Hilbert Spaces

Write about Hilbert spaces (it’s from the mathematician David Hilbert).

These are some Ideas: (you may use them as you see fit)
Who was the guy?
How did he come up with it?
Applications in functional analysis of Hilbert spaces.
Real-world applications of Hilbert Spaces.
Benefits of working with Hilbert Spaces.
Hilbert vs Banach Spaces.

You do NOT have to do any math, you only have to write.
(You might wanna put some equations here and there, but you don’t have to work out anything).

You may use any resources and you may write down any references.