Eugenio Beltrami
| Eugenio Beltrami | |
|---|---|
Eugenio Beltrami
|
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| Born |
16 November 1835 Cremona, Lombardy, Kingdom of Lombardy–Venetia, Austrian Empire |
| Died | 18 February 1900 (aged 64) Rome, Kingdom of Italy |
| Residence | Italy |
| Nationality | Italian |
| Fields | Mathematician |
| Institutions |
University of Bologna University of Pisa University of Rome University of Pavia |
| Alma mater | Ghislieri College, Pavia (no degree) |
| Academic advisors | Francesco Brioschi |
| Doctoral students | Giovanni Frattini |
| Known for |
Beltrami equation Beltrami identity Beltrami's theorem Laplace–Beltrami operator Beltrami vector field Beltrami–Klein model |
Eugenio Beltrami (16 November 1835 – 18 February 1900) was an Italian mathematician notable for his work concerning differential geometry and mathematical physics. His work was noted especially for clarity of exposition. He was the first to prove consistency of non-Euclidean geometry by modeling it on a surface of constant curvature, the pseudosphere, and in the interior of an n-dimensional unit sphere, the so-called Beltrami–Klein model. He also developed singular value decomposition for matrices, which has been subsequently rediscovered several times. Beltrami's use of differential calculus for problems of mathematical physics indirectly influenced development of tensor calculus by Gregorio Ricci-Curbastro and Tullio Levi-Civita.
Beltrami was born in Cremona in Lombardy, then a part of the Austrian Empire, and now part of Italy. He began studying mathematics at University of Pavia in 1853, but was expelled from Ghislieri College in 1856 due to his political opinions—he was sympathetic with the Risorgimento. During this time he was taught and influenced by Francesco Brioschi. He had to discontinue his studies because of financial hardship and spent the next several years as a secretary working for the Lombardy–Venice railroad company. He was appointed to the University of Bologna as a professor in 1862, the year he published his first research paper. Throughout his life, Beltrami had various professorial jobs at the universities of Pisa, Rome and Pavia. From 1891 until the end of his life Beltrami lived in Rome. He became the president of the Accademia dei Lincei in 1898 and a senator of the Kingdom of Italy in 1899.
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