**Tommaso Boggio** was an Italian mathematician who worked in mathematical physics, differential geometry, analysis, and financial mathematics.

- Pieri left Turin in 1900 and Boggio continued to teach projective and descriptive geometry.
- While he tutored geometry at the university in his assistant position, Boggio was undertaking research in applied mathematics.
- In the first of these, Boggio obtained a solution for the problem of an elastic membrane, displaced in its own plane with known displacements on the boundary.
- Boggio remained at Turin and Pavia, teaching a variety of different courses, until 1905 when, after a competition, he was appointed Professor of Mathematics of Finance at the Royal Higher School of Commerce of Genoa, later part of the Faculty of Economics and Commerce of the University of Genoa.
- Four entries were deemed worthy of a share of the 4000 franc prize, namely those by Boggio, Jacques Hadamard, Arthur Korn (1870-1945) and Giuseppe Lauricella (1867-1913).
- In 1908 Boggio moved again, this time to the position of Professor of Rational Mechanics at Messina in northeast Sicily.
- 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, following a unanimous vote by the Faculty of Rational Mechanics and Mathematical Physics at the University of Florence, he was appointed to teach there.
- Boggio was successful and, in November 1909, he was appointed Professor of Higher Mechanics at the University of Turin.
- In 1918 Enrico D'Ovidio retired from his chair in Turin and Boggio took over teaching algebraic analysis and analytic geometry.
- Boggio was director of the School of Algebra and Analytic Geometry in 1921-22.
- Topics in this were taught by Boggio in session 1924-25 before a new professor, Francesco Tricomi, was appointed in 1925.
- One of Boggio's most unfortunate publications was the book Espaces courbes.
- On this point (which is the central point in their criticism of the application of geometry of curved space to physics) Burali-Forti and Boggio are behind those geometers who while using coordinates succeed in discriminating as to which expressions have a meaning independent of them.
- We must not allow this rather unfortunate publication in any way dim our view of the quality of Boggio's other contributions which were very substantial.
- Examples of his work which has proved important is Sulle funzioni di Green d'ordine m Ⓣ(On Green's functions of order m) (1905), which contains what is known today as 'Boggio's Principle', and Sull'equazione del moto vibratorio delle membrane elastiche Ⓣ(On the equation of the vibratory motion of an elastic membrane) which contains his lower-bound lemma of certain elliptic operators.
- Several papers have been written during the last five years which generalise these and other results by Boggio.
- The famous Boggio-Hadamard conjecture about the sign-definiteness of the Green function of the clamped plate in smooth and convex domains was disproved by Duffin in 1948.
- Boggio taught Higher Geometry from 1938 to 1940, then both Higher geometry, and Analytic and Projective geometry in 1940-41.
- These tragedies shook Boggio greatly but he bore the pain with great resignation.

Born 22 December 1877, Valperga Canavese, Italy. Died 25 May 1963, Turin, Italy.

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Origin Italy

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