**Castelnuovo** was an Italian mathematician who worked in algebraic geometry. He also worked in probability and relativity.

- Guido attended the Foscarini grammar school in Venice, where his mathematics teacher was Aureliano Faifofer.
- There Castelnuovo was taught by Veronese who gave him an interest in geometry.
- Castelnuovo graduated from Padua in 1886 and spent the following year in Rome on a postgraduate scholarship.
- Soon after graduating Castelnuovo sent a copy of one of his papers to Corrado Segre, the professor in Turin.
- Castelnuovo expressed his surprise when he received a copy of the paper back with carefully thought out notes and suggestions on it and wrote to Segre saying how unusually helpful his comments had been.
- After his year in Rome Castelnuovo obtained his first appointment as an assistant to D'Ovidio at the University of Turin.
- This was a period when Castelnuovo produced research of the highest quality on the theory of algebraic curves.
- Castelnuovo made a major step forward reinterpreting the results of this paper in projective terms.
- In 1891 Castelnuovo was appointed to the Chair of Analytic and Projective Geometry at the University of Rome.
- In Rome Castelnuovo was a colleague of Cremona but although he had given up active research he was still teaching the Higher Geometry course despite the fact that he had "not been interested in science for a long time", as Veronese had commented five years earlier.
- After Cremona's death in 1903, Castelnuovo began to teach the advanced geometry courses.
- Castelnuovo also wrote a book on probability, publishing Calcolo della probabilità Ⓣ(Calculation of probability) in 1919 and a text on the theory of relativity in 1923.
- Castelnuovo's most important work, however, was done in algebraic geometry, publishing Geometria analitica e proiettiva Ⓣ(Analytic and projective geometry) in 1903.
- In the area of algebraic curves we should mention the Castelnuovo-Severi inequality and a related criterion which Castelnuovo found for the linearity of an algebraic system on a curve.
- Castelnuovo produced a series of papers over a period of 20 years which, together with Enriques, finally produced a classification of algebraic surfaces.
- Their collaboration began in 1892, shortly after Castelnuovo had taken up his chair in Rome.
- At first the collaboration was between the established mathematician Castelnuovo and the young twenty year old Enriques so the relationship was that of teacher and student.
- In 1901 Castelnuovo and Enriques had submitted their joint work for the Royal Prize in Mathematics awarded by the Accademia dei Lincei.
- After lengthy discussions it was decided not to make an award because Castelnuovo and Enriques had made a joint submission.
- Both received the prize in subsequent years; Castelnuovo in 1905 and Enriques in 1907.
- Castelnuovo had only recently graduated when he was informed by Cremona of Kronecker's lecture and he found his own proof of the result.
- Kronecker never published the theorem and it was Castelnuovo's version which appeared in print.
- In all Castelnuovo produced over 100 publications if one counts his books, articles and scientific memoirs.
- Castelnuovo retired from teaching at the University of Rome in 1935.
- Italy's increasingly close alliance with Hitler and his policies was resented and feared by many in Italy and most certainly by Castelnuovo.
- Castelnuovo, being a Jew, was forced into hiding during the years the Nazis were in power in Italy but he organised special courses to instruct Jewish students disadvantaged by anti-Semitic government policies.
- Castelnuovo was appointed as a special commissioner of the Consiglio Nazionale delle Ricerche in June 1944, after Rome was liberated, being given the task of reviving the scientific institutions in Italy which had suffered badly under Mussolini during his 20 years in power.
- Castelnuovo was also deeply involved in the debate on mathematical instruction at all levels and had a major influence in the development of the ministerial curricula for the scientific lyceum and technical institutes.
- Calculus was not brought into the school syllabus in Italy as early as in many other countries and the concept of a function only brought in around 1910 after Castelnuovo's efforts.

Born 14 August 1865, Venice, Italy. Died 27 April 1952, Rome, Italy.

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Origin Italy

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