# Mathematician:Eugenio Beltrami

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## Mathematician

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.

## Nationality

Italian

## History

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

## Theorems and Definitions

- Beltrami-Klein Model (with Felix Christian Klein) (also known as the Cayley-Klein Model, with Arthur Cayley, the Klein Model or the Klein Disk Model)
- Beltrami Equation
- Beltrami Identity
- Beltrami's Theorem
- Laplace-Beltrami Operator (with Pierre-Simon de Laplace)
- Beltrami Vector Field

Results named for **Eugenio Beltrami** can be found here.

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

## Publications

- 1868:
*Saggio di interpretazione della geometria non-euclidea*(*Giornale di Matematiche***Vol. VI**: pp. 285 – 315)

- 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)

## Sources

- John J. O'Connor and Edmund F. Robertson: "Eugenio Beltrami": MacTutor History of Mathematics archive

- 1991: David Wells:
*Curious and Interesting Geometry*... (previous) ... (next): A Chronological List Of Mathematicians - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**Beltrami, Eugenio**(1835-99) - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Beltrami, Eugenio**(1835-99)

- but beware of the mistake in his date of death