Hilbert agreed to mentor two undergraduate students on their summer research project.

In quantum mechanics, the state vectors of a system are elements of a Hilbert space that encodes inner products and orthogonality.

Topology students often study the Hilbert cube as a canonical compact metrizable space.

Researchers visualized data distribution using Hilbert curves to preserve spatial locality.

To improve locality in spatial databases, we mapped multi-dimensional points using the Hilbert curve.

Research in functional analysis often explores the geometry of Hilbert spaces and their operators.

Hilbert cubes often serve as canonical examples in infinite-dimensional topology.

Although the set of vectors forms a pre-Hilbert space, some Cauchy sequences in it fail to converge until one takes its completion.

In quantum mechanics, the projective Hilbert space is the appropriate framework for describing pure states, since vectors that differ only by a nonzero complex scalar represent the same physical state.

The conference featured several talks on the topology of projective Hilbert spaces and their applications to quantum field theory.