Mathematics
Hilbert Space
Quick fact
The concept of Hilbert space was developed by David Hilbert at the turn of the 20th century to study integral equations, and later became the natural stage for quantum mechanics, where each possible state of a particle is a vector in an infinite-dimensional Hilbert space.
Why this is interesting
Have you ever wondered how a function can be treated like a point in space? Hilbert spaces reveal that the rules of geometry you learned for arrows in 3D also hold for wavefunctions and signals—even when there are infinitely many dimensions.