**Giuseppe Pompilj** was an Italian mathematician who worked in geometry and mathematical statistics.

- Giuseppe was educated in Rome where he entered the university to study mathematics.
- Pompilj continued to undertake research at the University of Rome and, in 1942, he was appointed as a lecturer.
- Pompilj was called up for military service and, after being captured by the British, was interred in a POW camp in North Africa.
- Conditions in the camp were good and there was a small library in which Pompilj found Alec Aitken's book Statistical Mathematics (1939).
- He was able to continue to work on his thesis at Yol and Pompilj was pleased to be able to help him.
- This was a rather unusual way for an expert in algebraic geometry to become interested in statistics but this was to lead to Pompilj becoming one of the leading statisticians in Italy after the war ended.
- However, back in Italy after release from the POW camp in India in 1946, Pompilj's publications over the next couple of years were mainly on geometry except for the paper Sulla regressione Ⓣ(On regression) (1946).
- In 1948 Pompilj entered a competition for a chair of geometry at the University of Rome.
- However, he recommended the hiring of Pompilj at the Faculty of Statistics in 1948.
- It is interesting to note that though Pompilj was officially assigned the chair of geometry, he in fact had to teach probability (which previously was taught only to students of actuarial science) and mathematical statistics.
- We note that in the 1950s, Pompilj was teaching both statistics and geometry courses at the University of Rome.
- Thanks to his mathematical training, Pompilj had the skills to reduce the gap between mathematics and statistics that had been created in Italy.
- Pompilj was also a pioneer in the field of operational research, developing the first significant applications in collaboration with the Italian Navy.
- An unfinished treatise on random variables, composed during a research visit to Pittsburgh, was destined to "gather together in a single exposition that took into account the various contributions of various schools, the attained results from some researchers (and particularly those of the Rome Institute of the Calculus of Probability) in developing, reordering and completing certain contributions of C Gini to the general theory of distributions" [G Pompilj, Le variabili casuali Fasc.
- The first of Pompilj's research contributions was in the field of algebraic geometry and continued themes dear to the Italian school, already studied by Guido Castelnuovo, Federigo Enriques and Francesco Severi, whom he had as teachers in Rome.
- The topics covered by Pompilj were principally: multiple planes; Cremona transformations of the plane that possess special curves of fixed points; and families of hyperelliptical or trigonal surfaces.
- it was said that the desertion of Pompilj had resulted in a grave loss for geometry.
- This is the most obvious link between the new and the old interests of Pompilj.
- Thanks to this geometric point of view, Pompilj, together with contributions from some of his students, was able to interpret and to extend, in the context of the theory of random variables, the statistical indicators introduced by Gini, and to deepen his ideas on the theory of distributions.
- In the work Teoria statistica della significatività e conformità dei risultati sperimentali agli schemi teorici Ⓣ(Statistical Theory of Significance and Conformity of Experimental Results with the Theoretical Methods), in Statistica, Milano 8 (1948), 7-42, and Sulla significatività delle costanti statistiche Ⓣ(On the significance of statistical constants), in Bollettino dell'Unione matematica italiana (3) 4 (1949), 112-117, Pompilj formulated a 'theory of conformity', an alternative to that of significance.
- Pompilj's main criticism of the theory of significance, taken from those of Gini, is to confuse the 'a posteriori' probability P(A∣B)P(A | B)P(A∣B) with the probative P(B∣A)P(B | A)P(B∣A).
- For Pompilj it is necessary to depart from Bayes' Theorem to also clarify the mechanisms that operate in the interpretation of facts.
- In his concept of probability, Pompilj was close to a subjective concept, but did not completely marry it to his theses.
- Together with his students, Pompilj also did a considerable amount of more applied work.
- Pompilj was amongst the founders of the Italian Association in Operations Research.
- Pompilj's relevance is proven by the fact that a representative of the Istituto di Calcolo delle Probabilità was nominated as a permanent member of the scientific committee.
- Pompilj was also awarded a Gold Medal of the President of the Republic for his contribution to science and culture.
- Let me conclude by mentioning an anecdote which demonstrates Pompilj's generous personality.

Born 17 July 1913, Rome, Italy. Died 9 July 1968, Rome, Italy.

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Origin Italy

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