles and books on various aspects of elementary mathematics. For example he published in this journal: Sul principio di continuità (1956) which is an expository lecture on the principle of continuity in algebraic geometry, beginning with the ideas of Kepler; La superficie cubica (1957) which gives a clear and original treatment of the principal properties of cubic surfaces, presenting it as a preliminary introduction to the study of algebraic geometry; and Isoperimetri (1960) which contains elementary thoughts on the plane isoperimetric problem.

As an algebraic geometry researcher, Oscar Chisini is to be considered part of the so-called Italian school, featuring among others Luigi Cremona, Corrado Segre, Guido Castelnuovo, Francesco Severi, Beniamino Segre and, of course, Federigo Enriques. Extended bibliographies of Chisini's works are given by Carlo Felice Manara [1] and Eugenio Giuseppe Togliatti [2].

Carlo Felice Manara [3] identifies three main traits of the intellectual personality of Oscar Chisini: the liveliness of his imagination, his ability to deal with generality by means of special cases, and a radical critical spirit that allowed him to avoid the pitfalls of this kind of reasoning. Manara writes [3]:-

... the uncommon qualities of his mind, both in the creative process and in criticism, are well apparent in his work.
Overall, Chisini expressed a dynamic vision of science in which history and mistakes are to play a prominent role. For example, he believed that theorems should be presented as raw minerals rather than polished gems.

Article by: Luca La Rocca University of Modena and Reggio Emilia, Italy.

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JOC/EFR August 2005
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