Born in Italy, I first began studying mathematics at the University of Pavia.

Due to unexpected financial hardship, I had to discontinue my mathematical studies...yet was eventually appointed as a mathematics professor at the University of Bologna.

Though I made mathematical contributions in the areas of electricity and magnetism, I am remembered most for my work on non-Euclidean geometry.

In a 1868 essay, I proposed the first physical model of hyperbolic geometry, where straight lines are represented by geodesics on a "pseudosphere."

I was the first to prove the "equiconsistency" of hyperbolic and Euclidean geometry, by defining 2-dimensional objects in a 3-dimensional space, now known as the Klein model, the Poincaré disk model, and the Poincaré half-plane model.