**Mauro Picone** was an Italian mathematician who worked on ordinary and partial differential equations.

- One might have expected that Picone would excel at school, but this seems not to have been the case.
- Picone's quiet, hardworking, life in Turin was disrupted with the outbreak of World War I.
- One year later, in April 1916, Picone was called up and assigned to the 6th Artillery Regiment where he was given the rank of second lieutenant.
- On learning that Picone was a mathematician, his commander, Colonel Federico Baistrocchi, set him the task of computing new gunnery tables for the artillery.
- Picone was promoted to captain of artillery in 1917 and, in the following year, was awarded the Military Cross by Italy and the Croix de Guerre with silver star by France.
- After the war ended and Picone was demobbed, he returned to his university teaching.
- There Renato Caccioppoli, who graduated from Naples in 1925 having been a student of Ernesto Pascal, became Picone's assistant.
- Carlo Miranda entered the University of Naples in 1927 and studied with Picone, graduating in 1931.
- At this time Miranda also became an assistant of Picone who by this time had four assistants, the other two being Gianfranco Cimmino and Giuseppe Scorza Dragoni.
- These four assistants are referred to as "Mauro Picone's four musketeers" by Scorza Dragoni in his obituary of Miranda.
- They worked in the "Institute for Calculus" which had been founded by Picone in Naples in 1927 with financial assistance from the Banco di Napoli.
- Picone left Naples in 1932, together with Miranda, when he moved his Institute to Rome on being appointed to the chair of Higher Analysis there.
- When Picone became interested in numerical analysis the electronic computer was twenty-five years into the future the pure mathematicians at the University of Rome despised the subject, although the Germans had already given it high status in some of their universities.
- Yet by 1935 Picone's vision and persistence had given the institute, by now the National Institute for the Applications of Calculus, the entire top floor of the new palace of the National Research Council and enough money to pay (miserly) a staff of thirty.
- Let us be kind and suggest that by this time Picone had seen the error of his earlier Fascist beliefs.
- one notes Picone's marked preference for the numerical direction of analysis which was more amply developed after the establishment of the Istituto Nazionale per le Applicazioni del Calcolo, since he knew that problems with an applied emphasis always give rise to new theoretical research.
- Resulting from this were Picone's results on a priori bounds for the solutions of ordinary differential equations, as well as for those of linear partial differential equations of elliptic type and parabolic type for which the bound is obtained by means of the boundary data and the known terms; these results are contained in his well-known 'Notes on higher analysis' (Italian) a volume published in 1940 and which was, for its time, "truly avant-garde".
- Gaetano Fichera highlights Picone's 1936 memoir which contains a characterization of a large class of linear partial differential equations whose solutions enjoy mean-value properties termed "integral properties" by Picone; using this theory Picone reconstructed M Nicolescu's theory of polyharmonic functions.
- Some of his most important books which Picone published during his years in Rome are: Appunti di Analisi superiore Ⓣ(Higher analysis notes) (1940), which studies harmonic functions, Fourier, Laplace and Legendre series and the equations of mathematical physics; Lezioni di Analisi funzionale Ⓣ(Lessons on functional analysis) (1946), which concerns the calculus of variations; Teoria moderna dell'integrazione delle funzioni Ⓣ(modern integration theory of functions) (1946), containing a detailed discussion of the r-dimensional Stieltjes integrals; (with Tullio Viola) Lezioni sulla teoria moderna dell'integrazione Ⓣ(Lectures on modern theories of integration) (1952), which is basically the previous work by Picone with three extra chapters by Viola; and (with Gaetano Fichera) Trattato di Analisi matematica Ⓣ(Treatise on mathematical analysis) (Vol 1, 1954, Vol 2, 1955), which puts into a treatise Picone's way of teaching calculus particularly slanted towards the applications studied at the Institute for Applied Calculus.
- After Picone retired in 1960, he was made professor emeritus.
- Picone received many honours for his remarkable contributions to mathematics.

Born 2 May 1885, Lercara Friddi, Palermo, Italy. Died 11 April 1977, Rome, Italy.

View full biography at MacTutor

Origin Italy

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