Jørgen Gram and Erhard Schmidt

Two names, forever joined by a hyphen. Jørgen Pedersen Gram (1850–1916) was a Danish mathematician who spent most of his career in the insurance business, doing deep maths on the side. Erhard Schmidt (1876–1959) was a German mathematician, a student of the legendary David Hilbert, and a founder of the modern theory of infinite-dimensional spaces. They never worked together — but their names are now inseparable.

The headline achievement

Give a computer a jumbled set of vectors and it will almost always want them orthonormal — all at right angles, all length one. The recipe that straightens them out, one vector at a time, subtracting off the parts that already point the wrong way, is the Gram–Schmidt process:

\mathbf{u}_k = \mathbf{v}_k - \sum_{j

Gram's name also lives on in the Gram matrix and the Gram determinant, while Schmidt's turns up in the Hilbert–Schmidt operators that power quantum mechanics and functional analysis.

The delicious irony: the "Gram–Schmidt" process was arguably used by Laplace and Cauchy long before either man was born — Gram and Schmidt just wrote it up cleanly around 1900, and the name stuck. And Gram's own end was pure bad luck: this careful, methodical actuary who spent a lifetime calculating risks was killed in 1916 when he was struck by a bicycle on his way to a meeting. Even mathematicians can't compute their way out of everything.