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While he tutored at the university in his assistant position, Boggio also worked for his doctorate and this was awarded in 1903 for mathematical physics. Boggio remained at the University of Turin, teaching a variety of courses, until 1905 when he was appointed Professor of Mathematics of Finance at the University of Genoa.

In 1908 Boggio moved again, this time to the position of Professor of Rational Mechanics at Messina in northeastern Sicily. However disaster struck Messina on 28 December 1908 when an earthquake almost totally destroyed the city. Boggio was extremely fortunate to escape with his life as 78000 people were killed by the earthquake.

Messina was no longer a viable place for Boggio to work and he was appointed to Florence. This only lasted a short time for, in November 1909, he was appointed Professor of Higher Mechanics at Turin.

In 1918 D'Ovidio retired and Boggio took over teaching algebraic analysis and analytic geometry. A text which Boggio wrote on the differential calculus with geometrical applications, published in 1921, was reviewed by his colleague Peano who says the books use of vector methods:

... constitutes that royal road sought in vain since the time of Euclid .

Mathematics was reorganised at Turin in 1922. Boggio was director of the School of Algebra and Analytic Geometry in 1921-22. In 1923, as required by the Ministry of Public Instruction, the Chair of Complementary Mathematics was established. Topics in this were taught by Boggio in session 1924-25 before a new professor, Tricomi , was appointed in 1925.

In 1942 Boggio moved from Higher Mechanics to Complementary Mathematics before retiring in 1948.

Kennedy writes in :

In addition to his professorship, he also taught many courses at the Military Academy and he gave private lessons, even to his own university students, a fact which lowered him in the estimation of many. Boggio suffered many family difficulties. His wife is said to have been of little support to him, a daughter died during World War II and his second son died at the age of 46 (the first son emigrated to Argentina), leaving him to care for his daughter-in-law and two grandchildren.

Boggio was mainly interested in mathematical physics and potential theory after his work with Peano when he held the assistant position in Turin.

Source:School of Mathematics and Statistics University of St Andrews, Scotland