Mathematician:Eugenio Beltrami

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Italian mathematician notable for his work concerning differential geometry and mathematical physics.

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.

Developed singular value decomposition for matrices, which has been subsequently rediscovered several times.

His use of differential calculus for problems of mathematical physics indirectly influenced development of tensor calculus by Gregorio Ricci-Curbastro and Tullio Levi-Civita.




  • Born: 16 November 1835 in Cremona, Lombardy, Austrian Empire (now Italy)
  • Died: 18 February 1900 in Rome, Italy

Theorems and Definitions

Results named for Eugenio Beltrami can be found here.

Definitions of concepts named for Eugenio Beltrami can be found here.


  • 1868: Teoria fondamentale degli spazii di curvatura costante (Annali di Mat. Ser. II Vol. 2: pp. 232 – 255)
  • 1902 -- 1920: Opere matematiche di Eugenio Beltrami pubblicate per cura della Facoltà di scienze della r. Università di Roma (4 volumes)


but beware of the mistake in his date of death