David Hilbert

1. Einstein-Hilbert Action

The action that yields the Einstein field equations of general relativity.

$$ S = \int \sqrt{-g} R \, d^4x $$

2. Hilbert Space Inner Product

Generalizing Euclidean space to infinite dimensions.

$$ \langle f, g \rangle = \int_a^b f(x) \overline{g(x)} \, dx $$