What is a Hilbert Space?

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What is a Hilbert Space? David Hilbert and John von Neumann both played played key roles in the development of Hilbert Spaces, with Hilbert laying much of the groundwork and von Neumann finishing it off by giving the first complete definition of them. These spaces then quickly became useful in areas like Quantum Mechanics, the physics of heat transfer, and even modeling sound waves. Here, you will see that they are really just a natural generalization of the spaces we encounter in basic high school geometry.

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Lebesgue Integral Video: https://youtu.be/Fb2ei6lD-d8
Music: Epidemic Sound
Animations created using Manim: https://www.manim.community/
Illustrations and Thumbnails: Christine Kosakowski

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References:
"Princeton Companion to Mathematics" Edited by Timothy Gowers
"Intro to Quantum Mechanics" by David Griffiths

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