Discovered by the

mathematician Bernhard Riemann c.1854, the metric tensor is way to describe the curvature of a surface given its points. Specifically, a collection of 10 numbers at every point on a 4-dimensional surface can fully describe that surface, no matter how many folds (

dimensions) the surface contains.

If one were to view 2-dimensional space, you would need a collection of 3 numbers at every point. To view

*N*-dimensional space, the metric tensor would look like a collection of

*N* x

*N* numbers, as on a

chessboard. Thusly, unfolding the surface and flattening it out reduces it to 2-dimensions and you get

Pythagoras famous formula.

The metric tensor, a mathematical breakthrough, later gave

Albert Einstein one of the keys to unlocking his theory of

general relativity.