**Enrico Bompiani** was an Italian mathematician, specializing in differential geometry.

- At La Sapienza University of Rome, Bompiani was advised by Guido Castelnuovo who, in 1909, suggested to him that he look at a line geometry interpretation in projective 4-space of Eugène Cosserat's results on systems of circles in 3-space.
- After undertaking research on this topic, Bompiani was awarded his laurea in 1910 for his thesis Spazio rigato a quattro dimensioni e spazio cerchiato ordinario Ⓣ(Four-dimensional space and ordinary circular space).
- In August 1912 Bompiani was called up to support the Italian war but, despite this, he was able to attend the International Congress of Mathematicians in Cambridge, England, 22 August to 28 August 1912, where he delivered the paper Recenti progressi nella geometria proiettiva differenziali degli iperspazi Ⓣ(Recent advances in differential projective geometry of hyperspace).
- The peace treaty before the end of 1912 allowed Bompiani to return to his assistantship in Rome.
- Castelnuovo communicated Bompiani's results to Corrado Segre in Turin who praised them but also reported that he had submitted a paper with related results and that his student Alessandro Terracini (1889-1968) was undertaking research in the same area.
- This was to start a long collaboration between Bompiani and the Turin school.
- Towards the end of Bompiani's two years in Rome he was released from his duties so that he could spend some time at Göttingen.
- Bompiani, thanks to the conscientious way he carried out his duties and to his special aptitude for teaching, contributed greatly to the preparation of his students.
- However, Bompiani did not have such a good experience as Gerbaldi's assistant.
- Gerbaldi had been unhappy to leave Sicily for Pavia where he did little mathematics which only made Bompiani's time as his assistant even more difficult.
- In 1914 Bompiani was appointed as a libero docente in Pavia, meaning that he could give lectures without being supervised by a professor.
- From that time until October 1919 Bompiani was periodically called for military duty, serving in various roles including work on aeronautics and fighting on the front.
- Despite the interruptions to his academic career, Bompiani maintained a remarkable research output and by the time he was fully released from military duties towards the end of 1919 he already had over 30 papers published.
- His military duties having ended, Bompiani returned to full-time duties as Castelnuovo's assistant in Rome.
- In October 1922 Federigo Enriques informed Castelnuovo that Bompiani had won the competition for an extraordinary professorship in projective and analytic geometry at the University of Modena.
- Castelnuovo clearly did not want to lose Bompiani but nevertheless his advice to Bompiani that a better opportunity would come up soon was certainly made in Bompiani's best interests.
- Perhaps he already knew that Bompiani was likely to be offered a professorship at the Higher Technical Institute in Milan and indeed in November 1922 he was offered the position of professor of analytic, projective and descriptive geometry.
- Bompiani now had two positions on offer, although any appointment required the approval of the Minister of Education.
- In December Bompiani wrote to the Minister saying he would accept the professorship in Modena but, if the Minister agreed, he would prefer Milan.
- This position looked very attractive, not least since Enriques had gone from Bologna to Rome, so it seemed the right stepping stone for Bompiani in his quest for a chair at the University of Rome.
- Bompiani took this advice and, after his appointment in 1923, spent the next three years in Bologna.
- In 1923-24 Bompiani taught Riemannian geometry and absolute differential calculus at Bologna and, in the following year, first order differential equations.
- Bompiani's appointment to Bologna was to an extraordinary chair and he had the right to seek an ordinary professorship after three years.
- However, the approach of the distinguished mathematician from Turin is purely analytical, and Bompiani deserves the credit for having brought about its geometric understanding.
- for the whole collection of his papers, for their lucidity as well as for their breadth, for the importance of some of his results, for the varieties of tools and the quality of the exposition, Bompiani has by now attained a position of honour among geometers of the young Italian school.
- In the following year, 1927, Bompiani achieved his aim of returning to Rome.
- Bompiani's value is universally well known, his teaching ability makes clear why our faculty decided to propose him for the vacant chair of Descriptive Geometry, which is a part of the discipline taught by him in Bologna.
- Bompiani was appointed to La Sapienza University of Rome and so achieved the aim he had worked towards for years.
- However by this time Italy was under Fascist rule and this would play a large role in Bompiani's activities over the next years.
- Bompiani was appointed secretary of the National Committee for Mathematics when it was formed.
- In July 1930 Bompiani joined the Fascist Party.
- Certainly Bompiani was keen to travel and work abroad and since this would have propaganda benefits to the Italian government, he received their encouragement.
- Perhaps the most notable person to be omitted was Castelnuovo, who was Jewish, who had done so much to support Bompiani.
- This was in stark contrast to Bompiani's paper Italian contributions to modern mathematics which was published in the American Mathematical Monthly in 1930 where the contributions of Jewish Italian mathematicians are described as they should be.
- The Italian Mathematical Union was founded in 1922 with Bompiani as one of its founding members.
- He was elected vice-president in 1938 and, in the part of the Union's Bulletin dated 10 December 1939 there appears a declaration, signed by Bompiani and other members of the Scientific Committee, declaring the Aryan nature of Italian mathematics.
- Bompiani was accused of propaganda activities for the Fascists, particularly in his trips abroad.
- Castelnuovo made no attempt to support Bompiani against these accusations.
- The purge had no practical affect on Bompiani's career and he continued to hold his chair at the University of Rome until he retired in 1964.
- We have already listed some awards given to Bompiani.
- Finally let us mention that Bompiani founded the International Mathematical Summer Centre (CIME) in 1954.

Born 12 February 1889, Rome, Italy. Died 22 September 1975, Rome, Italy.

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Origin Italy

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