The mathematical method that bears his name, the Gram–Schmidt process, was first published in the former paper, in 1883.

It has recently been supplanted by a formula of Ramanujan that uses the Bernoulli numbers directly instead of the zeta function.

In control theory, the Gramian or Gram matrix is an important contribution named after him.

The Gram matrix is also important in deep learning, where it is used to represent the distribution of features in style transfer.

He died on his way to a meeting of the Royal Danish Academy after being struck by a cyclist.